Comparative studies on constructal optimizations of discrete heat generation components based on entransy dissipation minimization and maximum temperature minimization

Abstract

A three-dimensional (3D) turbulent heat dissipation model of cylindrical discrete heat generation components is established on a conductive basis. The whole solid section is set in a square channel with adiabatic walls, and the components, cooled by clean air flowing through the channel, are arranged in a line with equal spacings. The influences of the heat conductivities of the components, intensities of heat sources and velocity of fluid flow on the maximum temperature (MT) of components, the equivalent thermal resistance (ETR) based on entransy dissipation of the heat dissipation system, and the averaged Nu number are investigated with the constructal theory considering variable properties, compressibility and viscous dissipation of air. The total heat generation rate and the total heat conductivity of heat sources are fixed as the constraint conditions. The circumstances in which heat generation rates and heat conductivities of heat sources are unequal are considered. The results show that for the fixed total heat generation rate of heat sources, despite MT or ETR that is taken as the performance index for thermal design, there exists an optimal intensity distribution of heat sources for the best thermal performance of the system. In fact, for different objectives, the optimal intensity distributions of heat sources are corresponding to the best match between the distributions of heat sources and the distributions of temperature gradient. There are different optimal distributions for different velocities of the fluid flow and different optimization objectives. Besides, the averaged Nu number increases with the increase of intensity difference in heat sources, which means that the convective heat transfer is enhanced, but this phenomenon is relatively weak when the velocity of fluid flow is low. For the fixed total heat generation rate of heat sources, when the intensities of heat sources are equal and the thermal conductivities of heat sources are lower than that of the conductive basis, increasing heat conductivities of the heat sources can evidently improve thermal performance of the system; the MT can be lowest when the conductivities of heat sources increase along the fluid flow; and the ETR is lowest when the conductivities of heat sources are equal. Both the MT and the ETR decrease with the increasing velocity of fluid flow. The results can provide some theoretical guidelines for the practical thermal design of the electronic components with different materials and different heat generation rates.