Abstract
Differentially heated enclosure with heat-generating porous layer on inner walls is studied computationally for non-Darcy flow and thermal non-equilibrium models. In this study, this problem is investigated for different internal and external Rayleigh numbers, Darcy numbers, porosity-scaled thermal conductivity ratio, solid-/fluid-scaled heat transfer coefficient and dimensionless thickness of the porous layer. The results indicate that the dimensionless thickness of the porous layer has an important effect on the heat transfer in the enclosure. It was found that the thermal non-equilibrium model is needed for small values of the porosity-scaled thermal conductivity ratio and the solid-/fluid-scaled heat transfer coefficient. It is shown that the convection of heat due to internal heat generation is increased in the enclosure when the ratio of internal Rayleigh number to external Rayleigh number is larger.
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Abbreviations
- d :
-
Thickness of porous layer (m)
- D :
-
Height of square porous enclosure (m)
- Da :
-
Darcy number
- g :
-
Acceleration due to gravity \((\hbox {ms}^{-2})\)
- \(h_v\) :
-
Volumetric heat transfer coefficient \((\hbox {Wm}^{-3}\hbox {K}^{-1}\))
- H :
-
Dimensionless volumetric heat transfer coefficient
- k :
-
Thermal conductivity \((\hbox {Wm}^{-1}\hbox {K}^{-1})\)
- K :
-
Permeability of porous layer \((\hbox {m}^2)\)
- Nu :
-
Average Nusselt number
- p :
-
Pressure \((\hbox {Nm}^{-2})\)
- P :
-
Dimensionless pressure
- Pr :
-
Prandtl number
- \(Ra_E\) :
-
External Rayleigh number
- \(Ra_I\) :
-
Internal Rayleigh number
- \(q^{\prime \prime \prime }\) :
-
Rate of volumetric heat generation \((\hbox {Wm}^{-3})\)
- t :
-
Time (s)
- T :
-
Temperature (K)
- u, v :
-
Velocity components along x and y axes, respectively \((\hbox {ms}^{-1})\)
- U, V :
-
Dimensionless velocity components
- x, y :
-
Cartesian coordinates
- X, Y :
-
Dimensionless coordinate
- \(\alpha \) :
-
Thermal diffusivity \( (\hbox {m}^2\hbox {s}^{-1})\)
- \(\beta \) :
-
Thermal expansion \((\hbox {K}^{-1})\)
- \(\gamma \) :
-
Porosity-scaled conductivity ratio
- \(\varepsilon \) :
-
Porosity
- \(\eta \) :
-
Dimensionless thickness of porous layer
- \(\Theta \) :
-
Dimensionless temperature
- \(\nu \) :
-
Kinematic viscosity \((\hbox {m}^2\hbox {s}^{-1})\)
- \(\xi \) :
-
Thermal diffusivity ratio
- \(\rho \) :
-
Fluid density \((\hbox {kgm}^{-3})\)
- \(\tau \) :
-
Dimensionless time
- f :
-
Fluid
- s :
-
Solid
- C :
-
Cold
- H :
-
Hot
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Baytaş, A.F., Baytaş, A.C. Thermal Non-equilibrium Natural Convection in a Square Enclosure with Heat-Generating Porous Layer on Inner Walls. Transp Porous Med 120, 167–182 (2017). https://doi.org/10.1007/s11242-017-0914-0
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DOI: https://doi.org/10.1007/s11242-017-0914-0