A numerical study of the effect of thermal radiation on the forced air cooling of low heat flux electronic chips mounted on one side of a vertical channel

A numerical study of steady, laminar, two-dimensional combined convection and radiation air cooling of four identical rectangular electronic chips (made of silicon) mounted on the left side of a vertical channel is presented in this paper. The conduction in the walls (composed of copper-epoxy) as well as in the chips in which energy is generated due to joule heating is also taken into account. The outside walls are treated as insulated. At the channel inlet the velocity is uniform. The stream function-vorticity-temperature approach with the finite-difference-based methodology has been applied to obtain flow and thermal fields in the fluid, temperature distributions in the chips and the walls, and pressure distribution in the fluid. The parameters varied to study the effect of radiation on the cooling of the silicon chips are: Reynolds number, Grashof number, emissivity of the chips and of the inside wall surfaces, chip height, chip width, and the gap between the successive chips. The energy generation rate is such that it gives rise to average heat flux in the chips in the range of 281.25 W/m
²
to 1.875×10
³
W/m
²
, which is relatively low. The results reveal that there is a 14.28% drop in the dimensionless maximum temperature of the chips at Re = 500, Gr = 8.65 × 105 as compared to the case when the radiation effect is not considered. The increase in emissivity of the chips from 0.1 to 0.9 results in considerable rise in the temperature of the wall opposite to the chips accompanied by a small drop in the chip temperature. The pumping power increases by 82.69% when the chip height is increased from 0.3 to 0.6. However, increasing the chip width results in rise in pumping power by 30%. There is only a marginal drop in pumping power requirement when radiation is considered in the modeling. The novelty of this work lies in the use of realistic chip and wall materials, investigation of the effect of various geometrical parameters, calculation of pressure distribution and pumping power, and reporting of radiation effect on the walls opposite to the chips. This is only work so far which solves the flow, thermal and pressure fields in electronics cooling using stream function-vorticity-temperature approach and applies Gebhart's absorption factor method for calculation of radiation exchange.