Optimal geometry of L and C-shaped channels for maximum heat transfer rate in natural convection

The present paper documents the geometric optimization of L and C-shaped channels in laminar natural convection subject to global constraints. The objective is to maximize the heat transfer rate from the hot wall to the coolant fluid. Three different configurations were considered: (i) an L-shaped asymmetric vertical heated channel with an adiabatic horizontal inlet, (ii) an asymmetric vertical heated channel with an adiabatic vertical outlet, and finally, (iii) a C-shaped vertical channel with horizontal inlet and outlet. The two first configurations are free to morph according to two degrees of freedom: the wall-to-wall spacing and inlet (or outlet) height. The third configuration is optimized with respect to the wall-to-wall spacing, and the heights of the inlet and outlet ports. The effect of the inlet or outlet horizontal adiabatic duct lengths is also investigated. The optimization is performed numerically by using the finite element technique, in the range 105 < Ra < 107 for Pr = 0.7, where Ra is the Rayleigh number based on a fixed total height H of the channel. The numerical results show that optimization is relevant, since the three degrees of freedom considered have a strong effect on the heat transfer delivered from the hot wall to the fluid. The optimal geometric characteristics obtained numerically (i.e., optimal spacing, optimal height and lengths) are reported and correlated within a 7.5% maximal disagreement range.