Entropy Generation Analysis of a Flat Plate Boundary Layer with VariousSolution Methods

Abstract

Steady state boundary layer equations over a flat plate with a constant wall temperature can be solved by an integral solution (with three profiles for velocity and temperature), a similarity solution (exact) and a Blasius series solution. The analysis of entropy generation for each solution is carried out. The results show that the exact solution (similarity) is the one that minimizes the rate of total entropy generation in the boundary layer. Then, the Blasius solution has the least entropy generation of all. The bell-shaped profile (sinus profile) in the integral solution generates less entropy than the piecewise linear profile, consequently. So, with this method, if the exact solution for a specified problem were not available, one could evaluate the approximate solutions and recognize the best one among them. By introducing a new non-dimensional number (Ej number), which is the ratio of thermal entropy to friction entropy generation, one can recognize which of them is dominant in the boundary layer. Also, it is observed that variation of the total entropy generation is the same as the variation of boundary layer thickness, so, the non-dimensional total entropy generation for various solutions is constant.