Journal articles: 'Quadratic Boussinesq approximation'

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Gravanis, Elias, Evangelos Akylas, and Ernestos Nikolas Sarris. "Approximate Solutions for Horizontal Unconfined Aquifers in the Buildup Phase." Water 16, no. 7 (April 2, 2024): 1031. http://dx.doi.org/10.3390/w16071031.

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We construct approximate analytical solutions of the Boussinesq equation for horizontal unconfined aquifers in the buildup phase under constant recharge and zero-inflow conditions. We employ a variety of methods, which include wave solutions, self-similar solutions, and two classical linear approximations of the Boussinesq equation (linear and quadratic), to explore the behavior and performance of the solutions derived from each method against the Boussinesq equation and the exact (non-closed form) analytical solutions. We find that the wave approximation, which is of a conceptual nature, encapsulates quite faithfully the characteristics of the nonlinear Boussinesq equation solution and, overall, performs much better than the other methods, for which the relatively low performance can be attributed to the specific mathematical features of their construction. These endeavors might be useful for theoretical and modeling purposes related to this problem.

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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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Saprykina, Yana, Burak Aydogan, and Berna Ayat. "Wave Energy Dissipation of Spilling and Plunging Breaking Waves in Spectral Models." Journal of Marine Science and Engineering 10, no. 2 (February 1, 2022): 200. http://dx.doi.org/10.3390/jmse10020200.

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On the basis of field experiments and modeling, the dependence of the dissipation of the energy of waves breaking by plunging and spilling on the frequency of wave spectra was investigated. It was shown that the modeling of wave breaking should take into account the compensation of the nonlinear growth of higher wave harmonics, which occurs in different ways for waves breaking with different types and for different methods of modeling a nonlinear source term. The study revealed that spilling breaking waves have a frequency selectivity of energy dissipation at frequencies of second and third harmonics for the Boussinesq and SWAN models for any method of modeling a nonlinear source term. Plunging breaking waves have a quadratic dependence of the dissipation coefficient on frequency in the Boussinesq model and SWAN model with the SPB approximation for a nonlinear source term. The SWAN model with default LTA approximation for plunging breaking waves also assumes frequency-selective energy dissipation. The discrepancy between the LTA default method and others can be explained by the overestimation of the contribution of the second nonlinear harmonic and by inaccurate approximation for the biphase. It is possible to improve the accuracy of LTA and SPB methods by tuning SWAN model coefficients.

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Hassan, A. R., S. O. Salawu, A. B. Disu, and O. R. Aderele. "Thermodynamic analysis of a tangent hyperbolic hydromagnetic heat generating fluid in quadratic Boussinesq approximation." Journal of Computational Mathematics and Data Science 4 (August 2022): 100058. http://dx.doi.org/10.1016/j.jcmds.2022.100058.

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Srinivas Reddy, C., B. Mahanthesh, P. Rana, and K. S. Nisar. "Entropy generation analysis of tangent hyperbolic fluid in quadratic Boussinesq approximation using spectral quasi-linearization method." Applied Mathematics and Mechanics 42, no. 10 (September 29, 2021): 1525–42. http://dx.doi.org/10.1007/s10483-021-2773-8.

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Ohaegbue, A. D., S. O. Salawu, R. A. Oderinu, E. O. Fatunmbi, and A. O. Akindele. "Thermal dissipation of two-step combustible tangent hyperbolic fluid with quadratic Boussinesq approximation and convective cooling." Results in Materials 22 (June 2024): 100565. http://dx.doi.org/10.1016/j.rinma.2024.100565.

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Alboussière, Thierry, and Yanick Ricard. "Rayleigh–Bénard stability and the validity of quasi-Boussinesq or quasi-anelastic liquid approximations." Journal of Fluid Mechanics 817 (March 16, 2017): 264–305. http://dx.doi.org/10.1017/jfm.2017.108.

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The linear stability threshold of the Rayleigh–Bénard configuration is analysed with compressible effects taken into account. It is assumed that the fluid under investigation obeys a Newtonian rheology and Fourier’s law of thermal transport with constant, uniform (dynamic) viscosity and thermal conductivity in a uniform gravity field. Top and bottom boundaries are maintained at different constant temperatures and we consider here mechanical boundary conditions of zero tangential stress and impermeable walls. Under these conditions, and with the Boussinesq approximation, Rayleigh (Phil. Mag., vol. 32 (192), 1916, pp. 529–546) first obtained analytically the critical value $27\unicode[STIX]{x03C0}^{4}/4$ for a dimensionless parameter, now known as the Rayleigh number, at the onset of convection. This paper describes the changes of the critical Rayleigh number due to the compressibility of the fluid, measured by the dimensionless dissipation parameter ${\mathcal{D}}$ and due to a finite temperature difference between the hot and cold boundaries, measured by a dimensionless temperature gradient $a$. Different equations of state are examined: ideal gas equation, Murnaghan’s model (often used to describe the interiors of solid but convective planets) and a generic equation of state with adjustable parameters, which can represent any possible equation of state. In the perspective to assess approximations often made in convective models, we also consider two variations of this stability analysis. In a so-called quasi-Boussinesq model, we consider that density perturbations are solely due to temperature perturbations. In a so-called quasi-anelastic liquid approximation model, we consider that entropy perturbations are solely due to temperature perturbations. In addition to the numerical Chebyshev-based stability analysis, an analytical approximation is obtained when temperature fluctuations are written as a combination of only two modes, one being the original symmetrical (between top and bottom) mode introduced by Rayleigh, the other one being antisymmetrical. The analytical solution allows us to show that the antisymmetrical part of the critical eigenmode increases linearly with the parameters $a$ and ${\mathcal{D}}$, while the superadiabatic critical Rayleigh number departs quadratically in $a$ and ${\mathcal{D}}$ from $27\unicode[STIX]{x03C0}^{4}/4$. For any arbitrary equation of state, the coefficients of the quadratic departure are determined analytically from the coefficients of the expansion of density up to degree three in terms of pressure and temperature.

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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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Okoya, Samuel S., Anthony Rotimi Hassan, and Sulyman Olakunle Salawu. "ON FREE CONVECTION FLOW OF A MOVING VERTICAL PERMEABLE PLATE WITH QUADRATIC BOUSSINESQ APPROXIMATION AND VARIABLE THERMAL CONDUCTIVITY." Heat Transfer Research 52, no. 7 (2021): 55–66. http://dx.doi.org/10.1615/heattransres.2021037973.

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Fujimura, K., and S. Yamada. "Hexagons and triangles in the Rayleigh–Bénard problem: quintic-order equations on a hexagonal lattice." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2098 (June 3, 2008): 2721–39. http://dx.doi.org/10.1098/rspa.2007.0340.

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On a weakly nonlinear basis, we revisit the pattern formation problem in the Boussinesq convection, for which nonlinear terms of the quadratic order are known to vanish from amplitude equations. It is thus necessary to proceed to the quintic-order approximation in order for the amplitude equations to be generic. By deriving the quintic amplitude equations from the governing PDEs, we examined the bifurcation of steady solutions under rigid–free, rigid–rigid and free–free boundary conditions. Right above the criticality, all the axial solutions are obtained including up- and down-hexagons under the asymmetric boundary conditions and hexagons and regular triangles under the symmetric conditions. Hexagons and regular triangles are unstable whereas rolls are stable as has already been predicted by the cubic-order amplitude equations. Irrespective of the boundary conditions, quintic-order terms stabilize hexagons except near the criticality; rolls and hexagons thus coexist stably in an open region. This suggests that amplitude equations of higher order are possible to predict re-entrant hexagons .

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RamReddy, C., and P. Naveen. "Analysis of activation energy in quadratic convective flow of a micropolar fluid with chemical reaction and suction/injection effects." Multidiscipline Modeling in Materials and Structures 16, no. 1 (September 5, 2019): 169–90. http://dx.doi.org/10.1108/mmms-12-2018-0217.

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Purpose The purpose of this paper is to analyze the combined effects of thermal radiation and activation energy with a chemical reaction on the quadratic convective flow of a micropolar fluid over an inclined plate. Convective thermal boundary condition and suction/injection effects are considered at the surface of an inclined plate. Design/methodology/approach The convection along with nonlinear Boussinesq approximation (i.e. quadratic convection or nonlinear convection) and usual boundary layer assumptions is employed in the mathematical formulation. Highly coupled nonlinear governing equations are tackled by a combined local non-similarity and successive linearization techniques. Findings The behavior of various pertinent parameters on the fluid flow characteristics is conferred through graphs and it reveals that the qualitative behaviors of velocity, temperature, skin friction and heat transfer rates of a micropolar fluid are similar for Biot number and radiation parameters. The suction/injection and activation energy parameters increase the concentration of the micropolar fluid within the boundary layer, while the chemical reaction parameter reduces the concentration in the same region. Further, this quadratic convection shows a strong influence on the fluid flow characteristics and then the impact of pertinent parameters is more prominent on the physical quantities, compared therewith results of the linear convection. Practical implications This kind of investigation is useful in the mechanism of combustion, aerosol technology, high-temperature polymeric mixtures and solar collectors which are operated at moderate to very high temperatures. Originality/value This attempt is a unique contribution to the establishment of both micropolar fluid and activation energy. This kind of study even in the absence of quadratic convection is not yet noted.

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Lien, F. S., and M. A. Leschziner. "Modelling 2D separation from a high lift aerofoil with a non-linear eddy-viscosity model and second-moment closure." Aeronautical Journal 99, no. 984 (April 1995): 125–44. http://dx.doi.org/10.1017/s0001924000027111.

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AbstractA computational study is presented, which examines the performance of variants of second-moment closure and non-linear eddy-viscosity models when used to predict attached and separated flows over a high lift aerofoil for a range of incidence angles. The capabilities of both model types, especially in respect of resolving the onset of suction-side separation at high incidence, are contrasted with those of a low-Re k-ε model based on the linear Boussinesq stress-strain relationship. The second-moment model contains a conventional linear approximation of the pressure straining process; a cubic (realisable) variant has been investigated in an earlier study and found to offer no advantages. The quadratic eddy-viscosity model features coefficients which are sensitised to the strain and vorticity invariants. While both models, in the form originally proposed, are superior to the linear eddy-viscosity variant, neither performs well in respect of resolving separation, unless modified so as to return the requisite low level of shear stress in the boundary layer approaching separation. Once separation is resolved with sufficient realism, the near wake aft of the trailing edge is also well represented. All models return poor representations of the far wake which is characterised by low levels of turbulence production to dissipation ratio.

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Kurkina, O. E., A. A. Kurkin, E. A. Rouvinskaya, and T. Soomere. "Propagation regimes of interfacial solitary waves in a three-layer fluid." Nonlinear Processes in Geophysics 22, no. 2 (March 4, 2015): 117–32. http://dx.doi.org/10.5194/npg-22-117-2015.

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Abstract. Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inviscid layers of arbitrary thickness and constant densities (stable configuration, Boussinesq approximation) bounded by a horizontal rigid bottom from below and by a rigid lid at the surface are described up to the second order of perturbation theory in small parameters of nonlinearity and dispersion. First, a pair of alternatives of appropriate KdV-type equations with the coefficients depending on the parameters of the fluid (layer positions and thickness, density jumps) are derived for the displacements of both modes of internal waves and for each interface between the layers. These equations are integrable for a very limited set of coefficients and do not allow for proper description of several near-critical cases when certain coefficients vanish. A more specific equation allowing for a variety of solitonic solutions and capable of resolving most near-critical situations is derived by means of the introduction of another small parameter that describes the properties of the medium and rescaling of the ratio of small parameters. This procedure leads to a pair of implicitly interrelated alternatives of Gardner equations (KdV-type equations with combined nonlinearity) for the two interfaces. We present a detailed analysis of the relationships for the solutions for the disturbances at both interfaces and various regimes of the appearance and propagation properties of soliton solutions to these equations depending on the combinations of the parameters of the fluid. It is shown that both the quadratic and the cubic nonlinear terms vanish for several realistic configurations of such a fluid.

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Kurkina, O. E., A. A. Kurkin, E. A. Rouvinskaya, and T. Soomere. "Propagation regimes of interfacial solitary waves in a three-layer fluid." Nonlinear Processes in Geophysics Discussions 2, no. 1 (January 6, 2015): 1–41. http://dx.doi.org/10.5194/npgd-2-1-2015.

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Abstract. Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inviscid immiscible layers of arbitrary thickness and constant densities (stable configuration, Boussinesq approximation) bounded by a horizontal rigid bottom from below and by a rigid lid at the surface are described up to the second order of perturbation theory in small parameters of nonlinearity and dispersion. First, a pair of alternatives of appropriate KdV-type equations with the coefficients depending on the parameters of the fluid (layer positions and thickness, density jumps) are derived for the displacements of both modes of internal waves and for each interface between the layers. These equations are integrable for a very limited set of coefficients and do not allow for proper description of several near-critical cases when certain coefficients vanish. A more specific equation allowing for a variety of solitonic solutions and capable of resolving most of near-critical situations is derived by means of the introduction of another small parameter that describes the properties of the medium and rescaling of the ratio of small parameters. This procedure leads to a pair of implicitly interrelated alternatives of Gardner equation (KdV-type equations with combined nonlinearity) for the two interfaces. We present a detailed analysis of the relationships for the solutions for the disturbances at both interfaces and various regimes of the appearance and propagation properties of soliton solutions to these equations depending on the combinations of the parameters of the fluid. It is shown both the quadratic and the cubic nonlinear terms vanish for several realistic configurations of such a fluid.

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Adesanya, Samuel Olumide, Tunde Abdulkadir Yusuf, and Ramoshweu Solomon Lebelo. "Nonlinear Mixed Convection in a Reactive Third-Grade Fluid Flow with Convective Wall Cooling and Variable Properties." Mathematics 10, no. 22 (November 15, 2022): 4276. http://dx.doi.org/10.3390/math10224276.

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Energy management and heat control whenever a reactive viscous fluid is the working medium has been one of the greatest challenges encountered by many in the field of chemical and industrial engineering. A mathematical approach to thedetermination of critical points beyond which the working environment becomes hazardous is presented in the present investigation together with the entropy generation analysis that guarantees the efficient management of expensive energy resources. In this regard, the nonlinear mixed convective flow behavior of a combustible third-grade fluid through a vertical channel with wall cooling by convection is investigated. The mathematical formulation captures the nonlinearities arising from second-order Boussinesq approximation and exponential dependence of internal heat generation, viscosity, and thermal conductivity on temperature. The resulting nonlinear boundary value problems were solved based on the spectral Chebyshev collocation method (SCCM) and validated with the shooting-Runge–Kutta method (RK4). The nonlinear effects on the flow velocity, temperature distribution, entropy generation, and Bejan heat irreversibility ratio are significant. Further analyses include the thermal stability of the fluid. Findings from the study revealed that flow, temperature, and entropy generation are enhanced byincreasing values of the Grashof number, the quadratic component of buoyancy, and the Frank-Kameneskii parameter, but are reducedbyincreasing the third-grade material parameter. Moreover, it was shown that increasing values of the third-grade parameter encourages the thermal stability of the flow, while increasing values of the linear and nonlinear buoyancy parameter destabilizes the flow. The present result is applicable to thick combustible polymers with increased molecular weight.

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Hallez, Yannick, and Jacques Magnaudet. "Buoyancy-induced turbulence in a tilted pipe." Journal of Fluid Mechanics 762 (December 8, 2014): 435–77. http://dx.doi.org/10.1017/jfm.2014.638.

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AbstractNumerical simulation is used to document the statistical structure and better understand energy transfers in a low-Reynolds-number turbulent flow generated by negative axial buoyancy in a long circular tilted pipe under the Boussinesq approximation. The flow is found to exhibit specific features which strikingly contrast with the familiar characteristics of pressure-driven pipe and channel flows. The mean flow, dominated by an axial component exhibiting a uniform shear in the core, also comprises a weak secondary component made of four counter-rotating cells filling the entire cross-section. Within the cross-section, variations of the axial and transverse velocity fluctuations are markedly different, the former reaching its maximum at the edge of the core while the latter two decrease monotonically from the axis to the wall. The negative axial buoyancy component generates long plumes travelling along the pipe, yielding unusually large longitudinal integral length scales. The axial and crosswise mean density variations are shown to be respectively responsible for a quadratic variation of the crosswise shear stress and density flux which both decrease from a maximum on the pipe axis to near-zero values throughout the near-wall region. Although the crosswise buoyancy component is stabilizing everywhere, the crosswise density flux is negative in some peripheral regions, which corresponds to apparent counter-gradient diffusion. Budgets of velocity and density fluctuations variances and of crosswise shear stress and density flux are analysed to explain the above features. A novel two-time algebraic model of the turbulent fluxes is introduced to determine all components of the diffusivity tensor, revealing that they are significantly influenced by axial and crosswise buoyancy effects. The eddy viscosity and eddy diffusivity concepts and the Reynolds analogy are found to work reasonably well within the central part of the section whereas non-local effects cannot be ignored elsewhere.

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Holm, Darryl D. "Variational principles for stochastic fluid dynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2176 (April 2015): 20140963. http://dx.doi.org/10.1098/rspa.2014.0963.

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This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler–Boussinesq and quasi-geostropic approximations.

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Bilal, Sardar, Maryam Rehman, Samad Noeiaghdam, Hijaz Ahmad, and Ali Akgül. "Numerical Analysis of Natural Convection Driven Flow of a Non-Newtonian Power-Law Fluid in a Trapezoidal Enclosure with a U-Shaped Constructal." Energies 14, no. 17 (August 28, 2021): 5355. http://dx.doi.org/10.3390/en14175355.

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Placement of fins in enclosures has promising utilization in advanced technological processes due to their role as heat reducing/generating elements such as in conventional furnaces, economizers, gas turbines, heat exchangers, superconductive heaters and so forth. The advancement in technologies in power engineering and microelectronics requires the development of effective cooling systems. This evolution involves the utilization of fins of significantly variable geometries enclosed in cavities to increase the heat elimination from heat-generating mechanisms. Since fins are considered to play an effective role in the escalation of heat transmission, the current study is conducted to examine the transfer of heat in cavities embedding fins, as well as the effect of a range of several parameters upon the transmission of energy. The following research is supplemented with the interpretation of the thermo-physical aspects of a power-law liquid enclosed in a trapezoidal cavity embedding a U-shaped fin. The Boussinesq approximation is utilized to generate the mathematical attributes of factors describing natural convection, which are then used in the momentum equation. Furthermore, the Fourier law is applied to formulate the streaming heat inside the fluid flow region. The formulated system describing the problem is non-dimensionalized using similarity transformations. The geometry of the problem comprises a trapezoidal cavity with a non-uniformly heated U-shaped fin introduced at the center of the base of the enclosure. The boundaries of the cavity are at no-slip conditions. Non-uniform heating is provided at the walls (l1 and l2), curves (c1,c2 and c3) and surfaces (s1 and s2) of the fin; the upper wall is insulated whereas the base and sidewalls of the enclosure are kept cold. The solution of the non-dimensionalized equations is procured by the Galerkin finite element procedure. To acquire information regarding the change in displacement w.r.t time and temperature, supplementary quadratic interpolating functions are also observed. An amalgam meshing is constructed to elaborate the triangular and quadrilateral elements of the trapezoidal domain. Observation of significant variation in the flow configurations for a specified range of parameters is taken into consideration i.e., 0.5≤n≤1.5 and 104≤Ra≤106. Furthermore, flow structures in the form of velocity profiles, streamlines, and temperature contours are interpreted for the parameters taken into account. It is deduced from the study that ascending magnitude of (Ra) elevates level of kinetic energy and magnitude of heat flux; however, a contrary configuration is encapsulated for the power-law index. Navier–Stokes equations constituting the phenomenon are written with the help of non-dimensionalized stream function, temperature profiles, and vortices, and the solutions are acquired using the finite element method. Furthermore, the attained outcomes are accessible through velocity and temperature profiles. It is worth highlighting the fact that the following analysis enumerates the pseudo-plastic, viscous and dilatant behavior of the fluid for different values of (n). This study highlights that the momentum profile and the heat transportation increase by increasing (Ra) and decline as the viscosity of the fluid increases. Overall, it can be seen from the current study that heat transportation increases with the insertion of a fin in the cavity. The current communication signifies the phenomenon of a power-law fluid flow filling a trapezoidal cavity enclosing a U-shaped fin. Previously, researchers have studied such phenomena mostly in Newtonian fluids, hence the present effort presents novelty regarding consideration of a power-law liquid in a trapezoidal enclosure by the placement of a U-shaped fin.

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Opadiran, Sunday Iyiola, and Samuel Segun Okoya. "Importance of convective boundary layer flows with inhomogeneous material properties under linear and quadratic Boussinesq approximations around a horizontal cylinder." Heliyon 7, no. 5 (May 2021): e07074. http://dx.doi.org/10.1016/j.heliyon.2021.e07074.

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Thriveni, K., and B. Mahanthesh. "Heat transport of hybrid nanomaterial in an annulus with quadratic Boussinesq approximation." Applied Mathematics and Mechanics, May 19, 2021. http://dx.doi.org/10.1007/s10483-021-2739-6.

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Mahanthesh, B., and Joby Mackolil. "Flow of nanoliquid past a vertical plate with novel quadratic thermal radiation and quadratic Boussinesq approximation: Sensitivity analysis." International Communications in Heat and Mass Transfer, November 2020, 105040. http://dx.doi.org/10.1016/j.icheatmasstransfer.2020.105040.

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Mahanthesh, B., C. Srinivas Reddy, N. Srikantha, and G. Lorenzini. "Entropy generation analysis of radiative heat transfer in Williamson fluid flowing in a microchannel with nonlinear mixed convection and Joule heating." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, February 2, 2022, 095440892210748. http://dx.doi.org/10.1177/09544089221074846.

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In this article, the spectral quasi-linearization (SQLM) method is implemented to solve the complicated differential equations governing the nonlinear mixed convective heat transfer of a Williamson fluid through a vertical microchannel. Unlike the conventional Boussinesq approximation, the quadratic Boussinesq approximation is taken into account in the formulation. The effects of Rosseland thermal radiation, Joule heating, and viscous dissipation are described in the thermal analysis subjected to the boundary conditions of convective thermal heating. The analysis of entropy production is also performed. The importance of various parameters governing velocity, Bejan number, temperature, and entropy generation was explored using graphic illustrations. It was found that the nonlinear density change with a temperature significantly affects the heat transport in the microchannel and thus increases the magnitude of the Bejan number and the production of entropy. Entropy production occurs maximum due to the boundary conditions of convection heating at the walls of the microchannel. Furthermore, due to a stronger viscous heating mechanism, the magnitude of the Bejan number is reduced, while the production of entropy increases significantly. As a limiting case of the problem, a comparison was made with results previously published in the literature and excellent agreement was established. The calculations provide a solid reference point for future CFD models and are relevant to the dynamics of polymers in microfluidic devices and the polymer industries.

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Thriveni, K., and B. Mahanthesh. "Optimization and sensitivity analysis of heat transport of hybrid nanoliquid in an annulus with quadratic Boussinesq approximation and quadratic thermal radiation." European Physical Journal Plus 135, no. 6 (June 2020). http://dx.doi.org/10.1140/epjp/s13360-020-00484-8.

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Subhashini, S. V., and S. Lenin Sindhu. "Analysis of an unsteady triple diffusion through quadratic Boussinesq approximation from a rotating cone in a rotating fluid." Journal of Analysis, August 2, 2023. http://dx.doi.org/10.1007/s41478-023-00630-2.

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Upreti, Himanshu, Alok Kumar Pandey, Tanya Gupta, and Subrahamanyam Upadhyay. "Exploring the nanoparticle’s shape effect on boundary layer flow of hybrid nanofluid over a thin needle with quadratic Boussinesq approximation: Legendre wavelet approach." Journal of Thermal Analysis and Calorimetry, September 26, 2023. http://dx.doi.org/10.1007/s10973-023-12502-9.

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Mushahary, Pungja, and Surender Ontela. "Entropy Analysis of Mixed Convective Electro-Magnetohydrodynamic Couple-Stress Hybrid Nanofluid Flow with Variable Electrical Conductivity in a Porous Channel." Physica Scripta, October 3, 2024. http://dx.doi.org/10.1088/1402-4896/ad831c.

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Abstract The paper presents a novel study to examine the irreversibility of quadratically mixed convective electro-magnetohydrodynamic (EMHD) flow of a couple-stress hybrid nanofluid (CSHNF) with variable properties in a vertical porous channel. The channel walls are exposed to an applied electric field effect and a uniform transverse magnetic field. The hybrid nanofluid considered is an ethylene glycol (C2H6O2) base mixed with multi-walled carbon nanotubes (MWCNT) and silver (Ag) nanoparticles (NPs), assuming the base fluid and nanoparticles to be in a state of thermal equilibrium following the Tiwari-Das nanofluid model. The potential applications of the study can be in microfluidics to nanofluidics, particularly in developing cooling technologies, EMHD pumps, high-end microelectromechanical systems (MEMS), and lab-on-a-chip (LOC) devices used in bioengineering. A constant pressure gradient acting in the flow direction and the buoyancy effect under the quadratic Boussinesq approximation drive the flow. The governing momentum and energy equations are nondimensionalized using pertinent dimensionless parameters and solved by the semi-analytical homotopy analysis method (HAM). The entropy generation and the Bejan numbers are derived to examine the irreversibilities in the system. To investigate the rate of shear stresses and heat transfer, skin friction coefficients and Nusselt numbers on the channel walls are determined. The analysis emphasizes the influence of nanoparticle concentration and electromagnetic field on the flow dynamics, temperature distribution, and system irreversibilities in the presence of porous media. It reveals the enhancement of fluid velocity and temperature degradation for higher concentrations. In contrast, both reduce for higher magnetic and electrical strength. With the enhancement of electrical joule heating and quadratic convection, a higher entropy generation rate is attained with a low rate of heat transfer irreversibility. However, it reduces with higher nanoparticle concentration, electrical strength, porosity, and variable electrical conductivity parameters under the dominance of heat transfer irreversibility.

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Mushahary, Pungja, and Ontela Surender. "Mixed convective magnetohydrodynamic and thermally radiative flow of reactive couple stress MWCNT–Ag/C2H6O2 hybrid nanofluid in a porous vertical channel: Entropy analysis." Physics of Fluids 35, no. 12 (December 1, 2023). http://dx.doi.org/10.1063/5.0177221.

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This paper is concerned with the analysis of the mixed convective magnetohydrodynamic (MHD) flow of a reactive couple stress multi-walled carbon nanotube −Ag/C2H6O2 hybrid nanofluid in a porous vertical channel subjected to quadratic thermal radiation along with a uniform inclined magnetic field applied to the channel walls. The flow is driven by the pressure gradient force and the buoyancy force, which is modeled based on the nonlinear Boussinesq approximation. The temperature-dependent reaction rate of the reactant molecule is derived using the Arrhenius law. The momentum and energy equations that govern the system are modeled in consideration of slip and convective conditions. The governing equations are non-dimensionalized by applying relevant dimensionless parameters and are solved using the homotopy analysis method (HAM). To analyze the irreversibilities in the system, the entropy generation number and the Bejan number are defined. Different important physical parameters developing in the system are considered for analysis, and their effects are scrutinized on the velocity and temperature profiles along with entropy generation. The emphasis is given to the concentration of nanoparticles along with the parameters arising due to the reactions of the fluid, buoyancy force, inclined magnetic field, thermal radiation, and porous material. The analysis reveals that the velocity and temperature of the fluid lowers with a higher concentration of nanoparticles, radiation parameter, and Hartmann number, whereas develops for the higher slip parameters and inclination of the magnetic field. The entropy generation rate increases with rising slip parameters and depletes for higher nanoparticle concentration, radiation parameter, Hartmann number, and inclination angle. The irreversibility in the system remains dominant due to heat transfer with higher Frank-Kameneskii and activation energy parameters, Hartmann number, and angle of inclination.

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Journal articles on the topic 'Quadratic Boussinesq approximation'

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