Effects of Nonuniform Heating and Wall Conduction on Natural Convection in a Square Porous Cavity Using LTNE Model (original) (raw)
Related papers
2015
Unsteady natural convection and heat transfer in a square cavity partially filled with porous media using a thermal<br> non-equilibrium model is studied in this paper. The left vertical wall is<br> maintained at a constant hot temperature Th and the right vertical wall<br> is maintained at a constant cold temperature Tc, while the horizontal<br> walls are adiabatic. The governing equations are obtained by applying<br> the Darcy model and Boussinesq approximation. COMSOL's finite<br> element method is used to solve the non-dimensional governing<br> equations together with specified boundary conditions. The governing<br> parameters of this study are the Rayleigh number (Ra = 10^5, and Ra = 10^6 ), Darcy namber (Da = 10^−2, and Da = 10^−3),<br> the modified thermal conductivity ratio (10^−1 ≤ γ ≤ 10^4), the inter-phase heat transfer coefficien (10^−1 ≤ H ≤ 10^3) and the<br> time dependent (0.001 ≤ τ ≤ 0.2). The results pre...
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.
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.
International Journal of Energy Research, 2003
The aim of the present paper is to study the steady state natural convection in a square porous enclosure using a thermal non-equilibrium model for the heat transfer between the fluid and the solid phases. The analysis assumes that the porous medium is homogeneous and isotropic. The present study also assumes the non-Darcy model of natural convection in porous media. It is assumed that the heat generation is only in solid phase. Two dimensional steady convection in a cavity bounded by isothermal walls at constant temperatures has been studied numerically by adopting a two-temperature model of microscopic heat transfer. Such a model, which allows the fluid and solid phases not to be in local thermal equilibrium, is found to modify the flow behaviour and heat transfer rates. Knowledge of this behaviour is very important for the design of the many engineering applications.
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.
Free convection in a square porous cavity using a thermal nonequilibrium model
International Journal of Thermal Sciences, 2002
Two-dimensional steady free convection in a square cavity bounded by isothermal vertical walls at different temperatures and adiabatic horizontal walls has been studied numerically by adopting a two-temperature model of heat transfer. Such a model, which allows the fluid and solid phases not to be in local thermal equilibrium, is found to modify the flow behaviour and heat transfer rates. Knowledge of this behaviour is important for the design of thermal insulation systems and other practical applications. As far as we know, this problem has not yet been studied in the available literature. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.
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 Flow in Porous Enclosure with Localized Heating from Below with Heat Flux
Unsteady natural convection flow in a two dimensional fluid saturated porous enclosure with localized heating form below with heat flux, symmetrical cooling from the sides and the insulated top wall has been investigated numerically. The governing equations are the Darcy's law for the porous media and the energy equation for the temperature field has been considered. The non-dimensional Darcy's law in terms of the stream function is solved by finite difference method using the successive over-relaxation (SOR) scheme and the energy equation is solved by Alternative Direction Alternative (ADI) scheme. The uniform heat flux source is located centrally at the bottom wall. The numerical results are presented in terms of the streamlines and isotherms, as well as the local and average rate of heat transfer for the wide range of the Darcy's Rayleigh number and the length of the heat flux source at the bottom wall.
Effect of Discrete Heating on Natural Convection in a Rectangular Porous Enclosure
Transport in Porous Media, 2010
The main objective of this article is to study the effect of discrete heating on free convection heat transfer in a rectangular porous enclosure containing a heat-generating substance. The left wall of the enclosure has two discrete heat sources and the right wall is isothermally cooled at a lower temperature. The top and bottom walls, and the unheated portions of the left wall are adiabatic. The vorticity-stream function formulation of the governing equations is numerically solved using an implicit finite difference method. The effects of aspect ratio, Darcy number, heat source length, and modified Rayleigh number on the flow and heat transfer are analyzed. The numerical results reveal that the rate of heat transfer increases as the modified Rayleigh number and the Darcy number increases, but decreases on increasing the aspect ratio. The average heat transfer rate is found to be higher at the bottom heater than at the top heater in almost all considered parameter cases except for ε = 0.5. Also, the maximum temperature takes place generally at the top heater except for the case ε = 0.5, where the maximum temperature is found at the bottom heater. Further, the numerical results reveal that the maximum temperature decreases with the modified Rayleigh number and increases with the aspect ratio.