Entropy generation and heat transfer in boundary layer flow over a thin needle moving in a parallel stream in the presence of nonlinear Rosseland radiation

Abstract

Analysis of entropy generation and heat transfer in the boundary layer flow over a thin needle moving in a parallel stream is performed in this work. Energy dissipation and nonlinear radiation terms are incorporated in the energy equation. It is assumed that the free stream velocity u∞ is in the direction of positive x−axis (axial direction) and the thin needle moves in the direction of free stream velocity. The problem is self-similar in the presence of viscous dissipation and non-linear Rosseland thermal radiation. The reduced self-similar governing equations are solved numerically using shooting and fourth order Runge-Kutta method. The expressions for dimensionless volumetric entropy generation rate and Bejan number are also obtained by selecting suitable similarity variables. The effects of the Eckert number, heating parameter, radiation parameter, Prandtl number, velocity ratio parameter and dimensionless size of a thin needle are described graphically in detail. The analysis reveals that the entropy generation decreases by decreasing the size of the thin needle. Entropy generation number increases with the increasing values of the Eckert number, Prandtl number and the temperature parameter. Moreover, it is observed that the Bejan number decreases by increasing the thermal radiation parameter. Validation of present analysis is performed by comparing the obtained results with those available in the existing literature and found a very good agreement.