Effect of Bejan and Prandtl numbers on the design of tube arrangements in forced convection of shear thinning fluids: A numerical approach motivated by constructal theory

In this work, the effects of the pressure drop (i.e. the Bejan number in dimensionless term) and of the Prandtl number have been investigated with reference to optimal geometries for maximizing the heat transfer density under forced convection of shear thinning fluids. Constructal Design associated with Design of Experiments and Response Surface methodologies have been employed to search computationally for the optimals. More specifically, after having fixed the power law index value, n, equal to 0.4, we studied the effect of the Bejan number, Be, ranging from 104 to 105 (for Pr = 1) and the effect of the Prandtl number, Pr, ranging from 1 to 10 (for Be = 105) on the maximum dimensionless heat transfer density. The optimal geometries here detected differ much from those referred to Newtonian fluids, as a consequence of the non-linear stress behavior with respect to strain rate. We observed that the optimal aspect ratio of the elliptical tubes, ropt, highlights different (opposite) behaviours with the augmentation of Be and Pr: while ropt deacreases as Be increases, it augments with higher Pr, suggesting that for flows characterized by thermal diffusivity the tubes should be more slender horizontally for better heat transfer performance. In the meantime, assigned ropt, the dimensionless optimal distance between tubes, S˜0, proved to be practically indepent of all the tested values of Bejan number and Prandtl number.