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ABSTRACT
The present work involves the entropy generation studies within the porous square and triangular (models 1 and 2) cavities subjected to various discrete heating strategies at side walls (cases 1–4: symmetric heater locations, case 5: asymmetric heater locations) during natural convection over the wide range of Darcy number, , for various fluids (Prm = 0.015 and 7.2) at
. Galerkin finite-element method has been used to solve the governing equations. The symmetric and asymmetric distributions of heaters have similar effects at lower Dam. However, the symmetric distribution of heaters corresponds to lower entropy generation rates at higher Dam. The triangular (model 1 and model 2) cavities are found to be optimal over the entire range of Dam (
) based on the higher heat transfer rate and optimal entropy generation rates.
Nomenclature
| Beav | = | average Bejan number |
| = | specific heat capacity of the fluid, J kg K−1 | |
| Dam | = | modified Darcy number |
| g | = | acceleration due to gravity, m s−2 |
| keff | = | Effective thermal conductivity, W m−1 K−1 |
| K | = | permeability, m2 |
| Km | = | modified permeability, m2 |
| L | = | Height of the square and triangular enclosures, m |
| Nu, | = | local and average Nusselt numbers |
| p | = | Pressure, Pa |
| P | = | dimensionless pressure |
| Prm | = | modified Prandtl number |
| Ram | = | modified Rayleigh number |
| Sθ, Sψ | = | dimensionless entropy generation due to heat transfer and fluid friction |
| T | = | temperature of the fluid, K |
| Tc, Th | = | temperature of cold wall and hot wall, K |
| u, v | = | x and y components of velocity, m s−1 |
| U, V | = | x and y components of dimensionless velocity |
| x, y | = | distances along x and y coordinates, m |
| X, Y | = | dimensionless distances along x and y coordinates |
| αeff | = | effective thermal diffusivity, m2 s−1 |
| β | = | volume expansion coefficient, K−1 |
| γ | = | penalty parameter |
| ν | = | kinematic viscosity, m2 s−1 |
| νf | = | kinematic viscosity of the fluid, m2 s−1 |
| ρ | = | density, kg m−3 |
| ρf | = | density of the fluid, kg m−3 |
| φ | = | angle with positive X-axis |
| ψ | = | dimensionless streamfunction |
| ϵ | = | porosity of the medium |
| Subscripts | = | |
| ll | = | length of the left wall |
| rl | = | length of the right wall |
Nomenclature
| Beav | = | average Bejan number |
| = | specific heat capacity of the fluid, J kg K−1 | |
| Dam | = | modified Darcy number |
| g | = | acceleration due to gravity, m s−2 |
| keff | = | Effective thermal conductivity, W m−1 K−1 |
| K | = | permeability, m2 |
| Km | = | modified permeability, m2 |
| L | = | Height of the square and triangular enclosures, m |
| Nu, | = | local and average Nusselt numbers |
| p | = | Pressure, Pa |
| P | = | dimensionless pressure |
| Prm | = | modified Prandtl number |
| Ram | = | modified Rayleigh number |
| Sθ, Sψ | = | dimensionless entropy generation due to heat transfer and fluid friction |
| T | = | temperature of the fluid, K |
| Tc, Th | = | temperature of cold wall and hot wall, K |
| u, v | = | x and y components of velocity, m s−1 |
| U, V | = | x and y components of dimensionless velocity |
| x, y | = | distances along x and y coordinates, m |
| X, Y | = | dimensionless distances along x and y coordinates |
| αeff | = | effective thermal diffusivity, m2 s−1 |
| β | = | volume expansion coefficient, K−1 |
| γ | = | penalty parameter |
| ν | = | kinematic viscosity, m2 s−1 |
| νf | = | kinematic viscosity of the fluid, m2 s−1 |
| ρ | = | density, kg m−3 |
| ρf | = | density of the fluid, kg m−3 |
| φ | = | angle with positive X-axis |
| ψ | = | dimensionless streamfunction |
| ϵ | = | porosity of the medium |
| Subscripts | = | |
| ll | = | length of the left wall |
| rl | = | length of the right wall |