ABSTRACT
This paper numerically studies the effects of design parameters on the thermal performance and flow resistance under the forced convection of a rectangular minichannel with short elliptical pin fins. The investigations show that fins with a higher fin height and streamwise-oriented major axis direction yield better heat transfer performance, and the volume fraction without fins should be near 0.92. Also, compared to solid metal materials, porous metal is a better choice for fins, which reduces pressure drop significantly with little thermal consumption at proper pore density.
Nomenclature
Afin | = | the surface areas of the fluid touches the fins (m2) |
Ab | = | the surface areas of the fluid touches the heated base region (m2) |
CF | = | Forchheimer coefficient |
cp | = | specific heat at constant pressure (J·kg−1·K−1) |
Dc | = | hydraulic diameter of channel (m) |
Df | = | hydraulic diameter of fins (m) |
df | = | fiber diameter of metal foam (m) |
dp | = | pore size of metal foam (m) |
G | = | shape function for metal foam |
h | = | heat transfer coefficient (W·m−2·K−1) |
hb | = | heat transfer coefficient of the fins (W·m−2·K−1) |
hfin | = | heat transfer coefficient of the base of the heated region (W·m−2·K−1) |
hc | = | height of channel (m) |
hf | = | height of fins (m) |
hv | = | volumetric heat transfer coefficient (W·m−3·K−1) |
K | = | permeability (m2) |
k | = | thermal conductivity (W·m−1·K−1) |
lc | = | length of channel (m) |
lh | = | length of hot area (m) |
Nu | = | Nusselt number |
ΔP | = | pressure drop across the pin-fin heat sink (Pa) |
Pr | = | Prandtl number |
PPI | = | pore density (m−1) |
q | = | heat flux (W·m−2) |
Re | = | Reynolds number |
st | = | transverse spacing between the adjacent pin fins (m) |
sl | = | longitudinal spacing between the adjacent pin fins (m) |
T | = | temperature (°C) |
wc | = | width of channel (m) |
wf | = | width of fins (m) |
V | = | dimensionless velocity in transverse direction |
u,v,w | = | velocity in x, y, z directions |
Greek symbols | = | |
ν | = | kinetic viscosity (m−2·s−1) |
ρ | = | density (kg·m−3) |
φ | = | porosity |
χ | = | tortuosity of porous matrix |
Subscripts | = | |
f | = | fluid phase |
s | = | solid phase, value obtained in solid pin-fin channel |
Nomenclature
Afin | = | the surface areas of the fluid touches the fins (m2) |
Ab | = | the surface areas of the fluid touches the heated base region (m2) |
CF | = | Forchheimer coefficient |
cp | = | specific heat at constant pressure (J·kg−1·K−1) |
Dc | = | hydraulic diameter of channel (m) |
Df | = | hydraulic diameter of fins (m) |
df | = | fiber diameter of metal foam (m) |
dp | = | pore size of metal foam (m) |
G | = | shape function for metal foam |
h | = | heat transfer coefficient (W·m−2·K−1) |
hb | = | heat transfer coefficient of the fins (W·m−2·K−1) |
hfin | = | heat transfer coefficient of the base of the heated region (W·m−2·K−1) |
hc | = | height of channel (m) |
hf | = | height of fins (m) |
hv | = | volumetric heat transfer coefficient (W·m−3·K−1) |
K | = | permeability (m2) |
k | = | thermal conductivity (W·m−1·K−1) |
lc | = | length of channel (m) |
lh | = | length of hot area (m) |
Nu | = | Nusselt number |
ΔP | = | pressure drop across the pin-fin heat sink (Pa) |
Pr | = | Prandtl number |
PPI | = | pore density (m−1) |
q | = | heat flux (W·m−2) |
Re | = | Reynolds number |
st | = | transverse spacing between the adjacent pin fins (m) |
sl | = | longitudinal spacing between the adjacent pin fins (m) |
T | = | temperature (°C) |
wc | = | width of channel (m) |
wf | = | width of fins (m) |
V | = | dimensionless velocity in transverse direction |
u,v,w | = | velocity in x, y, z directions |
Greek symbols | = | |
ν | = | kinetic viscosity (m−2·s−1) |
ρ | = | density (kg·m−3) |
φ | = | porosity |
χ | = | tortuosity of porous matrix |
Subscripts | = | |
f | = | fluid phase |
s | = | solid phase, value obtained in solid pin-fin channel |