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ABSTRACT
Vertical fins radially mounted on heated circular horizontal plates are capable of enhancing free-convection cooling effects. Here we have numerically and experimentally shown that fins whose cross sectional shape is trapezoidal can provide greater cooling effects than their rectangular counterparts. Simulations and experiments are based on the Galerkin finite element method and TES1310 type-K thermocouple measurements. Three mechanisms responsible for cooling effect improvements are identified: (1) dominance of cooling strength near the rims of circular plates; (2) vertical surface area increase due to trapezoidal geometries; and (3) entrained-flow retardation due to pseudo-stagnation pressures. Our work can help guide heat transfer communities to design fins of varying cross sectional area.
Nomenclature
| cp | = | specific heat |
| Gr | = | Grashof number, |
| g | = | gravitational acceleration |
| H | = | fin height |
| h | = | heat transfer coefficient |
| k | = | thermal conductivity |
| L | = | fin length |
| N | = | number of fins |
| p | = | pressure |
| Q | = | heat flow rate of the heat source |
| q | = | heat flux of the heat source |
| R | = | gas constant for air |
| Rth | = | thermal resistance |
| r | = | radius size of the microchip |
| rω | = | fin thickness ratio, ω1/ωo |
| T | = | temperature |
| Tavg | = | average temperature of the heat source |
| ωo | = | middle thicknesses of the fin |
| ω1 | = | outer thicknesses of the fin |
| v | = | resultant velocity of airflow |
| ω2 | = | inner thicknesses of the fin |
| u | = | x-component velocity |
| v | = | y-component velocity |
| w | = | z-component velocity |
| β | = | coefficient of thermal expansion short distance between the outer |
| ϵ | = | edge of the fin and the rim of the circular plate |
| μ | = | dynamic viscosity |
| υ | = | kinematic viscosity, μ/ρ |
| ρ | = | density of air |
| Subscripts | = | |
| avg | = | average temperature |
| f | = | fluid (air) |
| s | = | solid |
| ∞ | = | ambient air |
Nomenclature
| cp | = | specific heat |
| Gr | = | Grashof number, |
| g | = | gravitational acceleration |
| H | = | fin height |
| h | = | heat transfer coefficient |
| k | = | thermal conductivity |
| L | = | fin length |
| N | = | number of fins |
| p | = | pressure |
| Q | = | heat flow rate of the heat source |
| q | = | heat flux of the heat source |
| R | = | gas constant for air |
| Rth | = | thermal resistance |
| r | = | radius size of the microchip |
| rω | = | fin thickness ratio, ω1/ωo |
| T | = | temperature |
| Tavg | = | average temperature of the heat source |
| ωo | = | middle thicknesses of the fin |
| ω1 | = | outer thicknesses of the fin |
| v | = | resultant velocity of airflow |
| ω2 | = | inner thicknesses of the fin |
| u | = | x-component velocity |
| v | = | y-component velocity |
| w | = | z-component velocity |
| β | = | coefficient of thermal expansion short distance between the outer |
| ϵ | = | edge of the fin and the rim of the circular plate |
| μ | = | dynamic viscosity |
| υ | = | kinematic viscosity, μ/ρ |
| ρ | = | density of air |
| Subscripts | = | |
| avg | = | average temperature |
| f | = | fluid (air) |
| s | = | solid |
| ∞ | = | ambient air |