Second law analysis for a variable viscosity plane Poiseuille flow with asymmetric convective cooling

A second-law analysis of a pressure-driven variable viscosity fluid flow through a channel with asymmetric convective cooling at the walls is investigated. Flow is assumed to be steady, laminar and fully-developed. The effect of heat generation due to viscous dissipation is included. The resulting equations and boundary conditions are solved numerically, by using an efficient numerical shooting technique with a fourth order Runge–Kutta algorithm. The effect of variable viscosity parameter, the Brinkman number and the Biot numbers on the velocity, temperature and entropy generation profiles are provided and discussed with appropriate physical explanations.