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ABSTRACT
In this work, we study numerically the natural convection heat transfer and entropy generation characteristics inside a two-dimensional porous quadrantal enclosure heated nonuniformly from the bottom wall. The effect of Darcy number is significant in dictating the Nusselt number only for higher values of Rayleigh number and the variation is more profound for larger values of Darcy number. The variation of entropy generation rate is significant with the Darcy number only for higher values of Rayleigh number. The entropy generation due to heat transfer is the significant contributor of irreversibility at low values of Darcy number, while for larger values of Darcy number and Rayleigh number entropy generation due to fluid friction becomes dominant.
Nomenclature
| cp | = | specific heat of the fluid, J kg−1 K−1 |
| Da | = | Darcy number |
| g | = | acceleration due to gravity, m s−2 |
| h | = | convective heat transfer coefficient, W m−2 K−1 |
| k | = | thermal conductivity, W m−1 K−1 |
| K | = | permeability, m2 |
| L | = | enclosure length, m |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| p | = | pressure, N m−2 |
| P | = | nondimensional pressure |
| Pr | = | Prandtl number |
| Re | = | Reynolds number |
| S | = | total dimensionless entropy |
| Sθ | = | dimensionless entropy generation due to heat transfer |
| Sψ | = | dimensionless entropy generation due to fluid friction |
| T | = | temperature, K |
| U, V | = | dimensionless x and y velocity components, respectively |
| u, v | = | x and y velocity components, respectively, m s−1 |
| x, y | = | axial and transverse coordinates, respectively, m |
| = | Greek symbols | |
| α | = | thermal diffusivity |
| β | = | coefficient of thermal expansion |
| θ | = | dimensionless temperature |
| µ | = | dynamic viscosity |
| υ | = | kinematic viscosity |
| ρ | = | density of fluid, kg m−3 |
| = | Subscripts | |
| avg | = | average |
| b | = | bottom wall |
| c | = | cold wall |
| min | = | minimum |
| max | = | maximum |
Nomenclature
| cp | = | specific heat of the fluid, J kg−1 K−1 |
| Da | = | Darcy number |
| g | = | acceleration due to gravity, m s−2 |
| h | = | convective heat transfer coefficient, W m−2 K−1 |
| k | = | thermal conductivity, W m−1 K−1 |
| K | = | permeability, m2 |
| L | = | enclosure length, m |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| p | = | pressure, N m−2 |
| P | = | nondimensional pressure |
| Pr | = | Prandtl number |
| Re | = | Reynolds number |
| S | = | total dimensionless entropy |
| Sθ | = | dimensionless entropy generation due to heat transfer |
| Sψ | = | dimensionless entropy generation due to fluid friction |
| T | = | temperature, K |
| U, V | = | dimensionless x and y velocity components, respectively |
| u, v | = | x and y velocity components, respectively, m s−1 |
| x, y | = | axial and transverse coordinates, respectively, m |
| = | Greek symbols | |
| α | = | thermal diffusivity |
| β | = | coefficient of thermal expansion |
| θ | = | dimensionless temperature |
| µ | = | dynamic viscosity |
| υ | = | kinematic viscosity |
| ρ | = | density of fluid, kg m−3 |
| = | Subscripts | |
| avg | = | average |
| b | = | bottom wall |
| c | = | cold wall |
| min | = | minimum |
| max | = | maximum |