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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 |