Numerical study of laminar natural convection in a complicated cavity heated from top with sinusoidal temperature and cooled from other sides (original) (raw)
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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.
International Journal of Heat and Mass Transfer, 1999
Natural convection in a 2-D vertical cylinder containing an isotropic porous media with internal heat generation was studied numerically for assessing the eect of Darcy's law with and without the Brinkman extension on the streamlines, isotherms and Nusselt numbers. Two cases were analyzed: (1) insulated walls at the top and bottom of the cylinder and cooled external walls; (2) isothermally cooled walls at all external surfaces. The eect of the Brinkman extension was signi®cant for high values of Da (10 À4 ±10 À1 ). In addition, the Nusselt number increases asymptotically as Da decreases. Also, four correlations for the average Nusselt number were derived. #
International Communications in Heat and Mass Transfer, 2008
Numerical investigations of steady natural convection flow through a fluid-saturated porous medium in a rectangular enclosure with a sinusoidal varying temperature profile on the bottom wall were conducted. All the walls of the enclosure are insulated except the bottom wall which is partially heated and cooled. The governing equations were written under the assumption of Darcy-law and then solved numerically using finite difference method. The problem is analyzed for different values of the Rayleigh number Ra in the range 10 ≤ Ra ≤ 1000, aspect ratio parameter AR in the range 0.25 ≤ AR ≤1.0 and amplitude λ of the sinusoidal temperature function in the range 0.25 ≤ λ ≤ 1.0. It was found that heat transfer increases with increasing of amplitude λ and decreases with increasing aspect ratio AR. Multiple cells were observed in the cavity for all values of the parameters considered.
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
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.
International Communications in Heat and Mass Transfer, 1999
A Pressure-velocity solution for natural convection for fluid saturated heat generating porous medium in a square enclosure is analysed by finite element method. The numerical solutions obtained for wide range of fluid Rayleigh number, Raf, Darcy number, Da, and heat generating number, Qd. The justification for taking these non-dimensional parameters independently is to establish the effect of individual parameters on flow patterns. It has been observed that peak temperature occurs at the top central part and weaker velocity prevails near the vertical wails of the enclosure due to the heat generation parameter alone. On comparison, the modified Rayleigh number used by the earlier investigators[4,6], can not explain explicitly the effect of heat generation parameter on natural convection within an enclosure having differentially heated vertical walls. At higher Darcy number, the peak temperature and peak velocity are comparatively more, resulting in better enhancement of heat transfer rate.
Leonardo Journal of …, 2008
The objective of this study is the comparison between the model of Darcy-Brinkman and the Navier-Stokes equations modified, in the case of the natural convection. The study is made in a porous vertical square cavity saturated by a Newtonian fluid. A cylindrical heat source maintained at a uniform heat flux is introduced into porous medium. The equations which describe the thermal transfer and the hydrodynamic flow of the two models are solved numerically by means of the software package Femlab 3.2 based on the finite element method. The results obtained are in the form of average kinetic energy per unit mass, the local and the average Nusselt numbers, the pressure and the viscous force per unit area. 121 Comparative Study between the Darcy-Brinkman Model and the Modified Navier-Stokes Equations ... Razli MEHDAOUI, Mohammed ELMIR, Belkacem DRAOUI, Omar IMINE, and Abdelkader MOJTABI [ Issue 12, January-June 2008 p. 121-134 square cavity (Fig. 1) of side length H, in presence of concentric cylindrical source of diameter D, submerged in porous media subjected to a uniform heat flux q. The walls of cavity are kept at uniform temperature T w .
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 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 heat transfer in a porous rectangular partially active heated wall is numerically investigated using finite element method. Three different cases of heating and cooling zone had been taken in the consideration along the vertical walls while the others are considered to be adiabatic. The governing equations are obtained by the applying of Darcy Model and Boussinesq approximation. Finite element method is used to solve the dimensionless governing equations with the specified boundary conditions. The investigated parameters in the present study are the modified Rayleigh number (10 # Ra # 10), aspect ratio 3 (0.5 # A# 2), finite wall thickness (0.02 # D# = 0.5) and the thermal conductivity ratio (0.1# K # 10). The results r are presented in terms of streamlines, isotherms and Nusselt number. The results indicate that as the aspect ratio, finite wall thickness increase, Nusselt number decrease. Also, as the modified Rayleigh number increases, the Nusselt number will increase. Case 1 and 2 gave approximately the same effects of heat transfer rate while case 3 give lower rate of heat transfer rate.