Convective flow and heat transfer in a tall porous cavity side-cooled with temperature profile (original) (raw)
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International Journal of Heat and Mass Transfer, 2007
In this paper natural convection flows in a square cavity filled with a porous matrix has been investigated numerically when the bottom wall is uniformly heated and vertical wall(s) are linearly heated whereas the top wall is well insulated. Darcy-Forchheimer model without the inertia term is used to simulate the momentum transfer in the porous medium. Penalty finite element method with bi-quadratic rectangular elements is used to solve the non-dimensional governing equations. Numerical results are presented for a range of parameters (Rayleigh number Ra, 10 3 6 Ra 6 10 6 , Darcy number Da, 10 À5 6 Da 6 10 À3 , and Prandtl number Pr, 0.2 6 Pr 6 100) in terms of stream functions and isotherm contours, and local and average Nusselt numbers.
NATURAL CONVECTION INDUCED BY VOLUMETRIC HEATING IN AN INCLINED POROUS CAVITY
Numerical and analytical studies are carried out to investigate natural convection in an inclined porous cavity filled with a volumetric heat source. Heat fluxes are imposed on the sidewalls to ensure a cooling process. The Darcy model is taken into account in the mathematical formulation of the problem. The density variation is modeled by Boussinesq approximation as the temperature values are limited. Numerical solutions are obtained for a wide range of governing parameters such as aspect ratio A, Rayleigh number R, inclination angle ϕ, and the dimensionless heat flux at the left active wall q L. The analytical solution is based on the parallel flow approximation and valid for A ≫ 1. The results elucidate an asymptotic tendency of the rate heat transfer with Rayleigh number. The normalized Nusselt number Nu L reach the maximum when ϕ = 80 deg and q L = 0.75. A good agreement between the analytical model and the numerical simulations is obtained in the case of a tall cavity.
International Journal of Heat and Mass Transfer, 2006
Natural convection flows in a square cavity filled with a porous matrix has been studied numerically using penalty finite element method for uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. Darcy-Forchheimer model is used to simulate the momentum transfer in the porous medium. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10 3 6 Ra 6 10 6 , Darcy number Da, 10 À5 6 Da 6 10 À3 , and Prandtl number Pr, 0.71 6 Pr 6 10) with respect to continuous and discontinuous thermal boundary conditions. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It has been found that the heat transfer is primarily due to conduction for Da 6 10 À5 irrespective of Ra and Pr. The conductive heat transfer regime as a function of Ra has also been reported for Da P 10 À4 . Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes the power law correlations between average Nusselt number and Rayleigh numbers are presented.
The conjugate natural convection heat transfer in a partially heated square porous enclosure had been studied numerically. The governing dimensionless equations are solved using COMSOL Multiphysics and Darcy model assumed to be used. The considering dimensionless parameters are modified Rayleigh number, finite wall thickness, thermal conductivity ratio and the heat source length. The results are presented in terms of streamlines, isotherms and local and average Nusselt number. The results indicate that; the heat transfer can be enhanced by increasing the modified Rayleigh number. When the heat source length increases, the local Nusselt number of fluid phase increases, while, a reverse behavior of the local Nusselt number along the heat source is found. As the Rayleigh number increase, the local Nusselt number for both fluid and solid phase increases, therefore, the heat transfer rate will be enhanced. On the other hand, when the thermal conductivity ratio increase, the local Nusselt number for the fluid phase increases, and the local Nusselt number along the heated wall decreases.
Natural convection in porous cavity with sinusoidal bottom wall temperature variation
International Communications in Heat and Mass Transfer, 2005
Numerical study of natural convection in a porous cavity is carried out in the present paper. Natural convection is induced when the bottom wall is heated and the top wall is cooled while the vertical walls are adiabatic. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value which is higher than the cold top wall temperature. The non-dimensional governing equations are derived based on the Darcy model. The effects of the amplitude of the bottom wall temperature variation and the heat source length on the natural convection in the cavity are investigated for Rayleigh number range 20-500. It is found that the average Nusselt number increases when the length of the heat source or the amplitude of the temperature variation increases. It is observed that the heat transfer per unit area of the heat source decreases by increasing the length of the heated segment. D
Natural Convection in an Inclined Porous Cavity with Spatial Sidewall Temperature Variations
Journal of Applied Mathematics, 2012
The natural convection in an inclined porous square cavity is investigated numerically. The left wall is assumed to have spatial sinusoidal temperature variations about a constant mean value, while the right wall is cooled. The horizontal walls are considered adiabatic. A finite difference method is used to solve numerically the nondimensional governing equations. The effects of the inclination angle of the cavity, the amplitude and wave numbers of the heated sidewall temperature variation on the natural convection in the cavity are studied. The maximum average Nusselt number occurs at different wave number. It also found that the inclination could influence the Nusselt number.
Computational Thermal Sciences: An International Journal, 2019
Numerical results of two-dimensional steady natural convection in a square cavity filled with porous medium by adopting a two-temperature model of heat transfer are presented. The left wall is linearly heated (by increasing or decreasing the wall temperature); the right wall is uniformly cooled while the horizontal top and bottom walls are considered insulated. A developed program (based on the finite-volume method and the semi-implicit method for pressure-linked equations algorithm) was utilized to numerically solve the governing Navier-Stokes equations with the associated boundary conditions. The controlling parameters on the fluid flow and heat transfer for this investigation are the interphase heat transfer coefficient (H), porosity-scaled conductivity ratio (γ), Rayleigh number (Ra), and Darcy number (Da) at Pr = 0.70.
Buoyancy induced convection in a porous cavity with partially thermally active sidewalls
International Journal of Heat and Mass Transfer, 2011
This study reports a numerical investigation of the convective flow and heat transfer in a square porous cavity with partially active thermal walls. Five different heating and cooling zones are considered along the vertical walls while the remaining portions of the side walls as well as the top and bottom of the cavity are adiabatic. The Brinkman Forchheimer extended Darcy model is used in the present study and the resulting governing equations are solved by finite volume method with SIMPLE algorithm. The computations are carried out for a wide range of parameters and the results are presented graphically. The results reveal that the location of heating and cooling zones has a significant influence on the flow pattern and the corresponding heat transfer in the enclosure. The location of partial heating has different effect on velocity and heat transfer, and the heat transfer rate approaches to a constant value for very low values of the Darcy number.
The effects of nonuniform heating and a finite wall thickness on natural convection in a square porous cavity based on the local thermal nonequilibrium (LTNE) model are studied numerically using the finite difference method (FDM). The finite-thickness horizontal wall of the cavity is heated either uniformly or nonuniformly, and the vertical walls are maintained at constant cold temperatures. The top horizontal insulated wall allows no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. The results of this study are obtained for various parametric values of the Rayleigh number, thermal conductivity ratio, ratio of the wall thickness to its height, and the modified conductivity ratio. Comparisons with previously published work verify good agreement with the proposed method. The effects of the various parameters on the streamlines, isotherms, and the weighted-average heat transfer are shown graphically. It is shown that a thicker bottom solid wall clearly inhibits the temperature gradient which then leads to the thermal equilibrium case. Further, the overall heat transfer is highly affected by the presence of the solid wall. The results have possible applications in the heat-storage fluid-saturated porous systems and the applications of the high power heat transfer.
The present study is concerned numerically with the mixed convection in a square lid-driven cavity with moving upper surface filled with saturated porous material. Both upper and lower surfaces are being insulated while the vertical walls of the enclosure subjected to sinusoidal temperatures variation with different amplitude and phase angle in order to enhance the heat transfer. Steady state laminar regime is considered. The transport equations for continuity, momentum, energy are solved. The numerical results are reported for the effect of Richardson number (Ri), Darcy number (Da), Prandtl number (Pr), amplitude ratio (ε) and phase deviation angle (ϕ) on the iso-contours of streamline, and temperature. In addition, the predicted results for both local and average Nusselt numbers are presented and discussed for various parametric conditions. This study was done for 10