Journal articles on the topic 'Non-Boussinesq approximation'
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ROTUNNO, R., J. B. KLEMP, G. H. BRYAN, and D. J. MURAKI. "Models of non-Boussinesq lock-exchange flow." Journal of Fluid Mechanics 675 (April 8, 2011): 1–26. http://dx.doi.org/10.1017/jfm.2010.648.
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Nearly all analytical models of lock-exchange flow are based on the shallow-water approximation. Since the latter approximation fails at the leading edges of the mutually intruding fluids of lock-exchange flow, solutions to the shallow-water equations can be obtained only through the specification of front conditions. In the present paper, analytic solutions to the shallow-water equations for non-Boussinesq lock-exchange flow are given for front conditions deriving from free-boundary arguments. Analytic solutions are also derived for other proposed front conditions – conditions which appear to the shallow-water system as forced boundary conditions. Both solutions to the shallow-water equations are compared with the numerical solutions of the Navier–Stokes equations and a mixture of successes and failures is recorded. The apparent success of some aspects of the forced solutions of the shallow-water equations, together with the fact that in a real fluid the density interface is a free boundary, shows the need for an improved theory of lock-exchange flow taking into account non-hydrostatic effects for density interfaces intersecting rigid boundaries.
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E. Ahmed, Sameh, Dalal Alrowaili, Ehab Mahmoud Mohamed, and Abdelraheem M. Aly. "Nanofluid Flows within Porous Enclosures Using Non-Linear Boussinesq Approximation." Computers, Materials & Continua 66, no. 3 (2021): 3195–213. http://dx.doi.org/10.32604/cmc.2021.012471.
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PRUŠA, VÍT, and K. R. RAJAGOPAL. "ON MODELS FOR VISCOELASTIC MATERIALS THAT ARE MECHANICALLY INCOMPRESSIBLE AND THERMALLY COMPRESSIBLE OR EXPANSIBLE AND THEIR OBERBECK–BOUSSINESQ TYPE APPROXIMATIONS." Mathematical Models and Methods in Applied Sciences 23, no. 10 (July 12, 2013): 1761–94. http://dx.doi.org/10.1142/s0218202513500516.
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Viscoelastic fluid like materials that are mechanically incompressible but are compressible or expansible with respect to thermal stimuli are of interest in various applications ranging from geophysics and polymer processing to glass manufacturing. Here we develop a thermodynamical framework for the modeling of such materials. First we illustrate the basic ideas in the simpler case of a viscous fluid, and after that we use the notion of natural configuration and the concept of the maximization of the entropy production, and we develop a model for a Maxwell type viscoelastic fluid that is mechanically incompressible and thermally expansible or compressible. An important approximation in fluid mechanics that is frequently used in modeling buoyancy driven flows is the Oberbeck–Boussinesq approximation. Originally, the approximation was used for studying the flows of viscous fluids in thin layers subject to a small temperature gradient. However, the approximation has been used almost without any justification even for flows of non-Newtonian fluids induced by strong temperature gradients in thick layers. Having a full system of the governing equations for a Maxwell type viscoelastic mechanically incompressible and thermally expansible or compressible fluid, we investigate the validity of the Oberbeck–Boussinesq type approximation for flows of this type of fluids. It turns out that the Oberbeck–Boussinesq type approximation is in general not a good approximation, in particular if one considers "high Rayleigh number" flows. This indicates that the Oberbeck–Boussinesq type approximation should not be used routinely for all buoyancy driven flows, and its validity should be thoroughly examined before it is used as a mathematical model.
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Godin, Oleg A. "Wentzel–Kramers–Brillouin approximation for atmospheric waves." Journal of Fluid Mechanics 777 (July 16, 2015): 260–90. http://dx.doi.org/10.1017/jfm.2015.367.
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Ray and Wentzel–Kramers–Brillouin (WKB) approximations have long been important tools in understanding and modelling propagation of atmospheric waves. However, contradictory claims regarding the applicability and uniqueness of the WKB approximation persist in the literature. Here, we consider linear acoustic–gravity waves (AGWs) in a layered atmosphere with horizontal winds. A self-consistent version of the WKB approximation is systematically derived from first principles and compared to ad hoc approximations proposed earlier. The parameters of the problem are identified that need to be small to ensure the validity of the WKB approximation. Properties of low-order WKB approximations are discussed in some detail. Contrary to the better-studied cases of acoustic waves and internal gravity waves in the Boussinesq approximation, the WKB solution contains the geometric, or Berry, phase. The Berry phase is generally non-negligible for AGWs in a moving atmosphere. In other words, knowledge of the AGW dispersion relation is not sufficient for calculation of the wave phase.
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Lamb, K. G. "Energetics of internal solitary waves in a background sheared current." Nonlinear Processes in Geophysics 17, no. 5 (October 8, 2010): 553–68. http://dx.doi.org/10.5194/npg-17-553-2010.
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Abstract. The energetics of internal waves in the presence of a background sheared current is explored via numerical simulations for four different situations based on oceanographic conditions: the nonlinear interaction of two internal solitary waves; an internal solitary wave shoaling through a turning point; internal solitary wave reflection from a sloping boundary and a deep-water internal seiche trapped in a deep basin. In the simulations with variable water depth using the Boussinesq approximation the combination of a background sheared current, bathymetry and a rigid lid results in a change in the total energy of the system due to the work done by a pressure change that is established across the domain. A final simulation of the deep-water internal seiche in which the Boussinesq approximation is not invoked and a diffuse air-water interface is added to the system results in the energy remaining constant because the generation of surface waves prevents the establishment of a net pressure increase across the domain. The difference in the perturbation energy in the Boussinesq and non-Boussinesq simulations is accounted for by the surface waves.
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Hamimid, Saber, Messaoud Guellal, and Madiha Bouafia. "Numerical study of natural convection in a square cavity under non-boussinesq conditions." Thermal Science 20, no. 5 (2016): 1509–17. http://dx.doi.org/10.2298/tsci130810084h.
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Natural convection in a differentially heated cavity has been carried out under large temperature gradient. The study has been performed by direct simulations using a two-dimensional finite volume numerical code solving the time-dependent Navier-Stokes equations under the Low Mach Number approximation. The LMN model constitutes an important numerical problem for low speed flows. It is based on the filtering of acoustic waves from the complete Navier-Stokes equations. Various simulations were conducted including constant or variable transport coefficients and both small and large temperature differences. A comparison between an incompressible code based on the Boussinesq approximation and the LMN compressible code shows that the incompressible model is not sufficient to simulate natural convective flow for large temperature differences.
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Nargund, Achala, R. Madhusudhan, and S. B. Sathyanarayana. "HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS." JOURNAL OF ADVANCES IN PHYSICS 10, no. 3 (October 6, 2015): 2825–33. http://dx.doi.org/10.24297/jap.v10i3.1322.
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In this paper, Homotopy analysis method is applied to the nonlinear coupleddifferential equations of classical Boussinesq system. We have applied Homotopy analysis method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-Sykes plot for the region of convergence. We have applied Pade for the HAM series to identify the singularity and reflect it in the graph. The HAM is a analytical technique which is used to solve non-linear problems to generate a convergent series. HAM gives complete freedom to choose the initial approximation of the solution, it is the auxiliary parameter h which gives us a convenient way to guarantee the convergence of homotopy series solution. It seems that moreartificial degrees of freedom implies larger possibility to gain better approximations by HAM.
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Ricard, Yanick, Thierry Alboussière, Stéphane Labrosse, Jezabel Curbelo, and Fabien Dubuffet. "Fully compressible convection for planetary mantles." Geophysical Journal International 230, no. 2 (March 22, 2022): 932–56. http://dx.doi.org/10.1093/gji/ggac102.
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SUMMARY The numerical simulations of convection inside the mantle of the Earth or of terrestrial planets have been based on approximate equations of fluid dynamics. A common approximation is the neglect of the inertia term which is certainly reasonable as the Reynolds number of silicate mantles, or their inverse Prandtl number, are infinitesimally small. However various other simplifications are made which we discuss in this paper. The crudest approximation that can be done is the Boussinesq approximation (BA) where the various parameters are constant and the variations of density are only included in the buoyancy term and assumed to be proportional to temperature with a constant thermal expansivity. The variations of density with pressure and the related physical consequences (mostly the presence of an adiabatic temperature gradient and of dissipation) are usually accounted for by using an anelastic approximation (AA) initially developed for astrophysical and atmospheric situations. The BA and AA cases provide simplified but self-consistent systems of differential equations. Intermediate approximations are also common in the geophysical literature although they are invariably associated with theoretical inconsistencies (non-conservation of total energy, non-conservation of statistically steady state heat flow with depth, momentum and entropy equations implying inconsistent dissipations). We show that, in the infinite Prandtl number case, solving the fully compressible (FC) equations of convection with a realistic equation of state (EoS) is however not much more difficult or numerically challenging than solving the approximate cases. We compare various statistical properties of the Boussinesq, AA and FC simulations in 2-D simulations. We point to an inconsistency of the AA approximation when the two heat capacities are assumed constant. We suggest that at high Rayleigh number, the profile of dissipation in a convective mantle can be directly related to the surface heat flux. Our results are mostly discussed in the framework of mantle convection but the EoS we used is flexible enough to be applied for convection in icy planets or in the inner core.
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Korre, L., N. Brummell, and P. Garaud. "Boussinesq convection in a gaseous spherical shell." EAS Publications Series 82 (2019): 373–82. http://dx.doi.org/10.1051/eas/1982033.
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In this paper, we investigate the dynamics of convection in a spherical shell under the Boussinesq approximation but considering the compressibility which arises from a non zero adiabatic temperature gradient, a relevant quantity for gaseous objects such as stellar or planetary interiors. We find that depth-dependent superiadiabaticity, combined with the use of mixed boundary conditions (fixed flux/fixed temperature), gives rise to unexpected dynamics that were not previously reported.
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Vargas, Edgar Villagran, Juan Ramón Collantes C., and Máximo A. Agüero Granados. "Boussinesq Solitons as Propagators of Neural Signals." KnE Engineering 3, no. 1 (February 11, 2018): 120. http://dx.doi.org/10.18502/keg.v3i1.1419.
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We consider certain approximation for determining the equation of motion for nerve signals by using the model of the lipid melting of membranes. The nerve pulses are found to display nonlinearity and dispersion during the melting transition. In this simplified model the nonlinear equation early proposed by Heimburg and coworkers transformed to the well known integrable Boussinesq non linear equation. Under specific values of the parametric space this system shows the existence of singular and regular soliton like structures. After their collisions the mutual creation and annihilation (each other) of nerve signals along the nerve, during their propagation, has been observed.Keywords: Boussinesq equation, singular solitons, single neurons, neural code.
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Enayati, Hooman, and Minel J. Braun. "2D/3D RANS and LES Calculations of Natural Convection in a Laterally-Heated Cylindrical Enclosure Using Boussinesq and Temperature-Dependent Formulations." International Journal of Heat and Technology 39, no. 6 (December 31, 2021): 1979–90. http://dx.doi.org/10.18280/ijht.390637.
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This article presents an investigation of fluid flow and natural convection heat transfer in a cylindrical enclosure heated laterally. Two-dimensional (2D) Reynolds-averaged Navier–Stokes (RANS) equations and three-dimensional (3D) Large Eddy Simulation (LES) calculations are conducted using commercial computational fluid dynamics (CFD) software, ANSYS FLUENT. The Rayleigh number (Ra) = 2E+7 is constant in all of the simulations and is based on a length scale that is equal to the ratio of volume to the lateral area of the reactor, i.e., R/2, where R is the radius of the reactor. The validity of the Boussinesq approximation is analyzed by comparing calculations using both the Boussinesq approximation and temperature-dependent properties (non-Boussinesq approach) using 2D RANS and 3D LES (Dynamic Smagorinsky) formulations. Moreover, 2D axisymmetric k-ω SST RANS model will be implemented to investigate whether the 2D axisymmetric model can give results that are comparable to those of the 3D LES (Dynamic Smagorinsky) model when the corresponding longitudinal or azimuthal cross section are compared. In other words, the validity of using a 2D model instead of a 3D model for the current geometry, flow regime and thermal boundary conditions will be discussed. The flow and temperature contours of these two types of simulations are analyzed, compared to determine the various aspects of each case and discussed for deeper physical insight.
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SUSLOV, S. A., and S. PAOLUCCI. "Nonlinear analysis of convection flow in a tall vertical enclosure under non-Boussinesq conditions." Journal of Fluid Mechanics 344 (August 10, 1997): 1–41. http://dx.doi.org/10.1017/s0022112097005971.
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A weakly nonlinear theory, based on the combined amplitude–multiple timescale expansion, is developed for the flow of an arbitrary fluid governed by the low-Mach-number equations. The approach is shown to be different from the one conventionally used for Boussinesq flows. The range of validity of the applied analysis is discussed and shown to be sufficiently large. Results are presented for the natural convection flow of air inside a closed differentially heated tall vertical cavity for a range of temperature differences far beyond the region of validity of the Boussinesq approximation. The issue of possible resonances of two different types is noted. The character of bifurcations for the shear- and buoyancy-driven instabilities and their interaction is investigated in detail. Lastly, the energy transfer mechanisms are analysed in supercritical regimes.
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Szmidt, J. K., and B. Hedzielski. "A new form of Boussinesq equations for long waves in water of non-uniform depth." Bulletin of the Polish Academy of Sciences: Technical Sciences 60, no. 3 (December 1, 2012): 631–43. http://dx.doi.org/10.2478/v10175-012-0075-9.
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Abstract The paper describes the non-linear transformation of long waves in shallow water of variable depth. Governing equations of the problem are derived under the assumption that the non-viscous fluid is incompressible and the fluid flow is a rotation free. A new form of Boussinesq-type equations is derived employing a power series expansion of the fluid velocity components with respect to the water depth. These non-linear partial differential equations correspond to the conservation of mass and momentum. In order to find the dispersion characteristic of the description, a linear approximation of these equations is derived. A second order approximation of the governing equations is applied to study a time dependent transformation of waves in a rectangular basin of water of variable depth. Such a case corresponds to a spatially periodic problem of sea waves approaching a near-shore zone. In order to overcome difficulties in integrating these equations, the finite difference method is applied to transform them into a set of non-linear ordinary differential equations with respect to the time variable. This final set of these equations is integrated numerically by employing the fourth order Runge - Kutta method.
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Sajjan, Kiran, Nehad Ali Shah, N. Ameer Ahammad, C. S. K. Raju, M. Dinesh Kumar, and Wajaree Weera. "Nonlinear Boussinesq and Rosseland approximations on 3D flow in an interruption of Ternary nanoparticles with various shapes of densities and conductivity properties." AIMS Mathematics 7, no. 10 (2022): 18416–49. http://dx.doi.org/10.3934/math.20221014.
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<abstract> <p>In current days, hybrid models have become more essential in a wide range of systems, including medical treatment, aerosol particle handling, laboratory instrument design, industry and naval academia, and more. The influence of linear, nonlinear, and quadratic Rosseland approximations on 3D flow behavior was explored in the presence of Fourier fluxes and Boussinesq quadratic thermal oscillations. Ternary hybrid nanoparticles of different shapes and densities were also included. Using the necessary transformation, the resulting partial differential system is transformed into a governing ordinary differential system, and the solution is then furnished with two mixed compositions (Case-Ⅰ and Case-Ⅱ). Combination one looked at aluminum oxide (Platelet), graphene (Cylindrical), and carbon nanotubes (Spherical), whereas mixture two looked at copper (Cylindrical), copper oxide (Spherical), and silver oxide (Platelet). Many changes in two mixture compositions, as well as linear, quadratic, and nonlinear thermal radiation situations of the flow, are discovered. Case-1 ternary combinations have a wider temperature distribution than Case-2 ternary mixtures. Carbon nanotubes (Spherical), graphene (Cylindrical), and aluminum oxide (Platelet) exhibit stronger conductivity than copper oxide (Spherical), copper (Cylindrical), and silver oxide (Platelet) in Case 1. (Platelet). In copper oxide (Spherical), copper (Cylindrical), and silver (Platelet) compositions, the friction factor coefficient is much higher. The combination of liquids is of great importance in various systems such as medical treatment, manufacturing, experimental instrument design, aerosol particle handling and naval academies, etc. Roseland's quadratic and linear approximation of three-dimensional flow characteristics with the existence of Boussinesq quadratic buoyancy and thermal variation. In addition, we combine tertiary solid nanoparticles with different shapes and densities. In many practical applications such as the plastics manufacturing and polymer industry, the temperature difference is remarkably large, causing the density of the working fluid to vary non-linearly with temperature. Therefore, the nonlinear Boussinesq (NBA) approximation cannot be ignored, since it greatly affects the flow and heat transport characteristics of the working fluid. Here, the flow of non-Newtonian elastomers is controlled by the tension of an elastic sheet subjected to NBA and the quadratic form of the Rosseland thermal radiation is studied.</p> </abstract>
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Tort, Marine, Bruno Ribstein, and Vladimir Zeitlin. "Symmetric and asymmetric inertial instability of zonal jets on the -plane with complete Coriolis force." Journal of Fluid Mechanics 788 (January 5, 2016): 274–302. http://dx.doi.org/10.1017/jfm.2015.710.
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Symmetric and asymmetric inertial instability of the westerly mid-latitude barotropic Bickley jet is analysed without the traditional approximation which neglects the vertical component of the Coriolis force, as well as the contribution of the vertical velocity to the latter. A detailed linear stability analysis of the jet at large Rossby numbers on the non-traditional $f$-plane is performed for long waves in both the two-layer rotating shallow-water and continuously stratified Boussinesq models. The dependence of the instability on both the Rossby and Burger numbers of the jet is investigated and compared to the traditional case. It is shown that non-traditional effects significantly increase the growth rate of the instability at small enough Burger numbers (weak stratifications) for realistic aspect ratios of the jet. The main results are as follows. (i) Two-layer shallow-water model. In the parameter regimes where the jet is inertially stable on the traditional $f$-plane, the symmetric inertial instability with respect to perturbations with zero along-jet wavenumber arises on the non-traditional $f$-plane. Both non-traditional symmetric and asymmetric (small but non-zero wavenumbers) inertial instabilities have higher growth rates than their traditional counterparts. (ii) Continuously stratified model. It is shown that by a proper change of variables the linear stability problem for the barotropic jet, on the non-traditional $f$-plane, can be rendered separable and analysed along the same lines as in the traditional approximation. Neutral, weak and strong background stratifications are considered. For the neutral stratification the jet is inertially unstable if the traditional approximation is relaxed, while its traditional counterpart is not. For a sufficiently weak stratification, both symmetric and asymmetric inertial instabilities have substantially higher growth rates than in the traditional approximation. The across-jet structure of non-traditional unstable modes is strikingly different, as compared to those under the traditional approximation. No discernible differences between the two approximations are observed for strong enough stratifications. The influence of dissipation and non-hydrostatic effects upon the instability is quantified.
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Amina Ould Larbi, Redha Rebhi, Soufiane Rahal, Giulio Lorenzini, Laidi Maamar, Younes Menni, and Hijaz Ahmad. "Impact of Non-Newtonian Fluids' Rheological Behavior on Double- Diffusive Natural Convection in an Inclined Square Porous Layer." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 99, no. 2 (November 11, 2022): 17–47. http://dx.doi.org/10.37934/arfmts.99.2.1747.
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In the current study, natural convection is numerically simulated in a shallow, porous, square cavity that is filled with a non-Newtonian fluid. In terms of temperature and concentration gradients (heat and mass fluxes), the active wall was seen as uniform and constant, whereas the other walls are adiabatic and impermeable. To analyze the behavior of shear-thinning fluids, a Carreau-Yasuda model is utilized, which is suitable for many non-Newtonian fluids. It is presummated that the fluid will fulfill the Boussinesq approximation, be laminar, and be incompressible.
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Appleby, J. C., and D. G. Crighton. "Internal gravity waves generated by oscillations of a sphere." Journal of Fluid Mechanics 183 (October 1987): 439–50. http://dx.doi.org/10.1017/s0022112087002714.
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We consider the radiation of internal gravity waves from a spherical body oscillating vertically in a stratified incompressible fluid. A near-field solution (under the Boussinesq approximation) is obtained by separation of variables in an elliptic problem, followed by analytic continuation to the frequencies ω < N of internal wave radiation. Matched expansions are used to relate this solution to a far-field solution in which non-Boussinesq terms are retained. In the outer near field there are parallel conical wavefronts between characteristic cones tangent to the body, but with a wavelength found to be shorter than that for oscillations of a circular cylinder. It is also found that there are caustic pressure singularities above and below the body where the characteristics intersect. Far from the source, non-Boussinesq effects cause a diffraction of energy out of the cones. The far-field wave-fronts are hyperboloidal, with horizontal axes. The case of horizontal oscillations of the sphere is also examined and is shown to give rise to the same basic wave structure.The related problem of a pulsating sphere is then considered, and it is concluded that certain features of the wave pattern, including the caustic singularities near the source, are common to a more general class of oscillating sources.
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Wei, Lin, Guo Boling, and Shang Yadong. "The Periodic Initial Value Problem and Initial Value Problem for the Non-Newtonian Boussinesq Approximation." Applicable Analysis 82, no. 8 (August 2003): 787–808. http://dx.doi.org/10.1080/00036810310001603189.
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DeAndrade, C. R., A. V. Pantaleão, and E. L. Zaparoli. "CONJUGATE MIXED CONVECTION IN AIR-COOLED HEAT SINKS USING A NON-BOUSSINESQ APPROACH." Revista de Engenharia Térmica 2, no. 1 (June 30, 2003): 44. http://dx.doi.org/10.5380/reterm.v2i1.3515.
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This work reports a numerical study of the mixed convection in finned duct flow that occurs in heat sinks devices. The laminar flow is considered fully developed and the convection-conduction coupling is treated by a conjugated approach. The mathematical formulation of this problem is constituted by the mass, momentum and energy equations. The partial differential equations system is solved by the Galerkin finite element method, adopting a pressure Poisson equation to establish the pressure-velocity coupling and to obtain a mass conserving flow. The results using the classical Boussinesq approximation (density varies linearly with the temperature in the buoyancy-term) are compared with the non-Boussinesq approach (density variation in all terms of the governing equations) showing that both the heat transfer and friction factor are affected by the new considerations. The duct aspect ratio and the solid to fluid thermal conductivity ratio influences on the heat transfer rate are also analyzed. This analysis tool was also shown appropriate for the optimization of electronic components air-cooled heat sinks.
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RamReddy, Ch, P. Naveen, and D. Srinivasacharya. "Influence of Non-linear Boussinesq Approximation on Natural Convective Flow of a Power-Law Fluid along an Inclined Plate under Convective Thermal Boundary Condition." Nonlinear Engineering 8, no. 1 (January 28, 2019): 94–106. http://dx.doi.org/10.1515/nleng-2017-0138.
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Abstract In the present investigation, a problem of natural convective flow of a non-Newtonian power-law fluid over an inclined plate saturated in a non-Darcy porous medium is considered. Also, the nonlinear Boussinesq approximation and convective thermal boundary condition are taken into account to address heat and mass transfer phenomena of thermal systems which are operated at moderate and very high temperatures. The steady-state boundary layer equations are non-dimensionalized into non-similar form and then solved numerically by the local non-similarity method with successive linearisation method (SLM). The effects of various physical parameters on the fluid flow, heat and mass transfer characteristics are depicted graphically and analysed in detail.
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Muti, H., H. Demir, and P. G. Siddheshwar. "Energy Stability of Benard-Darcy Two-Component Convection of Maxwell Fluid." International Journal of Applied Mechanics and Engineering 18, no. 1 (March 1, 2013): 125–35. http://dx.doi.org/10.2478/ijame-2013-0009.
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Energy stability of a horizontal layer of a two-component Maxwell fluid in a porous medium heated and salted from below is studied under the Oberbeck-Boussinesq-Darcy approximation using the Lyapunov direct method. The effect of stress relaxation on the linear and non-linear critical stability parameters is clearly brought out with coincidence between the two when the solute concentration is dilute. Qualitatively, the result of porous and clear fluid cases is shown to be similar. In spite of lack of symmetry in the problem it is shown that non linear exponential stability can be handled.
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Kim, Minwoo, Cheol-Ho Kim, and Chan Joo Jang. "Projection of future sea level rise in the East Asian Seas based on Global Ocean-Sea Ice Coupled Model with SRES A1B Scenario." Korea Society of Coastal Disaster Prevention 8, no. 4 (October 30, 2021): 281–86. http://dx.doi.org/10.20481/kscdp.2021.8.4.281.
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To project the future sea level rise in the East Asian Seas due to global warming, regional sea level variations are downscaled from three climate system models (GFDL-CM2.1, ECHAM5/MPI-OM, MIROC3.2(hires)) using a global ocean-sea ice coupled model with non-Boussinesq approximation. Based on the SRES A1B Scenario, the projected ensemble mean sea level rise (rate of rise) for the East Sea, Yellow Sea and East China Sea from 1995 to 2050 is 15.60cm (2.84mm/year), 16.49cm (3.0mm/year) and 16.43cm (2.99mm/year), respectively. With the inclusion of the future change of land ice melting and land water storage, the mean sea level rise (rate of rise) increases to 33.55cm (6.10mm/year) for the East Sea, and 34.38~34.44cm (6.25~6.26mm/year) for the Yellow and East China Seas. The present non-Boussinesq ocean model experiment shows that the future sea level rise in the East Sea is mainly due to the steric component changes by heat content increase. On the other hand, the future sea level rise in the Yellow and East China Seas appears to be mainly associated with the non-steric component change by water mass convergence.
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Yang, Fei, Xuejun Shao, Xudong Fu, and Ehsan Kazemi. "Simulated Flow Velocity Structure in Meandering Channels: Stratification and Inertia Effects Caused by Suspended Sediment." Water 11, no. 6 (June 15, 2019): 1254. http://dx.doi.org/10.3390/w11061254.
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In this study, the coupled effects of sediment inertia and stratification on the pattern of secondary currents in bend-flows are evaluated using a 3D numerical model. The sediment inertia effect, as well as the stratification effect induced by the non-uniform distribution of suspended sediment, is accounted for by adopting the hydrodynamic equations without the Boussinesq approximation. The 3D model is validated by existing laboratory experimental results. Simulation results of a simplified meandering channel indicate that sediment stratification effect enhances the intensity of secondary flow via reducing eddy viscosity, while sediment inertia effect suppresses it. The integrated effects result in an increase and a reduction in the secondary flow, respectively, at lower and higher concentrations (near-bed volumetric concentrations of 0.015 and 0.1 are, respectively, considered in this study). This suggests that the dominance of the suspended sediment effect depends on the sediment concentration profile. With the increase of concentration under a specific sediment size, the secondary flow rises to reach a maximum, and then decreases. Moreover, as the sediment concentration increases, an exponentially decaying rate has been found for the secondary flow. It is concluded that in the numerical simulation of flow in meandering channels, when concentration is high, the variable-density hydrodynamic equations without the Boussinesq approximation should be considered.
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KURTULDU, H., K. MISCHAIKOW, and M. F. SCHATZ. "Measuring the departures from the Boussinesq approximation in Rayleigh–Bénard convection experiments." Journal of Fluid Mechanics 682 (July 22, 2011): 543–57. http://dx.doi.org/10.1017/jfm.2011.244.
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Algebraic topology (homology) is used to characterize quantitatively non-Oberbeck–Boussinesq (NOB) effects in chaotic Rayleigh–Bénard convection patterns from laboratory experiments. For fixed parameter values, homology analysis yields a set of Betti numbers that can be assigned to hot upflow and, separately, to cold downflow in a convection pattern. An analysis of data acquired under a range of experimental conditions where NOB effects are systematically varied indicates that the difference between time-averaged Betti numbers for hot and cold flows can be used as an order parameter to measure the strength of NOB-induced pattern asymmetries. This homology-based measure not only reveals NOB effects that Fourier methods and measurements of pattern curvature fail to detect, but also permits distinguishing pattern changes caused by modified lateral boundary conditions from NOB pattern changes. These results suggest a new approach to characterizing data from either experiments or simulations where NOB effects are expected to play an important role.
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Kumar, Pardeep, and Gursharn Singh. "Analysis of Stability in Couple-Stress Magneto-Fluid." Nepal Journal of Mathematical Sciences 2, no. 2 (October 9, 2021): 35–42. http://dx.doi.org/10.3126/njmathsci.v2i2.40034.
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The aim of the present research was to study the effect of magnetic field on the layer of electrically conducting couple-stress fluid heated from below in porous medium. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, the dispersion relation is obtained. The stationary convection, stability of the system and oscillatory modes are discussed. For the case of stationary convection, it is found that the couple-stress parameter and magnetic field have stabilizing effect on the system whereas the medium permeability has a destabilizing effect on the system. The magnetic field introduces oscillatory modes in the system which was non-existent in its absence. A sufficient condition for the non-existent of overstability is also obtained.
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Tayeb, Mhamed, Mohamed Nadjib Bouaziz, and Salah Hanini. "Influence of Non-Linear Boussinesq Approximation and Convective Thermal Boundary Condition on MHD Natural Convection Flow of a Couple Stress-Nanofluid in a Porous Medium." Nano Hybrids and Composites 26 (August 2019): 45–61. http://dx.doi.org/10.4028/www.scientific.net/nhc.26.45.
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Nonlinear density and temperature variation’s role (NDT) on the magnetohydrodynamic (MHD) natural convective flow of couple stress fluid with nanoparticles through a vertical porous channel modeled as Darcy-Forchheimer flow is the purpose of our work. The nanoparticles volume fraction is taken into consideration (Buongiorno model). The nonlinear partial differential equations governing this flow were transformed into ordinary differential equations via the similarity technique and simulated numerically using Matlab, following boundary value problem (BVP4c) code. Graphical illustrations, including non-dimensional velocity, temperature, concentration, nanoparticle’s concentration and numerical results containing Nusselt and Sherwood numbers were presented for different values of the non-linear part of the Boussinesq approximation; couple stress parameter, and the Biot number on the walls.
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Kumar, Pardeep. "Stability Analysis in Couple-Stress Rotatory Fluid." WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER 16 (June 29, 2021): 49–58. http://dx.doi.org/10.37394/232012.2021.16.8.
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The aim of the present research was to study the effect of uniform rotation on the layer of a couple-stress fluid heated from below in porous medium. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, the dispersion relation is obtained. The stationary convection, stability of the system and oscillatory modes are discussed. For the case of stationary convection, it is found that rotation has a stabilizing effect, whereas the couple-stress parameter and medium permeability have both stabilizing and destabilizing effects on the system. It is found that the presence of rotation introduces oscillatory modes in the system which were non-existent in its absence. A sufficient condition for the non-existent of overstability is also obtained.
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Demou, Andreas D., and Dimokratis G. E. Grigoriadis. "Direct numerical simulations of Rayleigh–Bénard convection in water with non-Oberbeck–Boussinesq effects." Journal of Fluid Mechanics 881 (October 28, 2019): 1073–96. http://dx.doi.org/10.1017/jfm.2019.787.
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Rayleigh–Bénard convection in water is studied by means of direct numerical simulations, taking into account the variation of properties. The simulations considered a three-dimensional (3-D) cavity with a square cross-section and its two-dimensional (2-D) equivalent, covering a Rayleigh number range of $10^{6}\leqslant Ra\leqslant 10^{9}$ and using temperature differences up to 60 K. The main objectives of this study are (i) to investigate and report differences obtained by 2-D and 3-D simulations and (ii) to provide a first appreciation of the non-Oberbeck–Boussinesq (NOB) effects on the near-wall time-averaged and root-mean-squared (r.m.s.) temperature fields. The Nusselt number and the thermal boundary layer thickness exhibit the most pronounced differences when calculated in two dimensions and three dimensions, even though the $Ra$ scaling exponents are similar. These differences are closely related to the modification of the large-scale circulation pattern and become less pronounced when the NOB values are normalised with the respective Oberbeck–Boussinesq (OB) values. It is also demonstrated that NOB effects modify the near-wall temperature statistics, promoting the breaking of the top–bottom symmetry which characterises the OB approximation. The most prominent NOB effect in the near-wall region is the modification of the maximum r.m.s. values of temperature, which are found to increase at the top and decrease at the bottom of the cavity.
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Tu, Ken Ming, Kuo Ann Yih, and Jyh Horng Chou. "APPLICATION OF TAGUCHI EXPERIMENTAL METHOD IN NUMERICAL SIMULATION OF VARIABLE VISCOSITY AND INTERNAL HEAT GENERATION EFFECTS ON NATURAL CONVECTION IN POROUS MEDIA." Latin American Applied Research - An international journal 50, no. 4 (September 25, 2020): 277–81. http://dx.doi.org/10.52292/j.laar.2020.84.
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This study uses an optimization approach representation of the numerical solution for the variable viscosity, the uniform blowing/suction and the internal heat source effects on the free convection flow over a vertical permeable plate in porous media with a non-linear Boussinesq approximation. The internal heat source is of an exponential decaying form. The partial differential equations are transformed into non-similar equations and solved by Keller box method (KBM). Compared with the previously published articles, the results are considered to be very consistent. Numerical results for the local Nusselt number with the four parameters: 1) the blowing/suction parameter , 2) the viscosity-variation parameter , 3) internal heat source coefficient , 4) the non-linear temperature parameter are expressed in tables. Through the Taguchi method to predict the best point of the maximum of local Nusselt number is , , , .
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Schneider, Nicolas, and Serge Gauthier. "Vorticity and mixing in Rayleigh–Taylor Boussinesq turbulence." Journal of Fluid Mechanics 802 (August 3, 2016): 395–436. http://dx.doi.org/10.1017/jfm.2016.461.
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The Rayleigh–Taylor instability induced turbulence is studied under the Boussinesq approximation focusing on vorticity and mixing. A direct numerical simulation has been carried out with an auto-adaptive multidomain Chebyshev–Fourier–Fourier numerical method. The spatial resolution is increased up to $(24\times 40)\times 940^{2}=848\,M$ collocation points. The Taylor Reynolds number is $\mathit{Re}_{\unicode[STIX]{x1D706}_{zz}}\approx 142$ and a short inertial range is observed. The nonlinear growth rate of the turbulent mixing layer is found to be close to $\unicode[STIX]{x1D6FC}_{b}=0.021$. Our conclusions may be summarized as follows.(i) The simulation data are in agreement with the scalings for the pressure ($k^{-7/3}$) and the vertical mass flux ($k^{-7/3}$).(ii) Mean quantities have a self-similar behaviour, but some inhomogeneity is still present. For higher-order quantities the self-similar regime is not fully achieved.(iii) In the self-similar regime, the mean dissipation rate and the enstrophy behave as $\langle \overline{\unicode[STIX]{x1D700}}\rangle \propto t$ and $\langle \overline{\unicode[STIX]{x1D714}_{i}\,\unicode[STIX]{x1D714}_{i}}^{1/2}\rangle \propto t^{1/2}$, respectively.(iv) The large-scale velocity fluctuation probability density function (PDF) is Gaussian, while vorticity and dissipation PDFs show large departures from Gaussianity.(v) The pressure PDF exhibits strong departures from Gaussianity and is skewed. This is related to vortex coherent structures.(vi) The intermediate scales of the mixing are isotropic, while small scales remain anisotropic. This leaves open the possibility of a small-scale buoyancy. Velocity intermediate scales are also isotropic, while small scales remain anisotropic. Mixing and dynamics are therefore consistent.(vii) Properties and behaviours of vorticity and enstrophy are detailed. In particular, equations for these quantities are written down under the Boussinesq approximation.(viii) The concentration PDF is quasi-Gaussian. The vertical concentration gradient is both non-Gaussian and strongly skewed.
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Opadiran, Sunday Iyiola, and Samuel Segun Okoya. "Influence of Non-Linear Radiation and Viscous Dissipation on the Convective Fluid Flow with Variable Viscosity and Quadratic Boussinesq Approximation across a Cylinder with Uniform Heat Flux at the Wall." Defect and Diffusion Forum 419 (October 20, 2022): 37–56. http://dx.doi.org/10.4028/p-xw16zz.
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This study examines the effect of non-linear radiation and viscous dissipation on the convective Newtonian fluid flow with temperature-dependent viscosity and the quadratic Boussinesq approximation around a cylinder with uniform heat flux at the wall. The coupled partial differential equations of the problem are non-dimensionalized with appropriate variables and reduced via stream functions. Regular perturbation technique is employed to transform the nonlinear coupled partial differential equations into a system of nonlinear coupled ordinary differential equations solved using the Trapezoidal method. A surge in the radiative parameter was found to heighten the fluid’s velocity and temperature, while an increase in the dissipative effect enhances the skin friction and heat transfer distributions. The limiting cases of the model considered and the results obtained in this study are consistent with those in the literature.
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Pei, Binbin, FangBo Li, Zhengyuan Luo, Liang Zhao, and Bofeng Bai. "Dynamics of mixing flow with double-layer density stratification: Enstrophy and vortical structures." Physics of Fluids 34, no. 10 (October 2022): 104107. http://dx.doi.org/10.1063/5.0121554.
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Previous studies on stratified shear layers involving two streams with different densities have been conducted under the Boussinesq approximation, while the combined effect of stratified instability and mean shear in relation to multi-layer density stratification induced by scalar fields remains an unresolved fundamental question. In this paper, the shear-driven mixing flow involving initial double-layer density interfaces due to the compositional differences are numerically investigated, in which the mean shear interacts with Rayleigh–Taylor instability (RTI). Since its critical role in dynamics of shear layers and scalar transport, we focus on the evolution of entrophy and vortical structures. We find that the dynamics of mixing layers are determined by the mean shear and the distance between the initial density stratification. The mean shear and the Kelvin–Helmholtz instability dominate the evolution of shear layers at the initial stage. The increase in mean shear, therefore, is favorable for turbulent mixing, irrespective of effect of RTI. However, once the transition of turbulence occurs, the mean shear becomes weaker and RTI becomes prominent. This promotes the destruction of hairpin vortex and generation of vortex tube. In addition, the interaction of mean shear with RTI becomes weaker with increasing distance between initial density stratification. Furthermore, the viscous dissipation of enstrophy is larger than enstrophy production in the turbulent region due to the effect of RTI. The baroclinic term has the larger contribution in the turbulent region than near the turbulent/non-turbulent interface, which is different from the results of stably stratified flow under the Boussinesq approximation.
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Mehaddi, Rabah, Olivier Vauquelin, and Fabien Candelier. "Analytical solutions for turbulent Boussinesq fountains in a linearly stratified environment." Journal of Fluid Mechanics 691 (December 5, 2011): 487–97. http://dx.doi.org/10.1017/jfm.2011.487.
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AbstractThis paper theoretically investigates the initial up-flow of a vertical turbulent fountain (round or plane) in a linearly stratified environment. Conservation equations (volume, momentum and buoyancy) are written under the Boussinesq approximation assuming an entrainment proportional to the vertical velocity of the fountain. Analytical integration leads to exact values of both density and flow rate at the maximal height reached by the fountain. This maximal height is expressed as a function of the release conditions and the stratification strength and plotted from a numerical integration in order to exhibit overall behaviour. Then, analytical expressions for the maximal height are derived from asymptotic analysis and compared to experimental correlations available for forced fountains. For weak fountains, these analytical expressions constitute a new theoretical model. Finally, modified expressions are also proposed in the singular case of an initially non-buoyant vertical release.
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Laidoudi, Houssem, and Houari Ameur. "Investigation of the Natural Convection within a Cold Circular Enclosure Containing Three Equal-Sized Cylinders of Hot Surface." Defect and Diffusion Forum 409 (May 2021): 49–57. http://dx.doi.org/10.4028/www.scientific.net/ddf.409.49.
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The present work is conducted for studying the natural convection in a circular enclosure that contains three equal-sized cylinders in tandem arrangement. The outer cylinder has a cold surface and the enclosure internals have hot surfaces. The relation between the density of the fluid and the temperature is treated by the Boussinesq approximation. The fluid used for the investigation is Newtonian and incompressible. The results present the roles of some non-dimensional parameters (Rayleigh (Ra) and Prandtl (Pr) numbers) on the buoyancy-driven flow and the convective heat transfer. The obtained results revealed an intensification of the v-velocity component in the annular space and an enhancement in the heat transfer rates with the rise of Rayleigh number.
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Kolyshkin, Andrei, Valentina Koliskina, Inta Volodko, and Ilmārs Iltins. "Convective Instability of a Steady Flow in an Annulus Caused by Internal Heat Generation." Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences. 74, no. 4 (August 1, 2020): 293–98. http://dx.doi.org/10.2478/prolas-2020-0045.
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AbstractLinear stability of convective motion in a tall vertical annulus was analysed in the paper. The base flow was generated by a non-uniform distribution of heat sources in the radial direction. The base flow velocity and temperature were obtained analytically solving the system of Navier-Stokes equations under the Boussinesq approximation. The linear stability problem was solved for axi-symmetric and asymmetric perturbations by a collocation method based on the Chebyshev polynomials. Numerical results showed that there were three destabilising factors: (1) increase of the gap between the cylinders, (2) increase of the density of internal heat sources towards to the outer boundary of the annulus and (3) increase of the Prandtl number.
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Scotti, Alberto, and Brian White. "Diagnosing mixing in stratified turbulent flows with a locally defined available potential energy." Journal of Fluid Mechanics 740 (January 6, 2014): 114–35. http://dx.doi.org/10.1017/jfm.2013.643.
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AbstractA local available potential energy (APE) density useful as suitable diagnostic tool in turbulent stratified flows is considered under the Boussinesq approximation. The local APE is positive, and in the limit of infinitesimal perturbation from an equilibrium state recovers the Lorenz energy cycle definition of APE. In a turbulent stratified flow, the APE can be Reynolds-decomposed into non-trivial mean and turbulent components, which are connected to the mean and turbulent kinetic energy by suitably defined fluxes. We show that the turbulent buoyancy flux $\overline{w'b'}$ and the rate of production of turbulent APE coincide only under very special circumstances. The framework is applied to derive some global bounds on the mixing efficiency of some representative flows.
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Khan, Zar Ali, Muhammad Ishaq, Usman Ghani, Rooh ullah, and Saqib Iqbal. "Analysis of magnetohydrodynamics flow of a generalized viscous fluid through a porous medium with Prabhakar-like fractional model with generalized thermal transport." Advances in Mechanical Engineering 14, no. 10 (October 2022): 168781322211329. http://dx.doi.org/10.1177/16878132221132949.
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It is looked into how fractional MHD and viscous fluid naturally flow across a vertical plate that oscillates with a steady heat flux in a porous medium. The analytical solution for non-dimensional momentum was generated using the Laplace transform and the Boussinesq approximation. Comparisons are presented between Fourier’s law-described classical thermal transport and Prabhakar-like fractional time free convection flows in terms of temperature and velocity. By using fractional viscous fluid, we were able to produce conventional viscous fluid solutions and complete their objective. Finally, diagrams are used to show how different parameters such as Prandtl number, fractional parameters, Grashof number, effective permeability, time on temperature and velocity, and graphically recovered the solution available in the literature.
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Horn, Susanne, Olga Shishkina, and Claus Wagner. "On non-Oberbeck–Boussinesq effects in three-dimensional Rayleigh–Bénard convection in glycerol." Journal of Fluid Mechanics 724 (April 29, 2013): 175–202. http://dx.doi.org/10.1017/jfm.2013.151.
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AbstractRayleigh–Bénard convection in glycerol (Prandtl number $\mathit{Pr}= 2547. 9$) in a cylindrical cell with an aspect ratio of $\Gamma = 1$ was studied by means of three-dimensional direct numerical simulations (DNS). For that purpose, we implemented temperature-dependent material properties into our DNS code, by prescribing polynomial functions up to seventh order for the viscosity, the heat conductivity and the density. We performed simulations with the common Oberbeck–Boussinesq (OB) approximation and with non-Oberbeck–Boussinesq (NOB) effects within a range of Rayleigh numbers of $1{0}^{5} \leq \mathit{Ra}\leq 1{0}^{9} $. For the highest temperature differences, $\Delta = 80~\mathrm{K} $, the viscosity at the top is ${\sim }360\hspace{0.167em} \% $ times higher than at the bottom, while the differences of the other material properties are less than $15\hspace{0.167em} \% $. We analysed the temperature and velocity profiles and the thermal and viscous boundary-layer thicknesses. NOB effects generally lead to a breakdown of the top–bottom symmetry, typical for OB Rayleigh–Bénard convection. Under NOB conditions, the temperature in the centre of the cell ${T}_{c} $ increases with increasing $\Delta $ and can be up to $15~\mathrm{K} $ higher than under OB conditions. The comparison of our findings with several theoretical and empirical models showed that two-dimensional boundary-layer models overestimate the actual ${T}_{c} $, while models based on the temperature or velocity scales predict ${T}_{c} $ very well with a standard deviation of $0. 4~\mathrm{K} $. Furthermore, the obtained temperature profiles bend closer towards the cold top plate and further away from the hot bottom plate. The situation for the velocity profiles is reversed: they bend farther away from the top plate and closer towards to the bottom plate. The top boundary layers are always thicker than the bottom ones. Their ratio is up to 2.5 for the thermal and up to 4.5 for the viscous boundary layers. In addition, the Reynolds number $\mathit{Re}$ and the Nusselt number $\mathit{Nu}$ were investigated: $\mathit{Re}$ is higher and $\mathit{Nu}$ is lower under NOB conditions. The Nusselt number $\mathit{Nu}$ is influenced in a nonlinear way by NOB effects, stronger than was suggested by the two-dimensional simulations. The actual scaling of $\mathit{Nu}$ with $\mathit{Ra}$ in the NOB case is $\mathit{Nu}\propto {\mathit{Ra}}^{0. 298} $ and is in excellent agreement with the experimental data.
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Pourrajab, Rashid, and Aminreza Noghrehabadi. "Bioconvection of Nanofluid Past Stretching Sheet in a Porous Medium in Presence of Gyrotactic Microorganisms with Newtonian Heating." MATEC Web of Conferences 220 (2018): 01004. http://dx.doi.org/10.1051/matecconf/201822001004.
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In this study, the effect of Newtonian heating on the boundary layer flow and heat transfer over a stretching surface in a porous medium in the presence of gyrotactic microorganisms and nanoparticle fractions are analysed. The governing equations are reduced to a system of couple non-linear ordinary differential equations, subjected to the Boussinesq approximation and asymmetric heat conditions. The reduced governing ordinary differential equations are then solved numerically. The solutions obtained are graphically represented. The effects of the controlling parameters on the flow, heat, nanoparticle concentration and the density of motile microorganisms have been examined. The results of the present study show the flow velocity, heat and mass transfer and motile microorganism characteristics on the stretching sheet are strongly influenced by the bioconvection parameters and Newtonian.
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Farooq, Ali Ahmad, Zahir Shah, Poom Kumam, Ebraheem O. Alzahrani, Meshal Shutaywi, and Talha Anwar. "Darcy–Boussinesq Model of Cilia-Assisted Transport of a Non-Newtonian Magneto-Biofluid with Chemical Reactions." Applied Sciences 10, no. 3 (February 7, 2020): 1137. http://dx.doi.org/10.3390/app10031137.
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The model developed in this study presents a mathematical approach to the physiological transport of seminal liquid due to ciliary movements, which are attached with the lumen of the ductile efferent in the male reproductive system. The rheological properties of the seminal liquids were described using the Jeffrey liquid model. The problem described an electromagnetic mixed convective flow of a Jeffrey liquid through a vertical channel with heat and mass transfers. The effects of chemical reactions and the external heat generation were included in the formulation. The flow took place through an active porous medium (due to thick cilia mat and other deposits) and was influenced by the Lorentz magnetic force. Four basic conservation laws of mass, momentum, energy, and concentration were utilized in the mathematical modeling. These are highly nonlinear equations, which were simplified due to a physiologically valid approach known as LAT (lubrication approximation theory). Analytical solutions for temperature, concentration, and velocity profiles were evaluated. The expressions describing the pressure–volume flow rate relationships were also obtained. Analysis of various physical and geometrical factors affecting the pressure–volume (pumping) characteristics was also presented. One of the main findings of our study is that the difference between our calculated values of the flow rate and the estimated values of the flow rate in the ductile efferent was negligibly small. Moreover, our results can be implemented in the artificial cilia pumping systems in microchannels.
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Bratsun, Dmitry, and Vladimir Vyatkin. "Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows." Fluids 4, no. 3 (September 19, 2019): 175. http://dx.doi.org/10.3390/fluids4030175.
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A class of closed-form exact solutions for the Navier–Stokes equation written in the Boussinesq approximation is discussed. Solutions describe the motion of a non-homogeneous reacting fluid subjected to harmonic vibrations of low or finite frequency. Inhomogeneity of the medium arises due to the transversal density gradient which appears as a result of the exothermicity and chemical transformations due to a reaction. Ultimately, the physical mechanism of fluid motion is the unequal effect of a variable inertial field on laminar sublayers of different densities. We derive the solutions for several problems for thermo- and chemovibrational convections including the viscous flow of heat-generating fluid either in a plain layer or in a closed pipe and the viscous flow of fluid reacting according to a first-order chemical scheme under harmonic vibrations. Closed-form analytical expressions for fluid velocity, pressure, temperature, and reagent concentration are derived for each case. A general procedure to derive the exact solution is discussed.
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Kameswaran, Peri K., B. Vasu, P. V. S. N. Murthy, and Rama Subba Reddy Gorla. "Mixed convection from a wavy surface embedded in a thermally stratified nanofluid saturated porous medium with non-linear Boussinesq approximation." International Communications in Heat and Mass Transfer 77 (October 2016): 78–86. http://dx.doi.org/10.1016/j.icheatmasstransfer.2016.07.006.
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Mohebalhojeh, Ali R., Mohammad Joghataei, and David G. Dritschel. "Toward a PV-Based Algorithm for the Dynamical Core of Hydrostatic Global Models." Monthly Weather Review 144, no. 7 (June 10, 2016): 2481–502. http://dx.doi.org/10.1175/mwr-d-15-0379.1.
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Abstract The diabatic contour-advective semi-Lagrangian (DCASL) algorithms previously constructed for the shallow-water and multilayer Boussinesq primitive equations are extended to multilayer non-Boussinesq equations on the sphere using a hybrid terrain-following–isentropic (σ–θ) vertical coordinate. It is shown that the DCASL algorithms face challenges beyond more conventional algorithms in that various types of damping, filtering, and regularization are required for computational stability, and the nonlinearity of the hydrostatic equation in the σ–θ coordinate causes convergence problems with setting up a semi-implicit time-stepping scheme to reduce computational cost. The prognostic variables are an approximation to the Rossby–Ertel potential vorticity Q, a scaled pressure thickness, the horizontal divergence, and the surface potential temperature. Results from the DCASL algorithm in two formulations of the σ–θ coordinate, differing only in the rate at which the vertical coordinate tends to θ with increasing height, are assessed using the baroclinic instability test case introduced by Jablonowski and Williamson in 2006. The assessment is based on comparisons with available reference solutions as well as results from two other algorithms derived from the DCASL algorithm: one with a semi-Lagrangian solution for Q and another with an Eulerian grid-based solution procedure with relative vorticity replacing Q as the prognostic variable. It is shown that at intermediate resolutions, results comparable to the reference solutions can be obtained.
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NAND, SARVESHA, and Ashok Kumar Singh. "Free convection between vertical concentric annuli with induced magnetic field when inner cylinder is electrically conducting." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 13, no. 10 (October 30, 2014): 5063–74. http://dx.doi.org/10.24297/ijct.v13i10.2328.
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An analysis is made for the fully developed laminar free convective flow in an open ended vertical concentric annuli with constant heat flux and constant temperature on the inner and outer walls, in the presence of a radial magnetic field. The length of the cylinder is assumed to be infinite and radiation heat transfer from the hot surface is assumed to be negligible. The inner cylinder is taken to be magnetic conducting while the outer cylinder is non-conducting. Buoyancy effect is also considered along with Boussinesq approximation. The induced magnetic field is taken into account arising due to the motion of an electrically conducting fluid. The governing linear simultaneous ordinary differential equations are first obtained in the non dimensional form and solved analytically for the velocity, induced magnetic field, temperature field and  then skin-friction and induced current density are obtained. The expressions for the fluid flux and induced current flux in non-dimensional form have been also obtained. The effects of governing physical parameters occurring in the model are shown on the graphs and tables.
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Kumar, Pardeep. "Convection in Compressible Dusty Fluids." EQUATIONS 2 (July 1, 2022): 84–93. http://dx.doi.org/10.37394/232021.2022.2.14.
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The aim of the present research was to study the thermosolutal convection in compressible fluids with suspended particles in permeable media. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, it is found that that stable solute gradient introduces oscillatory modes which were non-existent in its absence. For the case of stationary convection, it is found that medium permeability and suspended particles have destabilizing effects whereas the stable solute gradient has a stabilizing effect on the system. This problem was further extended to include uniform rotation. In this case for stationary convection, the suspended particles are found to have destabilizing effect whereas stable solute gradient, rotation and compressibility have stabilizing effect on the system. The medium permeability has a destabilizing effect in the absence of rotation but has both stabilizing and destabilizing effects in the presence of rotation.
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Ch. Ramreddy, P. Naveen, and D. Srinivasacharya. "Non-Linear Boussinesq Approximation and Cross-Diffusion Effects on an Ostwald-de-Waele Power-Law Fluid Flow with Convective Boundary Condition." Advanced Science, Engineering and Medicine 10, no. 1 (January 1, 2018): 1–8. http://dx.doi.org/10.1166/asem.2018.2114.
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Livescu, Daniel. "Turbulence with Large Thermal and Compositional Density Variations." Annual Review of Fluid Mechanics 52, no. 1 (January 5, 2020): 309–41. http://dx.doi.org/10.1146/annurev-fluid-010719-060114.
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Density variations in fluid flows can arise due to acoustic or thermal fluctuations, compositional changes during mixing of fluids with different molar masses, or phase inhomogeneities. In particular, thermal and compositional (with miscible fluids) density variations have many similarities, such as in how the flow interacts with a shock wave. Two limiting cases have been of particular interest: ( a) the single-fluid non-Oberbeck–Boussinesq low–Mach number approximation for flows with temperature variations, which describes vertical convection, and ( b) the incompressible limit of mixing between miscible fluids with different molar masses, which describes the Rayleigh–Taylor instability. The equations describing these cases are remarkably similar, with some differences in the molecular transport terms. In all cases, strong inertial effects lead to significant asymmetries of mixing, turbulence, and the shape of mixing layers. In addition, density variations require special attention in turbulence models to avoid viscous contamination of the large scales.
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Burmasheva, Natalya V., and Evgeniy Yu Prosviryakov. "Influence of the Dufour Effect on Shear Thermal Diffusion Flows." Dynamics 2, no. 4 (October 24, 2022): 367–79. http://dx.doi.org/10.3390/dynamics2040021.
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The article considers thermal diffusion shear flows of a viscous incompressible fluid with spatial acceleration. The simulation uses a system of thermal diffusion equations (in the Boussinesq approximation), taking into account the Dufour effect. This system makes it possible to describe incompressible gases, for which this effect prevails, from a unified standpoint. It is shown that for shear flows, the system of equations under study is nonlinear and overdetermined. In view of the absence of a theorem on the existence and smoothness of the solution of the Navier–Stokes equation, the integration of the existing system seems to be an extremely difficult task. The article studies the question of the existence of a solution in the class of functions represented as complete linear forms in two Cartesian coordinates with non-linear (with respect to the third Cartesian coordinate) coefficients. It is shown that the system is non-trivially solvable under a certain condition (compatibility condition) constructed by the authors. The corresponding theorem is formulated and proven. These conclusions are illustrated by a comparison with the previously obtained results.
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Khan, Shahid, Mahmoud M. Selim, Khaled A. Gepreel, Asad Ullah, Ikramullah, Muhammad Ayaz, Wali Khan Mashwani, and Emel Khan. "An analytical investigation of the mixed convective Casson fluid flow past a yawed cylinder with heat transfer analysis." Open Physics 19, no. 1 (January 1, 2021): 341–51. http://dx.doi.org/10.1515/phys-2021-0040.
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Abstract The hydrodynamic flow of an incompressible and isotropic Casson fluid through a yawed cylinder is investigated by employing continuity, momentum, and energy equations satisfying suitable boundary conditions. The density variation is governed by Boussinesq approximation. The model equations consisting of coupled partial differential equations (PDEs) are transformed by applying non-similar transformation relations. The set of transformed PDEs is solved using the analytical technique of homotopy analysis method (HAM). The impacts of varying yaw angle, and mixed convection and Casson parameters over fluid velocity (chordwise and spanwise components), its temperature, Nusselt number, and skin friction coefficients are investigated and explained through various graphs. It is found that the enhancing yaw angle, Casson parameter, and convection parameter augment the fluid velocity, heat transfer rate, and skin friction and reduce the fluid temperature. The agreement of present and published results justifies the application of HAM in modeling the mixed convective Casson fluid flow past a yawed cylinder.
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LIÑÁN, AMABLE, and VADIM N. KURDYUMOV. "Laminar free convection induced by a line heat source, and heat transfer from wires at small Grashof numbers." Journal of Fluid Mechanics 362 (May 10, 1998): 199–227. http://dx.doi.org/10.1017/s0022112098008830.
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The buoyancy-induced laminar flow and temperature fields associated with a line source of heat in an unbounded environment are described by numerically solving the non-dimensional Boussinesq equations with the appropriate boundary conditions. The solution is given for values of the Prandtl number, the single parameter, ranging from zero to infinity. The far-field form of the solution is well known, including a self-similar thermal plume above the source. The analytical description close to the source involves constants that must be evaluated with the numerical solution.These constants are used when calculating the free convection heat transfer from wires (or cylinders of non-circular shape) at small Grashof numbers. We find two regions in the flow field: an inner region, scaled with the radius of the wire, where the effects of convection can be neglected in first approximation, and an outer region where, also in first approximation, the flow and temperature fields are those due to a line source of heat. The cases of large and small Prandtl numbers are considered separately. There is good agreement between the Nusselt numbers given by the asymptotic analysis and by the numerical analysis, which we carry out for a wide range of Grashof numbers, extending to very small values the range of existing numerical results; there is also agreement with the existing correlations of the experimental results. A correlation expression is proposed for the relation between the Nusselt and Grashof numbers, based on the asymptotic forms of the relation for small and large Grashof numbers.