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ABSTRACT
Entropy generation analysis is carried out during natural convection within entrapped porous triangular cavities for two cases based on the heating or cooling of the inclined and horizontal walls (case 1: hot inclined walls with cold horizontal walls and case 2: cold inclined walls with hot horizontal walls). The results are plotted in terms of the isotherms (θ), streamlines (ψ), and entropy generation maps (Sθ and Sψ). The total entropy generation (Stotal), average Bejan number (Beav), and average Nusselt number ( or
) as a function of Darcy number (Dam) at a high Rayleigh number (Ram = 106) have been studied for both cases 1 and 2 and the optimal case is recommended based on least Stotal and largest
or
.
Nomenclature
| Be | = | Bejan number |
| Da | = | Darcy number |
| g | = | acceleration due to gravity, m s−2 |
| K | = | permeability of the medium |
| L | = | height of each triangular cavity, m |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| Stotal | = | dimensionless total entropy generation due to heat transfer and fluid friction |
| Sθ | = | dimensionless entropy generation due to heat transfer |
| Sψ | = | dimensionless entropy generation due to fluid friction |
| Th | = | temperature of the hot wall, K |
| Tc | = | temperature of the cold wall, K |
| U | = | x component of dimensionless velocity |
| V | = | y component of dimensionless velocity |
| X | = | dimensionless distance along x coordinate |
| Y | = | dimensionless distance along y coordinate |
| α | = | thermal diffusivity, m2 s−1 |
| β | = | volume expansion coefficient, K−1 |
| γ | = | penalty parameter |
| θ | = | dimensionless temperature |
| ν | = | kinematic viscosity, m2 s−1 |
| ρ | = | density, kg m−3 |
| Φ | = | basis functions |
| ϕ | = | irreversibility distribution ratio |
| ψ | = | dimensionless streamfunction |
| Subscripts | = | |
| b | = | bottom wall |
| m | = | modified |
| t | = | top wall |
Nomenclature
| Be | = | Bejan number |
| Da | = | Darcy number |
| g | = | acceleration due to gravity, m s−2 |
| K | = | permeability of the medium |
| L | = | height of each triangular cavity, m |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| P | = | dimensionless pressure |
| Pr | = | Prandtl number |
| Stotal | = | dimensionless total entropy generation due to heat transfer and fluid friction |
| Sθ | = | dimensionless entropy generation due to heat transfer |
| Sψ | = | dimensionless entropy generation due to fluid friction |
| Th | = | temperature of the hot wall, K |
| Tc | = | temperature of the cold wall, K |
| U | = | x component of dimensionless velocity |
| V | = | y component of dimensionless velocity |
| X | = | dimensionless distance along x coordinate |
| Y | = | dimensionless distance along y coordinate |
| α | = | thermal diffusivity, m2 s−1 |
| β | = | volume expansion coefficient, K−1 |
| γ | = | penalty parameter |
| θ | = | dimensionless temperature |
| ν | = | kinematic viscosity, m2 s−1 |
| ρ | = | density, kg m−3 |
| Φ | = | basis functions |
| ϕ | = | irreversibility distribution ratio |
| ψ | = | dimensionless streamfunction |
| Subscripts | = | |
| b | = | bottom wall |
| m | = | modified |
| t | = | top wall |