Effect of secondary flows due to buoyancy and contraction on heat transfer in a two-section plate-fin heat sink

摘要

The effect of buoyancy forces on laminar heat transfer inside a variable width plate-fin heat sink is numerically analyzed: the configuration under investigation comprises an array of rectangular fins, the number of which is doubled at the streamwise middle length of the plate, leading to a stepwise reduction in the respective channel width and hydraulic diameter. The mixed convection problem is thoroughly examined for Archimedes numbers in the range Ar = 1.32-5.82 and Reynolds numbers, based on the channel hydraulic diameter before the stepwise reduction, in the range Re = 559-667, under the thermal boundary condition of axially constant heat flux. It is illustrated that the secondary flow pattern emanating from the flow contraction and manifested through the presence of a pair of counter-rotating horseshoe vortices and a pair of counter-rotating (fin) sidewall vortices interacts with longitudinal rolls created by buoyancy forces. In fact, the lower horseshoe vortices that are co-rotating with the buoyancy-induced rolls are significantly enhanced in magnitude and cause intense fluid mixing in the vicinity of the channel bottom wall, with a substantial distortion of the temperature field. The numerical results indicate that the joint action of the buoyancy-induced rolls and the combined secondary flow pattern has a beneficial impact on the heat sink thermal performance, a fact quantified through the circumferentially-averaged local Nusselt number distributions. The effect of the top lid thermal conductivity on the heat transfer inside the heat sink is also discussed. Finally, a comparative investigation is conducted between the present variable-channel-width configuration and two configurations of fixed-width heat sink designs. The comparative results reveal that the introduction of stepwise channels leads to superior heat transfer performance, i.e. lower values of the total thermal resistance with mitigated pressure drop penalty and increased temperature uniformity on the cooled surface.