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 |