Entropy generation in viscous flow due to generalized exponential wall velocity and temperature

Abstract

The study of entropy generation in convective transport processes is of current interest. For the better understanding of this phenomenon it is preferred to investigate it for those flows which admit an exact solution. This is the reason that majority of the published literature, concerning entropy generation analysis, has been done for the self-similar flows. Particular to the stretching sheet flows, which do also have important applications in industry, entropy production analysis is of particular importance. In this regard a two dimensional boundary layer flow due to an exponentially stretching wall (following generalized exponential form) has been considered in this study for the analysis of entropy generation. The stretching wall velocity and the wall temperature function have so properly been chosen that an similarity solution is possible. The modeled, equations are converted to ordinary differential equations by employing appropriate similarity transformations. These equations are solved numerically by using bvp-4c implemented in Matlab. To implement this method, differential equations are converted to set of first order equations and are solved. The problem has been analyzed for the heat transfer phenomenon and the entropy generation. The dimensionless form of entropy generation number requires m ≡ n for a similarity solution to exist. The enhancement is observed in the Nusselt number by enhancing the values of m, n, and Pr. Eventually, the entropy generation at the wall is maximum for increasing values of and However, for such a large values of of and the entropy profile reduces rapidly in the boundary layer thus avoiding a farther speed of entropy in the boundary layer. It is also noticed that to minimize the entropy generation across the boundary layer and also to get an enhanced rate of heat transfer some higher values of and must be chosen.