Abstract
This study reports a numerical simulation of the natural convection combined with thermal radiation in a square porous cavity with a thin isothermally heated plate placed horizontally or vertically at its center. The vertical walls of the cavity are cooled while the horizontal ones are adiabatic. The governing equations were solved using a finite volume method on a uniformly staggered grid system. The computational results are presented in the form of isotherm and streamline plots and Nusselt numbers. The effects of the Darcy number (\(10^{-5} \le \mathrm{Da} \le ~10^{-2})\), plate length (\(0.25\le D \le 0.75\)) and the radiation parameter (\(0 \le R_{d} \le 2\)) are investigated for the Rayleigh number Ra = \(10^{7}\). It is found that the Darcy number, the plate length and the radiation parameter enhance the overall heat transfer rate across the cavity.
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Abbreviations
- Da:
-
Darcy number
- g :
-
Gravitational acceleration
- K :
-
Permeability of the porous medium
- L :
-
Size of the cavity
- Nu:
-
Local Nusselt number
- \({\overline{\mathrm{Nu}}} \) :
-
Average Nusselt number
- P :
-
Dimensionless pressure
- p :
-
Dimensional pressure
- Pr:
-
Prandtl number
- \(q_{rx}, q_{ry}\) :
-
Radiation heat fluxes along horizontal and vertical axis
- Ra:
-
Rayleigh number
- \(R_{d}\) :
-
Thermal radiation parameter
- T :
-
Dimensional fluid temperature
- t :
-
Dimensional time
- \(T_\mathrm{h}\) :
-
Dimensional temperature at heated plate
- \(T_\mathrm{c}\) :
-
Dimensional temperature at cooled vertical walls
- u, v :
-
Dimensional velocity components along horizontal and vertical directions
- U, V :
-
Dimensionless velocity components along horizontal and vertical directions
- x :
-
Dimensional Cartesian coordinate measured along the bottom wall of the cavity
- y :
-
Dimensional Cartesian coordinate measured along the vertical wall of the cavity
- X, Y :
-
Dimensionless Cartesian coordinates
- \(\alpha _\mathrm{m}\) :
-
Overall thermal diffusivity of the porous medium
- \(\beta \) :
-
Coefficient of thermal expansion
- \(\beta _{r}\) :
-
Extinction coefficient
- \(\varepsilon \) :
-
Porosity of the porous medium
- \(\mu \) :
-
Dynamic viscosity
- \(\theta \) :
-
Dimensionless temperature
- \(\lambda _\mathrm{m}\) :
-
Overall thermal conductivity of the porous medium
- \(\rho \) :
-
Fluid density
- \(\left( {\rho C_\mathrm{p} } \right) _\mathrm{m} \) :
-
Overall heat capacity of the porous medium
- \(\left( {\rho C_\mathrm{p} } \right) _\mathrm{f} \) :
-
Heat capacity of the fluid
- \(\sigma \) :
-
Stephan–Boltzmann constant
- \(\tau \) :
-
Dimensionless time
- \(\Psi \) :
-
Dimensionless stream function
- c :
-
Cold
- h :
-
Hot
- m :
-
Porous medium
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Sivaraj, C., Sheremet, M.A. Natural Convection Coupled with Thermal Radiation in a Square Porous Cavity Having a Heated Plate Inside. Transp Porous Med 114, 843–857 (2016). https://doi.org/10.1007/s11242-016-0747-2
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DOI: https://doi.org/10.1007/s11242-016-0747-2