Variational entropy generation minimization of a channel flow: Convective heat transfer in a gas flow

Variational methods are used to optimize convective heat transfer in a channel gas flow. The minimization of a functional objective combining the rate of total entropy generation in the channel on the one hand and the total viscous dissipation on the other hand results in velocity and temperature fields. A weighting factor allows varying the relative importance of these two terms and a virtual body force field is applied to vary the velocity field pattern via the momentum equation source term. The result is velocity configurations that minimize the objective functional. This study shows that the velocity fields determined by the optimization process effectively lead to a reduction in the entropy generation rate in the flow as well as a reduction in the temperatures of the heated plate. In addition, the value of the weighting factor triggers the transition from slightly to highly perturbed velocity and temperature fields when compared to a non-optimized flow. The heat transfer enhancement is assessed and the increase of the Nusselt number is put in perspective with the reduction of the entropy generation rate and the increase of viscous friction. The results could be used to design passive technologies for enhancing wall-to-fluid heat transfer.