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ABSTRACT
In this study, the multiparameter constrained optimization procedure integrating the design of experiments (DOE), genetic algorithm (GA), and computational fluid dynamics (CFD) is proposed to design three-dimensional porous pin fins in a rectangular channel. The Forchheimer–Brinkman extended Darcy model and the two-equation energy model are adopted to describe the fluid flow and heat transfer characteristics in the porous media. The elliptical, coupled, steady-state, and three-dimensional governing partial differential equations for laminar forced convection with porous pin fins in a rectangular channel are solved numerically using the finite volume approach. The numerical optimization provides a reliable and economic mean of designing a heat transfer channel with porous pin fin arrays.
Nomenclature
| cF | = | Forchheimer coefficient, kJ/kg·K |
| Cp | = | specific heat at constant pressure, kJ/kg·K |
| D | = | hydraulic diameter, mm |
| df | = | fiber diameter of metal foam, mm |
| dp | = | pore size of metal foam, mm |
| G | = | shape function for metal foam |
| H | = | height of channel, mm |
| h | = | convection coefficient, W/m2·K |
| hv | = | volumetric heat transfer coefficient, W/m3·K |
| h′ | = | height of porous pin fins, mm |
| K | = | permeability, m2 |
| k | = | conduction coefficient, W/m·K |
| L | = | total channel length, mm |
| L1 | = | length of developing inlet block, mm |
| L2 | = | length of hot wall, mm |
| L3 | = | length of developing outlet block, mm |
| P | = | pressure drop, Pa |
| p | = | pitch of porous pin fins, mm |
| q” | = | heat flux, kW/m2 |
| Re | = | Reynolds number |
| T | = | temperature, K |
| Th | = | temperature at the heated surface, K |
| u | = | velocity in x direction, m/s |
| v | = | velocity in y direction, m/s |
| w | = | velocity in z direction, m/s |
| V | = | velocity vector, m/s |
| W | = | channel width, mm |
| x,y,z | = | coordinate direction, mm |
| α | = | dimensionless height |
| β | = | dimensionless pitch |
| γ | = | overall heat transfer efficiency |
| ϵ | = | porosity |
| µ | = | viscosity coefficient kg/m.s |
| ρ | = | density, kg/m3 |
| ν | = | dynamic viscosity coefficient, m2/s |
| χ | = | tortuosity of porous matrix |
| Subscripts | = | |
| in | = | Inlet |
| f | = | Fluid |
| s | = | Solid |
Nomenclature
| cF | = | Forchheimer coefficient, kJ/kg·K |
| Cp | = | specific heat at constant pressure, kJ/kg·K |
| D | = | hydraulic diameter, mm |
| df | = | fiber diameter of metal foam, mm |
| dp | = | pore size of metal foam, mm |
| G | = | shape function for metal foam |
| H | = | height of channel, mm |
| h | = | convection coefficient, W/m2·K |
| hv | = | volumetric heat transfer coefficient, W/m3·K |
| h′ | = | height of porous pin fins, mm |
| K | = | permeability, m2 |
| k | = | conduction coefficient, W/m·K |
| L | = | total channel length, mm |
| L1 | = | length of developing inlet block, mm |
| L2 | = | length of hot wall, mm |
| L3 | = | length of developing outlet block, mm |
| P | = | pressure drop, Pa |
| p | = | pitch of porous pin fins, mm |
| q” | = | heat flux, kW/m2 |
| Re | = | Reynolds number |
| T | = | temperature, K |
| Th | = | temperature at the heated surface, K |
| u | = | velocity in x direction, m/s |
| v | = | velocity in y direction, m/s |
| w | = | velocity in z direction, m/s |
| V | = | velocity vector, m/s |
| W | = | channel width, mm |
| x,y,z | = | coordinate direction, mm |
| α | = | dimensionless height |
| β | = | dimensionless pitch |
| γ | = | overall heat transfer efficiency |
| ϵ | = | porosity |
| µ | = | viscosity coefficient kg/m.s |
| ρ | = | density, kg/m3 |
| ν | = | dynamic viscosity coefficient, m2/s |
| χ | = | tortuosity of porous matrix |
| Subscripts | = | |
| in | = | Inlet |
| f | = | Fluid |
| s | = | Solid |