In the actual design circumstances, the radiation effect on the cooling performance of the extended surfaces must be taken into consideration. The central goal of this paper is to design the constructal architecture of a T-Y shaped assembly of fins by incorporating the thermal radiation with convection heat transfer. Our motivation in selecting a T-Y shaped assembly of fins is that the so-called assembly is of more cooling performance among the other shapes according to the literature. The temperature field and the peak temperature (hot spot) are calculated from a numerical approach based on finite element method. The peak temperature is minimized by manipulating the geometry of the assembly regarding the constraints of space and materials. A comparative study is executed among the present work and the published work. The comparison revealed that although the optimized geometry is approximately independent of the heat transfer mechanism, the hot spot temperature can be affected when the finned surfaces are exposed to thermal radiation in addition to convection. This issue is more pronounced when the emissivity of the finned surfaces is higher in comparison with the convection heat transfer coefficient.
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