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ABSTRACT
The aim of the present investigation is to analyze the effect of the motion of horizontal (cases 1a–1d) and vertical walls (case 2a–2c) on the entropy generation and heat transfer in a porous square cavity during mixed convection. The cavity is subject to the thermal boundary conditions such as the hot bottom wall, cold side walls, and thermally insulated top wall. Analysis has been done for various fluids with Prandtl number, Prm = 0.026–7.2, Grashof number, Gr = 105, Reynolds number, Re = 10–100, and Darcy number, Dam = 10−4–10−2. Numerical results are presented using streamfunction (ψ), local entropy generation due to fluid friction (Sψ), isotherms (θ), and local entropy generation due to heat-transfer (Sθ) contours. In addition, the total entropy generation (Stotal), average Bejan number (Beav), and overall heat-transfer rate at the hot bottom wall are analyzed and discussed.
Nomenclature
| Be | = | Bejan number |
| Dam | = | modified Darcy number |
| g | = | acceleration due to gravity, m s−2 |
| Gr | = | Grashof number |
| K | = | medium permeability |
| L | = | length of the square cavity, m |
| = | average Nusselt number | |
| P | = | dimensionless pressure |
| Prm | = | modified Prandtl number |
| Re | = | Reynolds number |
| Sθ | = | dimensionless entropy generation due to heat transport |
| Sψ | = | dimensionless entropy generation due to fluid friction |
| T | = | temperature of the fluid, K |
| U | = | x component of dimensionless velocity |
| U0 | = | characteristic velocity |
| V | = | y component of dimensionless velocity |
| X | = | dimensionless distance along x coordinate |
| Y | = | dimensionless distance along y coordinate |
| α | = | thermal diffusivity, m2s−1 |
| β | = | volume expansion coefficient, K−1 |
| γ | = | penalty parameter |
| θ | = | dimensionless temperature |
| ρ | = | density, kg m−3 |
| Φ | = | basis functions |
| ψ | = | dimensionless streamfunction |
| μ | = | dynamic viscosity, kg m−1 s−1 |
| ε | = | porosity of the medium |
| Subscripts | ||
| av | = | spatial average |
| eff | = | effective |
| Superscripts | ||
| e | = | element |
Nomenclature
| Be | = | Bejan number |
| Dam | = | modified Darcy number |
| g | = | acceleration due to gravity, m s−2 |
| Gr | = | Grashof number |
| K | = | medium permeability |
| L | = | length of the square cavity, m |
| = | average Nusselt number | |
| P | = | dimensionless pressure |
| Prm | = | modified Prandtl number |
| Re | = | Reynolds number |
| Sθ | = | dimensionless entropy generation due to heat transport |
| Sψ | = | dimensionless entropy generation due to fluid friction |
| T | = | temperature of the fluid, K |
| U | = | x component of dimensionless velocity |
| U0 | = | characteristic velocity |
| V | = | y component of dimensionless velocity |
| X | = | dimensionless distance along x coordinate |
| Y | = | dimensionless distance along y coordinate |
| α | = | thermal diffusivity, m2s−1 |
| β | = | volume expansion coefficient, K−1 |
| γ | = | penalty parameter |
| θ | = | dimensionless temperature |
| ρ | = | density, kg m−3 |
| Φ | = | basis functions |
| ψ | = | dimensionless streamfunction |
| μ | = | dynamic viscosity, kg m−1 s−1 |
| ε | = | porosity of the medium |
| Subscripts | ||
| av | = | spatial average |
| eff | = | effective |
| Superscripts | ||
| e | = | element |
