Heat transfer in asymmetric convective cooling and optimized entropy generation rate

Abstract

The steady viscous flow between two infinite parallel planes, is used to illustrate the possibility of minimizing the global entropy generation rate by cooling the external surfaces convectively in an asymmetric way. The flow is generated by both an axial pressure gradient and the uniform motion of the upper surface (generalized Couette flow). The temperature field is determined using boundary conditions of the third kind. The analytic expressions for the velocity and temperature fields of the fluid are used to calculate the global entropy generation rate explicitly. In dimensionless terms, this function depends on the dimensionless ratio of the two possible velocity scales (characterized by the magnitudes of the pressure gradient and the upper surface velocity), the dimensionless ambient temperature and the convective heat transfer coefficients (Biot numbers) of each surface which, in general, are not assumed to be the same. When the Biot numbers for each surface are equal, the entropy generation rate shows a monotonic increase. However, when the Biot numbers are different this function displays a minimum for specific cooling conditions. Besides, we calculate the local Nusselt number at the upper wall for minimum entropy generation conditions.