Entropy generation analysis of free convection from a constant temperature vertical plate using similarity solution

Abstract

This paper presents a similarity solution analysis of entropy generation due to heat transfer and fluid flow which has been carried out for laminar free convection from a constant temperature vertical plate in an infinite quiescent fluid. The governing partial differential equations are transformed into a set of ordinary differential equations using similarity variables. So an analytical expression, in terms of entropy generation, entropy generation number, Bejan number and irreversibility distribution ratio are derived using velocity and temperature similarity (exact) solution. The rate of entropy generation is investigated and discussed in details. The results presented by the similarity solution are compared with integral method results. The similarity solution presents more appropriate and correct distribution of entropy generation in boundary layer because more accuracy than integral method. It shows true position of maximum entropy generation and value of it. Also, the result shows that the exact solution minimizes the rate of total entropy generation in the boundary layer compared to integral solution. By introducing group parameter (GP number) which is the ratio of friction entropy to thermal entropy generation, one can recognize that one of the thermal entropy and friction entropy generation is dominated in the boundary layer.