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ABSTRACT
The natural convection is analyzed via the entropy generation approach in the differentially heated, porous enclosures with curved (concave or convex) vertical walls. The numerical simulations have been carried out for various fluids (Prandtl number: Prm = 0.015, 0.7, and 7.2) at various permeabilities (Darcy numbers: 10−5 ≤ Dam ≤ 10−2) for a high value of Rayleigh number (Ram = 106). The finite element method is employed to solve the governing equations and that is further used to calculate the entropy generation and average Nusselt number. The detailed spatial distributions of Sθ and Sψ are analyzed for all the wall curvatures. Overall, the case with the highly concave surfaces (case 3) is the optimal case at low Dam, whereas the cases with the less convex surfaces (cases 1 and 2) are the most efficient cases at high Dam.
Nomenclature
| Be | = | Bejan number |
| Dam | = | Darcy number |
| g | = | acceleration due to gravity, m s−2 |
| L | = | height or length of base of the enclosure, m |
| N | = | total number of nodes |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| p | = | pressure, Pa |
| P | = | dimensionless pressure |
| Prm | = | Prandtl number |
| Ram | = | Rayleigh number |
| S | = | dimensionless entropy generation |
| Sθ | = | dimensionless entropy generation due to heat transfer |
| Sψ | = | dimensionless entropy generation due to fluid friction |
| Stotal | = | dimensionless total entropy generation |
| T | = | temperature, K |
| Th | = | temperature of hot left wall, K |
| Tc | = | temperature of cold right wall, K |
| u | = | x component of velocity |
| U | = | x component of dimensionless velocity |
| v | = | y component of velocity |
| V | = | y component of dimensionless velocity |
| x | = | distance along x coordinate |
| X | = | dimensionless distance along x coordinate |
| y | = | distance along y coordinate |
| Y | = | dimensionless distance along y coordinate |
| Greek symbols | = | |
| α | = | thermal diffusivity, m2 s−1 |
| β | = | volume expansion coefficient, K−1 |
| ϵ | = | medium porosity |
| γ | = | penalty parameter |
| θ | = | dimensionless temperature |
| ν | = | kinematic viscosity, m2 s−1 |
| ρ | = | density, kg m−3 |
| Φ | = | basis functions |
| ϕ | = | irreversibility distribution ratio |
| φ | = | angle made by the tangent of curved wall with positive X axis |
| ψ | = | dimensionless streamfunction |
| Ω | = | two-dimensional domain |
| Subscripts | = | |
| eff | = | effective parameter |
| f | = | fluid |
| l | = | left wall |
| r | = | right wall |
Nomenclature
| Be | = | Bejan number |
| Dam | = | Darcy number |
| g | = | acceleration due to gravity, m s−2 |
| L | = | height or length of base of the enclosure, m |
| N | = | total number of nodes |
| Nu | = | local Nusselt number |
| = | average Nusselt number | |
| p | = | pressure, Pa |
| P | = | dimensionless pressure |
| Prm | = | Prandtl number |
| Ram | = | Rayleigh number |
| S | = | dimensionless entropy generation |
| Sθ | = | dimensionless entropy generation due to heat transfer |
| Sψ | = | dimensionless entropy generation due to fluid friction |
| Stotal | = | dimensionless total entropy generation |
| T | = | temperature, K |
| Th | = | temperature of hot left wall, K |
| Tc | = | temperature of cold right wall, K |
| u | = | x component of velocity |
| U | = | x component of dimensionless velocity |
| v | = | y component of velocity |
| V | = | y component of dimensionless velocity |
| x | = | distance along x coordinate |
| X | = | dimensionless distance along x coordinate |
| y | = | distance along y coordinate |
| Y | = | dimensionless distance along y coordinate |
| Greek symbols | = | |
| α | = | thermal diffusivity, m2 s−1 |
| β | = | volume expansion coefficient, K−1 |
| ϵ | = | medium porosity |
| γ | = | penalty parameter |
| θ | = | dimensionless temperature |
| ν | = | kinematic viscosity, m2 s−1 |
| ρ | = | density, kg m−3 |
| Φ | = | basis functions |
| ϕ | = | irreversibility distribution ratio |
| φ | = | angle made by the tangent of curved wall with positive X axis |
| ψ | = | dimensionless streamfunction |
| Ω | = | two-dimensional domain |
| Subscripts | = | |
| eff | = | effective parameter |
| f | = | fluid |
| l | = | left wall |
| r | = | right wall |