T-shaped assembly of fins with constructal entransy dissipation rate minimization

T-shaped assembly of fins is optimized by adopting an analytical method and taking the minimum mean thermal resistance in terms of entransy as optimization objective. The optimal construct of T-shaped assembly is obtained and compared with the optimal construct with maximum temperature difference minimization. The results show that for the two optimization objectives the thicknesses of the optimized fins are almost equal, but the lengths are different obviously: the former length of the elemental fin is almost half the value of the latter length, and the former length of the first-order fin is almost twice as large as the latter length. Compared with the latter optimal construct, the dimensionless mean thermal resistance corresponding to the former optimal construct decreases by 16.4%, and the corresponding dimensionless maximum thermal resistance increases by 9.74%. Both the minimizations of the EDR and the maximum temperature difference (MTD) should be combined to consider the efficiency and the temperature limitation simultaneously for designing the fins.