Numerical Investigation of Conjugate Natural Convection Heat Transfer from Discrete Heat Sources in Rectangular Enclosure (original) (raw)
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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.
International Journal of Thermal Sciences, 2007
Steady conjugate natural convection-conduction heat transfer in a two-dimensional porous enclosure with finite wall thickness is studied numerically in the present article. The horizontal heating is considered, where the vertical boundaries are isothermal at different temperatures with adiabatic horizontal boundaries. The Darcy model is used in the mathematical formulation for the porous layer and finite volume method is used to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (10 Ra 1000), the wall to porous thermal conductivity ratio (0.1 K r 10) and the ratio of wall thickness to its height (0.02 D 0.5). The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. The results including the streamlines and isotherm patterns and the local and average Nusselt number for different values of the governing parameters. It is found, in most of the cases that either increasing the Rayleigh number and the thermal conductivity ratio or decreasing the thickness of the bounded wall can increase the average Nusselt number for the porous enclosure (Nu p ). In special cases at low Ra and high conductive walls, the values of Nu p are increasing with the increase of the wall thickness.
A numerical study of non-Darcian natural convection heat transfer in a rectangular enclosure filled with porous medium saturated with viscous fluid was carried out. The effects of medium Rayleigh number, porosity, particle to fluid thermal conductivity ratio, Darcy number and enclosure aspect ratio on heat transfer were examined to demonstrate the ability Porosity Dimensionless temperature Viscosity (N.s/m 2 ) Density (kg/m 3 ) Dimensionless time Dimensionless stream function Dimensionless vorticity Subscripts d Dispersive e Effective f Fluid m Medium s Solid st Stagnant
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.
COMPUTATIONAL INVESTIGATION OF CONJUGATE HEAT TRANSFER IN CAVITY FILLED WITH SATURATED POROUS MEDIA
The conjugate natural convection heat transfer in a partially heated porous enclosure had been studied numerically. The governing dimensionless equations are solved using finite element method. Classical Darcy model have been used and the considering dimensionless parameters are modified Rayleigh number (10 ≤ Ra ≤ 10 3), finite wall thickness (0.02 ≤ D ≤ 0.5), thermal conductivity ratio (0.1 ≤ Kr ≤ 10), and the aspect ratio (0.5 ≤ A≤ 10). The results are presented in terms of streamlines, isotherms and local and average Nusselt number. The results indicate that heat transfer can be enhanced by increasing the modified Rayleigh number, and thermal conductivity ratio. Wall thickness effects on the heat transfer mechanism had been studied and it is found that; as the Wall thickness increases, the conduction heat transfer mechanism will be dominated. Also, increasing aspect ratio will increase the stream function and reduced the heat transfer rate.
Unsteady conjugate natural convection in a square enclosure filled with a porous medium
International Journal of Heat and Mass Transfer, 2010
Mathematical simulation of unsteady natural convection modes in a square cavity filled with a porous medium having finite thickness heat-conducting walls with local heat source in conditions of heterogeneous heat exchange with an environment at one of the external boundaries has been carried out. Numerical analysis was based on Darcy-Forchheimer model in dimensionless variables such as a stream function, a vorticity vector and a temperature. The special attention was given to analysis of Rayleigh number effect Ra = 10 4 , 10 5 , 10 6 , of Darcy number effect Da = 10 À5 , 10 À4 , 10 À3 , 1, of the transient factor effect 0 < s < 1000 and of the heat conductivity ratio k 2,1 = 3.7 Â 10 À2 , 5.7 Â 10 À4 , 6.8 Â 10 À5 on the velocity and temperature fields. The influence scales of the defining parameters on the average Nusselt number have been detected.
Natural convection flow in a porous enclosure with localized heating from bellow
In this study steady natural convection flow in a two-dimensional fluid saturated porous enclosure with localized heating from below has been investigated. A portion of the bottom surface is heated and the symmetrically cooled the side walls and the top and rest of the bottom walls are insulated. An implicit finite volume method with TDMA solver is used to solve the governing equations. Localized heating is simulated by a centrally located isothermal heat source on the bottom wall, and four different values of the dimensionless heat source length, 1/5, 2/5, 3/5 and 4/5 are considered. It is found that the flow field and the isotherm are symmetric owing to the symmetric boundary condition for the parameters considered here. It is also found that the increases of Rayleigh number and the heat source size enhance the heat transfer. The effect of heat source length and the Rayleigh number on streamlines and isotherms are presented, as well as the variation of the local rate of heat transfer in terms of the local Nusselt number from the heated wall. Finally, the average Nusselt number at the heated part of the bottom wall has been shown against Rayleigh number for the non-dimensional heat source length.
Natural convection in a square enclosure filled with a porous matrix is performed numerically by using the finite volume method. Three discrete heat sources are mounted at the top and the left and right sidewalls of the enclosure. The bottom wall is considered adiabatic while all the other walls are maintained at a cold temperature except at the heat source locations which are kept at a hot one. The length of the discrete heat source at the top wall is double than the heat sources at the sidewalls. From the other hand, the heat source at the top wall is considered fixed while the other heat sources are moving at five different locations. The influence of the Rayleigh, Prandtl, Darcy numbers and the heat source location on the flow and thermal fields are investigated. The considered parameters are Darcy number [Da = 10-3-10-5 ], Rayleigh number [Ra =10 3-10 6 ] and Prandtl number [Pr = 0.7, 6 and 1000]. It is found that the average Nusselt number increases for different heat source l...
Natural convection in a non-rectangular porous enclosure
Forschung im Ingenieurwesen, 1999
This paper describes a numerical solution procedure to study heat transfer process by two dimensional Ar natural convection phenomena in a non-rectangular en-Cp closure of arbitrary geometry. Momentum transfer in the fl.-.. ,f4 system is described by an elliptic partial differential equation, which governs the behaviour of the stream g function. An algebraic grid generation technique is used to H transform the governing equations into a body fitted K rectangular coordinate system that allows coincidence of L all boundary lines with the coordinate lines. Numerical n solutions of the resulting equations in the computational nx, ny domain are obtained using an alternating directional implicit method by adding false transient terms. Results from the numerical experiments in the case of a non-rectangular enclosure are obtained that show the magnitude and directions of convection currents and contours of the temperature. The effect of increase in the inclination of the upper boundary is to increase the average Nusselt number.