Academic literature on the topic 'Natural (free) convection'

The involvement of non-linear convection effects in a natural convective fluid flow and heat transfer along with the effects of magnetic field in a porous cavity is studied numerically. Cu-water filled cavity of higher temperature at the left wall and lower temperature at the right wall. The governing equations are organized to achieve the required flow by using two-dimensional equations of energy, continuity and momentum. Vorticity-stream function based dimensionless equations are solved using the finite difference techniques. The results are discussed for various dimensionless parameters such as the Darcy number, non-linear convection parameter, Hartmann number, Rayleigh number and solid volume fraction of the nanoparticles. An augment in streamline velocity and convection heat transfer are observed by increasing the Rayleigh number, non-linear convection parameter and Darcy number. The non-linear convection parameter has a lesser effect on the lower Rayleigh numbers. Diminished streamline intensity and reduction in convection heat transfer are noted for an increase in the strength of the applied magnetic field irrespective of the non-linear convection parameter.

This paper aims to renew interest on mixed thermal convection research and to emphasize three issues that arise from the present analysis: (i) a clear definition of the reference temperature in the Boussinesq approximation; (ii) a practical delimitation of the three convective modes, which are the forced convection (FC), mixed convection (MC) and natural (or free) convection (NC); (iii) and, finally, a uniform description of the set FC/MC/NC in the similarity framework. The planar case, for which analytical solutions are available, allows a detailed illustration of the answers here advanced to the above issues.

The demand for shape memory alloy (SMA) actuators for technical applications is steadily increasing; however SMA may have poor deactivation time due to relatively slow convective cooling. Convection heat transfer mechanism plays a critical role in the cooling process, where an increase of air circulation around the SMA actuator (i.e. forced convection) provides a significant improvement in deactivation time compared to the natural convection condition. The rate of convective heat transfer, either natural or forced, is measured by the convection heat transfer coefficient, which may be difficult to predict theoretically due to the numerous dependent variables. In this work, a study of free convective cooling of linear SMAactuators was conducted under various ambient temperatures to experimentally determine the convective heat transfer coefficient. A finite difference equation (FDE) was developed to simulate SMA response, and calibrated with the experimental data to obtain the unknown convectiveheat transfer coefficient, h. These coefficients are then compared with the available theoretical equations, and it was found that Eisakhaniet. almodel provides good agreement with the Experiment-FDE calibrated results. Therefore, FDE is reasonably useful to estimate the convective heat transfer coefficient of SMA actuator experiments under various conditions, with a few identified limitations (e.g. exclusion of other associative heat transfer factors).

Experimental results on free convection in a vertical annulus filled with a saturated porous medium are reported for height-to-gap ratios of 1.46, 1 and 0.545, and radius ratio of 5.338. In these experiments, the inner and outer walls are maintained at constant temperatures. The use of several fluid–solid combinations indicates a divergence in the Nusselt-number–Rayleigh-number relation, as also reported by previous investigators for horizontal layers and vertical cavities. The reason for this divergence is the use of the stagnant thermal conductivity of the fluid-filled solid matrix. A simple model is presented to obtain an effective thermal conductivity as a function of the convective state, and thereby eliminate the aforementioned divergence. A reasonable agreement between experimentally and theoretically determined Nusselt numbers is then achieved for the present and previous experimental results. It is thus concluded that a unique relationship exists between the Nusselt and Rayleigh numbers unless Darcy's law is inapplicable. The factors that influence the breakdown of Darcian behaviour are characterized and their effects on heat-transfer rates are explained. It is observed that, once the relation between the Nusselt and Rayleigh numbers branches out from that obtained via the mathematical formulation based on Darcy's law, its slope approaches that for a fluid-filled enclosure of the same geometry when the Rayleigh number is large enough. An iterative scheme is also presented for estimation of effective thermal conductivity of a saturated porous medium by using the existing results for overall heat transfer.

Objectives: The purposes of this work are to investigate the free convective heat transfer in an axis-symmetric open-ended cavity heated from below and to propose useful correlations of Nusselt number. Methods: The governing equations that model the fluid flow and the temperature field are solved using a control volume-based finite differences method. Under steady state condition, the natural convective flow is considered to be laminar, incompressible and axisymmetric. The Boussinesq approximation with constant thermophysical properties is adopted. Numerical experimentations are performed to deduce the optimum sizes of the calculation domain and the mesh grid. Findings: the obtained results indicate that when Rayleigh number (Ra) and aspect ratio (A) are low the heat transfer is weak and mainly conductive. The increase of Ra and A enhances the convective heat transfer mode thereby the heat transfer is ameliorated. Unlike the Rayleigh Bénard convection, the transition from conduction to convection produces at critical value of Rayleigh number (Rac) that is variable dependent on A. Novelty: To the best of authors knowledge, the formula of (Rac) elaborated in this work for the studied cavity is the first attempt. As well, correlation of Nusselt numbers (Nu) for the cold upper plate in terms of Ra and A is performed. Comparisons between Nu at the lower plate given in previous work and Nusselt number at the upper plate is conducted. Keywords: free convection; circular plates; Nusselt number correlations; open ended cavity; critical Rayleigh number

Pressurized water reactor nuclear plants, currently under construction, have been designed with passive containment cooling systems. Turbulent, natural-convective condensation, with high non-condensable mass fraction, on the walls of the containment vessel is a primary heat transfer mechanism in these new plant designs. A number of studies have been completed over the past two decades to justify use of the heat and mass transfer analogy for this scenario. A majority of these studies are founded upon natural-convective heat transfer correlations and apply a diffusion layer model to couple heat and mass transfer. Reasonable success in predicting experimental trends for vertical surfaces has been achieved when correction factors are applied. The corrections are attributed to mass transfer suction, film waviness or mist formation, even though little experimental evidence exists to justify these claims. This work examines the influence of film waves and mass transfer suction on the turbulent, natural-convective condensing flow with non-condensable gas present. Testing was conducted using 0.457 m x 2.13 m and a 0.914 m x 2.13 m condensing surfaces suspended in a large pressure vessel. The test surfaces could be rotated from vertical to horizontal to examine the inclination angle effect. The test facility implements relatively high accuracy calorimetric and condensate mass flow measurements to validate the measured heat and mass transfer rates. Test results show that application of the Bayley (1955) and Al-Arabi and Sakr (1988) heat transfer correlations using the heat and mass transfer analogy is appropriate for conditions in which the liquid film remains laminar. For transitional and wavy film flows, a clear augmentation in heat transfer was observed due to disruption of the gas layer by film waves. This result has implications for the scalability of existing correlations. A new correlation is proposed and results compared to several other datasets.

A parallel numerical method has been implemented for solving the Navier Stokes equations on Cartesian and non-orthogonal meshes. To ensure the accuracy of the code first, second and third order differencing schemes, with and without flux-limiters, have been implemented and tested. The most computationally expensive task in the code is the solution of linear equations, and a number of linear solvers have been tested to determine the most efficient. Krylov space, incomplete factorisation, and other iterative and direct solvers from the literature have been implemented, and have been compared with a novel black-box multigrid linear solver that has been developed both as a solver and as a preconditioner for the Krylov space methods. To further reduce execution time the code was parallelised, after a series of experiments comparing the suitability of different parallelisation techniques and computer architectures for the Navier Stokes solver. The code has been applied to the solution of two classes of problem. Two natural convection flows were studied, with an initial study of two dimensional Rayleigh Benard convection being followed by a study of a transient three dimensional flow, in both cases the results being compared with experiment. The second class of problems modelled were free surface flows. A two dimensional free surface driven cavity, and a two dimensional flume flow were modelled, the latter being compared with analytic theory. Finally a three dimensional ship flow was modelled, with the flow about a Wigley hull being simulated for a range of Reynolds and Froude numbers.

Thesis (Ph. D.)--University of Sydney, 2000.
Title from title screen (viewed Apr. 23, 2008). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the Dept. of Mechanical Engineering, Faculty of Engineering. Includes bibliography. Also available in print form.

High Rayleigh number(Ra) turbulent free convection has many unresolved issues related to the phenomenology behind the flux scaling, the presence of a mean wind and its effects, exponential probability distribution functions, the Prandtl number dependence and the nature of near wall structures. Few studies have been conducted in the high Prandtl number regime and the understanding of near wall coherent structures is inadequate for $Ra > 10^9$. The present thesis deals with the results of investigations conducted on high Rayleigh number turbulent free convection in the high Schmidt number(Sc) regime, focusing on the role of near wall coherent structures. We use a new method of driving the convection using concentration difference of NaCl across a horizontal membrane between two tanks to achieve high Ra utilising the low molecular diffusivity of NaCl. The near wall structures are visualised by planar laser induced fluorescence. Flux is estimated from transient measurement of concentration in the top tank by a conductivity probe. Experiments are conducted in tanks of $15\times15\times 23$cm (aspect ratio,AR = 0.65) and $10\times10\times 23$cm (AR = 0.435). Two membranes of 0.45$\mu$ and 35$\mu$ mean pore size were used. For the fine membrane (and for the coarse membrane at low driving potentials), the transport across the partition becomes diffusion dominated, while the transport above and below the partition becomes similar to unsteady non penetrative turbulent free convection above flat horizontal surfaces (Figure~\ref{fig:schem}(A)). In this type of convection, the flux scaled as $q\sim \Delta C_w ^{4/3}$,where $\Delta C_w$ is the near wall concentration difference, similar to that in Rayleigh - B\'nard convection . Hence, we are able to study turbulent free convection over horizontal surfaces in the Rayleigh Number range of $\sim 10^- 10 ^$ at Schmidt number of 602, focusing on the nature and role of near wall coherent structures. To our knowledge, this is the first study showing clear images of near wall structures in high Rayleigh Number - high Schmidt number turbulent free convection. We observe a weak flow across the membrane in the case of the coarser membrane at higher driving potentials (Figure \ref(B)). The effect of this through flow on the flux and the near wall structures is also investigated. In both the types of convection the near wall structure shows patterns formed by sheet plumes, the common properties of these patterns are also investigated. The major outcomes in the above three areas of the thesis can be summarised as follows \subsection* \label \subsubsection* \label The non-dimensional flux was similar to that reported by Goldstein\cite at Sc of 2750. Visualisations show that the near wall coherent structures are line plumes. Depending on the Rayleigh number and the Aspect ratio, different types of large scale flow cells which are driven by plume columns are observed. Multiple large scale flow cells are observed for AR = 0.65 and a single large scale flow for AR= 0.435. The large scale flow create a near wall mean shear, which is seen to vary across the cross section. The orientation of the large scale flow is seen to change at a time scale much larger than the time scale of one large scale circulation The near wall structures show interaction of the large scale flow with the line plumes. The plumes are initiated as points and then gets elongated along the mean shear direction in areas of larger mean shear. In areas of low mean shear, the plumes are initiated as points but gets elongated in directions decided by the flow induced by the adjacent plumes. The effect of near wall mean shear is to align the plumes and reduce their lateral movement and merging. The time scale for the merger of the near wall line plumes is an order smaller than the time scale of the one large scale circulation. With increase in Rayleigh number, plumes become more closely and regularly spaced. We propose that the near wall boundary layers in high Rayleigh number turbulent free convection are laminar natural convection boundary layers. The above proposition is verified by a near wall model, similar to the one proposed by \cite{tjfm}, based on the similarity solutions of laminar natural convection boundary layer equations as Pr$\rightarrow\infty$. The model prediction of the non dimensional mean plume spacing $Ra_\lambda^~=~\lambda /Z_w~=~91.7$ - where $Ra_\lambda$ is the Rayleigh number based on the plume spacing $\lambda$, and $Z_w$ is a near wall length scale for turbulent free convection - matches the experimental measurements. Therefore, higher driving potentials, resulting in higher flux, give rise to lower mean plume spacing so that $\lambda \Delta C_w^$ or $\lambda q^$ is a constant for a given fluid. We also show that the laminar boundary layer assumption is consistent with the flux scaling obtained from integral relations. Integral equations for the Nusselt number(Nu) from the scalar variance equations for unsteady non penetrative convection are derived. Estimating the boundary layer dissipation using laminar natural convection boundary layers and using the mean plume spacing relation, we obtain $Nu\sim Ra^$ when the boundary layer scalar dissipation is only considered. The contribution of bulk dissipation is found to be a small perturbation on the dominant 1/3 scaling, the effect of which is to reduce the effective scaling exponent. In the appendix to the thesis, continuing the above line of reasoning, we conduct an exploratory re-analysis (for $Pr\sim 1$) of the Grossman and Lohse's\cite scaling theory for turbulent Rayleigh - B\'enard convection. We replace the Blasius boundary layer assumption of the theory with a pair of externally forced laminar natural convection boundary layers per plume. Integral equations of the externally forced laminar natural convection boundary layer show that the mixed convection boundary layer thickness is decided by a $5^{th}$ order algebraic equation, which asymptotes to the laminar natural convection boundary layer for zero mean wind and to Blasius boundary layer at large mean winds. \subsubsection*{Effect of wall normal flow on flux and near wall structures} \label{sec:effect-wall-normal} For experiments with the coarser($35\mu$) membrane, we observe three regimes viz. the strong through flow regime (Figure~\ref{fig:schem}(b)), the diffusion regime (Figure \ref{fig:schem}(a)), and a transition regime between the above two regimes that we term as the weak through flow regime. At higher driving potentials, only half the area above the coarser membrane is covered by plumes, with the other half having plumes below the membrane. A wall normal through flow driven by impingement of the large scale flow is inferred to be the cause of this (Figure \ref{fig:schem}(b)). In this strong through flow regime, only a single large scale flow circulation cell oriented along the diagonal or parallel to the walls is detected. The plume structure is more dendritic than the no through flow case. The flux scales as $\Delta C_w^n$, with $7/3\leq n\leq 3$ and is about four times that observed with the fine membrane. The phenomenology of a flow across the membrane driven by the impingement of the large scale flow of strength $W_*$, the Deardorff velocity scale, explains the cubic scaling. We find the surprising result that the non-dimensional flux is smaller than that in the no through flow case for similar parameters. The mean plume spacings in the strong through flow regime are larger and show a different Rayleigh number dependence vis-a-vis the no through flow case. Using integral analysis, an expression for the boundary layer thickness is derived for high Schmidt number laminar natural convection boundary layer with a normal velocity at the wall. (Also, solutions to the integral equations are obtained for the $Sc\sim 1$ case, which are given as an Appendix.) Assuming the gravitational stability condition to hold true, we show that the plume spacing in the high Schmidt number strong through flow regime is proportional to $\sqrt{Z_w\,Z{_{v_i}}}$, where $Z{_{v_i}}$ is a length scale from the through flow velocity. This inference is fairly supported by the plume spacing measurements At lower driving potentials corresponding to the transition regime, the whole membrane surface is seen to be covered by plumes and the flux scaled as $\Delta C_w^{4/3}$. The non-dimensional flux is about the same as in turbulent free convection over flat surfaces if $\frac{1}{2}\Delta C $ is assumed to occur on one side of the membrane. This is expected to occur in the area averaged sense with different parts of the membrane having predominance of diffusion or through flow dominant transport. At very low driving potentials corresponding to the diffusion regime, the diffusion corrected non dimensional flux match the turbulent free convection values, implying a similar phenomena as in the fine membrane. \subsubsection*{Universal probability distribution of near wall structures} \label{sec:univ-prob-distr} We discover that the probability distribution function of the plume spacings show a standard log normal distribution, invariant of the presence or the absence of wall normal through flow and at all the Rayleigh numbers and aspect ratios investigated. These plume structures showed the same underlying multifractal spectrum of singularities in all these cases. As the multifractal curve indirectly represents the processes by which these structures are formed, we conclude that the plume structures are created by a common generating mechanism involving nucleation at points, growth along lines and then merging, influenced by the external mean shear. Inferring from the thermodynamic analogy of multifractal analysis, we hypothesise that the near wall plume structure in turbulent free convection might be formed so that the entropy of the structure is maximised within the given constraints.

The steady-state natural convection heat transfer from vertical rectangular fins extending perpendicularly from vertical rectangular base was investigated experimentally. The effects of geometric parameters and base-to-ambient temperature difference on the heat transfer performance of fin arrays were observed and the optimum fin separation values were determined. Two similar experimental set-ups were employed during experiments in order to take measurements from 30 different fin configurations having fin lengths of 250 mm and 340 mm. Fin thickness was maintained fixed at 3 mm. Fin height and fin spacing were varied from 5 mm to 25 mm and 5.75 mm to 85.5 mm, respectively. 5 heat inputs ranging from 25 W to 125 W were supplied for all fin configurations, and hence, the base and the ambient temperatures were measured in order to evaluate the heat transfer rate from fin arrays. The results of experiments have shown that the convection heat transfer rate from fin arrays depends on all geometric parameters and base-to-ambient temperature difference. The effect of these parameters on optimum fin spacing was also examined, and it was realized that for a given base-to-ambient temperature difference, an optimum fin spacing value which maximizes the convective heat transfer rate from the fin array is available for every fin height. The results indicated that the optimum fin spacings are between 8.8 mm and 14.7 mm, for the fin arrays employed in this work. Using the experimental results of present study and experimental results in available literature [2,3,9,10,11,12,14], a correlation for optimum fin spacing at a given fin length and base-to-ambient temperature difference was obtained as a result of scale analysis.

Experimental observations indicate the presence of attached, gravity induced, horizontal buoyant currents above large area fires. Their driving mechanism is indirect and resembles the one observed above heated horizontal plates. Classic plume modelling is satisfactory for providing information for the flow far from the source. In dealing with large areas and directing attention to the flow close to the source, the classic plume theory should fail because the radial pressure gradient that is responsible for the driving of the flow is squeezed in the long and thin classic plume assumption. For this we propose a new plume structure for the description of the buoyant flow above a circular region of large radius L as “The flow field must be divided into three regions. A region where the flow is predominantly horizontal and attached to the surface, a transition region from horizontal to vertical where separation of the attached current takes place, and a region where vertical flow is established and classic plume theory can be applied”. A model for the description of the gross properties of the horizontal currents is developed under the term “horizontal plume”. The modified Richardson number for the horizontal plume a, being analogous to the radius of the large area, is studied asymptotically in the limit a → ∞ and second order uniformly valid semi-analytical solutions are obtained. The hot plate experiment was set up in order to test the model and facilitate its improvement. A chapter is dedicated to the data analysis coming from thermocouple readings and visualisation of the flow using particle image velocimetry.In the remainder of this thesis two classic problems of laminar natural convection are revisited. That of the first order laminar boundary layer above an isothermal circular plate of radius a and the first order laminar boundary layer above the semi- infinite plate inclined to horizontal. In both cases allowances to variable property effects were made through the introduction of a nondimensional parameter λT, with its value set to zero implying the assumption of the Boussinesq approximation. For the circular plate, fourth order series solutions were obtained valid at the edge of the plate where the effects of λT and Prandtl number Pr are studied. Furthermore a finite difference scheme for the numerical solution of the nonsimilar partial integro- differential equation was developed using the Keller Box method and compared with results obtained from the commercial finite element software COMSOL Multiphysics 3.5a. For the semi-infinite plate, fourth order series approximations valid at the edge of the plate were obtained, while an extensive analysis for the effect of λT, Pr and inclination parameter σ was performed on the flow. Positions of the separation points when the inclination is negative (σ < 0) as a function of Pr and λT were recovered.

Orientador: Vicente Luiz Scalon
Banca: Helio Aparecido Navarro
Banca: Sergio Rodrigues Fontes
Resumo: A fluidodinâmica computacinal (CFD) tem sido utilizada, estudadda e implementada ao longa das duas últimas décadas na solução dos mais diversos problemas de engenharia. O princípio básico desta ciência é a aplicação de métodos numéricos em problemas que envolvam mecânica dos fluidos. Nesse contexto, este trabalho utiliza essa técnica para analisar o comportamento de um fluido incompreensível, que se encontra numa cavidade cilíndrica fechada onde as faces inferior e superior são adiabáticas e as superfícies laterais se encontram em diferentes temperaturas. Os perfis de velocidade e temperatura resultantes - ocasionados pela convecção natural - serão avaliados em todo o domínio do problema. Existe uma série de técnicas para a solução de problemas envolvendo escoamentos, sendo as mais comuns as que se utilizam do "Esquema de Passo Fracionado" proposto por Chorin no final da década de 60. Dentre as diversas soluções que se utilizam desta técnica, este trabalho optou pelo uso do método das características e do algoritmo CBS de solução proposto por Zienkiewicz e Codina (1995). Para a implementação do algoritmo de solução do problema proposto foi realizada uma discretização geral através do método dos elementos finitos usando-se de uma malha formada por elementos bilineares. A solução foi obtida a partir de um ambiente matemático adequado, a GNU-Octave (2008). Os resultados foram analisados para diferentes razões de curvatura, números de Rayleigh e métodos de solução, sendo plotados para as suas diversas variáveis buscando descrever o comportamento do fenônemo
Abstract: The Computational Fluid Dynamics (CFD) has been used, studied and performed through the last two decades to solve the series of problems in Engineering. The most basic aim of this science is the appliance of numerical methods in cases that envolve fluid mechanics. In this context, this work uses this technic to analyze the behaviour of an incompressible fluid, which is found in a closed cylindrical cavity, a place where the inferior and superior surfaces are adiabatic and the lateral surfaces are shown in different temperatures. The resultant profiles of speed and temperature - induced by the free convection - are going to be appraised in all the dominion of the problem. There is a set of technics to solve the problems which involve the drainage, but the most usual are those which use the techic "Fractional Step Method" offered by Chorin in the final of 60s. Among the several solutions that are solved through this technic, this research used the characteristics method and of the CBS algorthm, offered by Zienkiewicz e Codina (1995). For the implementation of the algorithm, it was realized a general discretization through the finite elements method, making use of a loop formed by bilinear elements. The resolution was obtained from an adequated mathematical ambient, the GNU-Octave (2008). The results were analysed for different curvature ratios, Rayleigh numbers and methods of solution, being plotted for its different variables searching to describe the behavior of the phenomenon
Mestre

Orientador: Vicente Luiz Scalon
Banca: Ivan De Domenico Valarelli
Banca: Carlos Alberto Carrasco Altemani
Resumo: Com a crise energética recente, houve uma nova conscientização da necessidade de utilização mais racional da energia. Desta feita, uma série de pesquisas com fontes alternativas de energia, que vinham sendo preteridos em função da impressão que a crise energética do início da década de 1970 havia passado, tem ganho nova força. Dentre todas as alternativas para aproveitamento de energia solar, uma das mais utilizadas são os chamados "sistemas domésticos de aquecimento de água". Este tipo de sistema, entretanto, ainda é complexo, constituído de uma série de dutos e conexões entre coletor e tanque armazenador, que contribuem para o elevado custo destes dispositivos. Uma alternativa para otimizar o custo final é o uso dos sistemas solar integrados coletor-tanque (ICS). Neste trabalho, foi avaliado o processo de movimentação natural do fluido em uma das geometrias mais comuns de sistemas deste tipo: a trapezoidal. Foi aplicada a condição de fluxo de calor constante na face inclinada para avaliação... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: The recent energy crisis has developed a new conscience for necessity of rational energy use. Several works treating about renewable energy was stopped in past based in a false idea that the 1970's energy crisis was finished. Nowadays, these works have been retaken with the large use of solar energy in the Solar Domestic Hot Water Systems. However, this device is quite complex and has several components like pipes and fittings coupling solar collectors and storage tanks. This characteristic makes it an expensive system and bring difficulties for his large use. An alternative to turn it cheaper is the construction of a device with solar collector and storage tank integrated in one single component (ICS). In this work was done an evaluation of free convection process in a common geometry of this device: the trapezoidal shape. For this analysis, a constant heat flux condition was applied to the inclined face for evaluation of free convection process. Numerical results... (Complete abstract click electronic access below)
Mestre

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A fluidodinâmica computacinal (CFD) tem sido utilizada, estudadda e implementada ao longa das duas últimas décadas na solução dos mais diversos problemas de engenharia. O princípio básico desta ciência é a aplicação de métodos numéricos em problemas que envolvam mecânica dos fluidos. Nesse contexto, este trabalho utiliza essa técnica para analisar o comportamento de um fluido incompreensível, que se encontra numa cavidade cilíndrica fechada onde as faces inferior e superior são adiabáticas e as superfícies laterais se encontram em diferentes temperaturas. Os perfis de velocidade e temperatura resultantes - ocasionados pela convecção natural - serão avaliados em todo o domínio do problema. Existe uma série de técnicas para a solução de problemas envolvendo escoamentos, sendo as mais comuns as que se utilizam do Esquema de Passo Fracionado proposto por Chorin no final da década de 60. Dentre as diversas soluções que se utilizam desta técnica, este trabalho optou pelo uso do método das características e do algoritmo CBS de solução proposto por Zienkiewicz e Codina (1995). Para a implementação do algoritmo de solução do problema proposto foi realizada uma discretização geral através do método dos elementos finitos usando-se de uma malha formada por elementos bilineares. A solução foi obtida a partir de um ambiente matemático adequado, a GNU-Octave (2008). Os resultados foram analisados para diferentes razões de curvatura, números de Rayleigh e métodos de solução, sendo plotados para as suas diversas variáveis buscando descrever o comportamento do fenônemo
The Computational Fluid Dynamics (CFD) has been used, studied and performed through the last two decades to solve the series of problems in Engineering. The most basic aim of this science is the appliance of numerical methods in cases that envolve fluid mechanics. In this context, this work uses this technic to analyze the behaviour of an incompressible fluid, which is found in a closed cylindrical cavity, a place where the inferior and superior surfaces are adiabatic and the lateral surfaces are shown in different temperatures. The resultant profiles of speed and temperature - induced by the free convection - are going to be appraised in all the dominion of the problem. There is a set of technics to solve the problems which involve the drainage, but the most usual are those which use the techic Fractional Step Method offered by Chorin in the final of 60s. Among the several solutions that are solved through this technic, this research used the characteristics method and of the CBS algorthm, offered by Zienkiewicz e Codina (1995). For the implementation of the algorithm, it was realized a general discretization through the finite elements method, making use of a loop formed by bilinear elements. The resolution was obtained from an adequated mathematical ambient, the GNU-Octave (2008). The results were analysed for different curvature ratios, Rayleigh numbers and methods of solution, being plotted for its different variables searching to describe the behavior of the phenomenon

Circuitos de convecção natural ou sistemas de circulação natural são empregados em diversas áreas da engenharia. Reatores nucleares refrigerados a água utilizam circuitos de circulação natural como método passivo de seguranca. Em situações críticas, sem qualquer controle externo, o sistema permanece em segurança por suas próprias características de funcionamento (intrinsecamente seguro). O trabalho proposto consiste em estudar numericamente o circuito de circulação natural de água, localizado no Instituto de Pesquisas Energéticas e Nucleares / Comissão Nacional de Energia Nuclear em São Paulo, por meio do uso de modelos matemáticos, objetivando determinar o padrão do escoamento em condições sem mudança de fase líquido-vapor. A comparação dos resultados de temperatura obtidos por cada um dos modelos de turbulência aos pontos instrumentados no circuito experimental, na condição transitória, revelou desvios significativos nas respostas do modelo de zero equação. Desvios intermediário foram observados nos modelos de transporte da viscosidade turbulenta (EVTE), k - ω, SST e SSG e resultados melhores foram vericados nos modelos k - ε e DES (com significativa superioridade do primeiro modelo).
Natural circulation loops apply to many engineering applications such as: water heating solar energy system (thermo-siphons), thermal management of electrical components (voltage converter), geothermal energy, nuclear reactors, etc. In pressurized water nuclear reactors, known as PWR\'s, the natural circulation loops are employed to ensure passive safety. In critical situations, the heat transfer will occur only by natural convection, without any external control or mechanical devices. This feature is desired and has been considered in modern nuclear reactor projects. This work consists of a numerical study of the natural circulation loop, located at the Instituto de Pesquisas Energeticas e Nucleares / Comissão Nacional de Energia Nuclear in São Paulo, Brazil, in order to establish the ow pattern in single phase conditions. The comparison of numerical results to experiments in transient condition revealed significant deviations for the Zero Equation turbulence model. Intermediate deviations for the Eddy Viscosity Turbulence Equation (EVTE), k - ω, SST e SSG models. And the best results are obtained by the k - ε e DES models (with better results for the k - ε model).

Thus far, we have implicitly assumed that chemical species move only by diffusion. In fact, a number of external forces can affect mass transport, with significant and interesting effects on chemical waves. In this chapter, we consider three types of fields: gravitational, electric, and magnetic. These always exist, though their magnitudes are usually very small. As we shall see, small fields can have surprisingly large effects. Gravity is a ubiquitous force that all living and chemical systems experience. People largely ignored the profound effect that living with gravity has upon us until humans spent significant time in space. Bone loss and changes to the vascular systems of astronauts (Nicogossian et al., 1994) are still not well understood. Eliminating the effects of gravity is not easy. Enormous cost and effort have been expended to simulate gravity-free conditions in drop towers, parabolic airplane flights, or in Earth orbit. A simple calculation seems to suggest that gravity should have negligible influence on chemical reactions. The mass of a molecule is on the order of 10-26 kg, which translates into a gravitational force of about 10-25 N. We can compare this with the force of attraction between the electron and the proton in a hydrogen atom, which is of the order 10-8 N. Even allowing for shielding effects, the electrostatic forces that cause chemical bonds to be made and broken will always be many orders of magnitude stronger than gravitational forces. So gravity does not affect the fundamental atomic and molecular interactions, but it can drastically alter the macroscopic transport of heat and matter through convection, or macroscopic fluid motion. Natural convection is the movement of fluid as the result of differences in density, so that denser fluid sinks and less dense fluid rises. This motion is resisted by the viscosity of the medium, which acts like friction does in slowing the motion of solids. The study of convection is an entire area of physics, and we will touch only on a few aspects. The reader is referred to some excellent texts on the subject (Tritton, 1988; Turner, 1979).

Vortex methods for simulating natural convection of an ideal gas in unbounded two-dimensional domains are presented. In particular, the redistribution method for diffusion is extended to enable simulation of nonlinear diffusion of an ideal gas in isobaric conditions encountered in unbounded low-Mach number flows. We also address the problem of handling source terms in grid-free vortex methods and propose a fast, accurate, and physically motivated method for solving the associated inverse problems. Examples include generation of baroclinic vorticity in non-reacting buoyancy driven flows, and in addition, generation of internal energy and species in buoyant reacting flows. Accuracy and speed of the proposed algorithms for nonlinear diffusion and vorticity generation are investigated separately. Simulations of natural convection of a “thermal patch” for Grashof number ranging from to 1562.5 to 25000 are presented.

The present study is concerned with natural convection ventilation in a two dimensional fully open enclosure (cavity) with thermally stratified ambient for both transient and steady-state flow. The left hand vertical wall of the enclosure is heated and the right hand facing boundary is open, with the top and bottom boundaries insulated. The numerical solutions will be obtained by solving the Navier-Stokes equations and the temperature transport equation on a non-staggered grid using an unsteady second-order finite-volume scheme with a pressure correction equation used to simultaneously provide an update for the pressure field and enforce the divergence free condition. Results will be presented for Rayleigh numbers in the range 1 × 105 to 1 × 1010 with Prandtl numbers in the range 0.2 to 1.0. It will be shown that the flow transits from steady to unsteady, at full development, with increasing Rayleigh number for Pr <= 1.0, as observed for the similar closed enclosure flow. For higher Prandtl numbers the flow is steady at full development for the full range of Rayleigh numbers considered, again as for the similar fully closed enclosure. Streamline and temperature contour plots will be presented to illustrate the basic flow behaviours and to demonstrate the effect of the Prandtl number.

Introduction of suspended nanoparticles into a base liquid will remarkably enhance energy transport process of the original liquid, which has been proved by a few experiments carried out by many authors. Irregular displacement and random distribution of the suspended nanoparticles as well as the interaction between nanoparticles and the adjacent liquid molecules make the modeling of flow and heat transfer in nanofluids very difficult. In this paper, a Lattice Boltzmann (LB) model for nanofluids has been developed. The external and internal forces, such as buoyancy, gravity, drag and Brownian force, and the mechanical and thermal interactions among the nanoparticles and their impact on the equilibrium velocity have been introduced. Along with a Gauss white noise model for Brownian motion, the double-distribution-function (DDF) approach, which treats temperature as a passive diffusing scalar and simulates it by a density-independent distribution function, was used to simulate free convection in nanofluids. By this model, the possible sedimentation and fluctuation of nanoparticles, and their impacts on the free convection in nanofluids have been observed and studied. A correlation formula for Nusselt number which characterized by properties of nanofluids has been obtained. The comparison of characteristics of natural convections between the nanofluids and its corresponding pure liquid has been done, and the possible mechanisms which enhance the heat transfer of natural convection in nanofluids have been discussed and revealed. This paper was also originally published as part of the Proceedings of the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems.

Abstract Convection in a horizontal, doubly layered porous medium has been investigated numerically. Both natural and mixed convection are considered for steady state heating from above. For natural convection, the effects of Rayleigh number on the Nusselt number are investigated. For mixed convection where a uniform flow enters at the side wall, the effects of both Rayleigh number and Peclet number are studied. The effects of the thickness of one layer as well as the length of the heated zone are also examined. Further, the permeability and the thermal conductivity ratios of the lower layer to the upper layer are varied from 0.1 to 100.0 and from 0.2 to 5.0, respectively.

Nanofluids are suspensions or colloids produced by dispersing nanoparticles in base fluids like water, oil or organic fluids, so as to improve their thermo-physical properties. Investigations reported in recent times have shown that the addition of nanoparticles significantly influence the thermophysical properties, such as the thermal conductivity, viscosity, specific heat and density of base fluids. The convective heat transfer coefficient also has shown anomalous variations, compared to those encountered in the base fluids. By careful selection of the parameters such as the concentration and the particle size, it has been possible to produce nanofluids with various properties engineered depending on the requirement. A mineral oil–boron nitride nanofluid system, where an increased thermal conductivity and a reduced electrical conductivity has been observed, is investigated in the present work to evaluate its heat transfer performance under natural convection. The modified mineral oil is produced by chemically dispersing boron nitride nanoparticles utilizing a one step method to obtain a stable suspension. The mineral oil based nanofluid is investigated under transient free convection heat transfer, by observing the temperature-time response of a lumped parameter system. The experimental study is used to estimate the time-dependent convective heat transfer coefficient. Comparisons are made with the base fluid, so that the enhancement in the heat transfer coefficient under natural convection situation can be estimated.

The numerical investigation of laminar natural convection of viscoplastic fluid in a two dimensional square enclosure has been reported in this work. The enclosed fluid is subjected to partial bi-heating from the bottom wall and symmetrical cooling from the sides under steady condition. Yield stress fluid has been heated through two heaters symmetrically placed on the either side of the centre of the bottom wall of the square enclosure. The viscoplastic fluid is the one which requires a minimum critical stress called yield stress to flow otherwise behave as a solid, have been modeled with Herschel–Bulkley model. Such fluids have significant technological relevance due to its wide application ranging from cosmetics products, food processing industries, pharmaceuticals to natural occurring like flow of debris and lava. The solution of governing partial differential equations has been approached using finite volume based formulation. Non uniform set of grid has been used. The effects of yield stress, heat flux, and power law index on the flow and thermal characteristics of the free convection of Herschel-Bulkley fluids have been studied for a particular value of Prandtl number. The flow and thermal fields have been investigated for the following ranges of conditions: Rayleigh number varies between 103 and 106 whereas power law index ranges from 0 to 1. The heat transfer characteristic has been depicted with the help of isotherms and the flow field has been illustrated by streamlines. The onset of convection is substantially delayed due to presence of yield stress of the fluid. This results in enhanced critical Rayleigh number for onset of convection. With increase in the Yield number in turn yield stress, results in the weakening of heat transfer through convection and at a particular relatively higher value of Yield number the heat transfer is solely taken place by conduction mode. Due to the symmetry in both heating and boundary conditions, the obtained isotherms and streamlines of the right half are symmetrical to the left half of the square enclosure. The conductive mode of heat transfer becomes dominated by increasing yield stress and reducing Ra and vice versa. The simultaneous presence of yielded and unyielded region presents an interesting pattern in the convection zone. Furthermore, it can be seen that rise in heat flux, in turn Ra, promotes the buoyancy driven circulation of viscoplastic fluid i.e. enhances natural convective heat transfer. In addition, the effect of power law index has been investigated. Power law index has little effect on thermal distribution and flow field.

In this paper transient natural convection in a vertical convergent channel with or without saturated porous medium is studied numerically. The investigation is carried out in laminar, two dimensional regime and employing the Brinkman-Forchheimer-extended Darcy model. The physical domain consists of two non-parallel plates which form a convergent channel. Both plates are heated at uniform heat flux. The solutions are achieved using the commercial code FLUENT. A finite-extension computational domain is employed to simulate the free-stream condition. The results are obtained for different convergence angles, for 0° to 5°, and porosity coefficient (0.4, 0.6 and 0.9), a channel aspect ratio equal to 10, a Rayleigh number equal to 104 and a Darcy number equal to 0.01. The dimensionless results are reported in terms of average and maximum wall temperatures, average Nusselt number as a function of time and at steady state wall temperature, local Nusselt number and temperature and stream function fields. The cases with porous medium in the channel shows that in conductive regime dominant, at initial time, average and maximum wall temperatures are lower than the case without porous medium in the channel. For the convective regime dominant, the lowest average and maximum wall temperatures are attained for the case without porour medium in the channel. At steady state, in the inlet zone the cases with porous medium present wall temperature lower than the no porous case. In the other part of the channel the opposite behaviour is detected.

Natural convection in rectangular enclosures is found in many real-world engineering applications. Included in these applications are the energy efficient design of buildings, operation and safety of nuclear reactors, solar collector design, passive energy storage, heat transfer across multi-pane windows, thermo-electric refrigeration and heating devices, and the design-for-mitigation of optical distortion in large-scale laser systems. A common industrial application of natural convection is free air cooling without the aid of fans and can happen on small scales such as computer chips to large scale process equipment. The enclosure phenomena can loosely be organized into two large classes: (1) horizontal enclosures heated from below and (2) vertical enclosures heated from the side. In addition to temperature gradient convection strength within the enclosure can vary due to the existence of heat sources with different strength. Numerical simulations are conducted for free convective flow of air with or without internal heat generation in two-dimensional rectangular enclosures of different aspect ratios. The objective of this numerical study is to investigate the effects of external temperature gradient, internal heat generation and aspect ratio (AR) of enclosure (ratio of the length of the isothermal walls to their separation distance), in free convective laminar flow of a fluid. Two-dimensional rectangular enclosures of different aspect ratio (1, 2, 4, 6, 8, and 10) with two adiabatic side walls and isothermal bottom (hot) and top (cold) walls are considered for the first configuration. Whereas for the second configuration, two adiabatic top and bottom walls, isothermal left side (cold) and right side (hot) walls are considered. Two principal parameters considered for the flow of fluid are the external Rayleigh number, RaE, which represents the effect due to the differential heating of the isothermal walls, and the internal Rayleigh number, RaI, which represents the strength of the internal heat generation. The effect of external temperature gradient and aspect ratio on natural convection has been observed by varying the value of external Rayleigh number (RaE) equal to 2×104, 2×105, and 2×106 and keeping the internal Rayleigh number constant (RaI = 2×105). Similarly, the effect of internal heat generation and aspect ratio on natural convection has been observed by varying the value of internal Rayleigh number (RaI) equal to 2×104, 2×105, and 2×106 and keeping the external Rayleigh number constant (RaE = 2×105). Significant changes in flow patterns and isotherms have been observed for all cases. Also the variation of average heat flux ratio (convective heat flux/corresponding conduction heat flux) along the hot and cold walls, and the convection strength have been calculated for all cases. It is found that the aspect ratio has a significant effect in fluid flow and heat transfer in the enclosures. The average heat flux ratio and the strength of convection increase with aspect ratio as the enclosure shape changes square (AR = 1) to shallow (AR > 1).