Heat transfer and entropy generation in a MHD Couette–Poiseuille flow through a microchannel with slip, suction–injection and radiation

Flow, heat transfer and entropy generation in a vertical microchannel made of two parallel porous plates (the injection plate kept at rest while the suction plate is moving in upward/downward direction) under the combined action of buoyancy force and transverse magnetic field are studied. Variable pressure gradient (favorable/adverse) due to Couette–Poiseuille (C–P) flow is considered here. This is one of the fundamental problems of applied science and engineering. Slip conditions for the velocity at plates are implemented for both moving-plate directions and pressure gradients with the help of classical C–P flow. The basic equations are solved numerically by using Runge–Kutta–Fehlberg method along with shooting technique. Numerical results are in concordance with previously published results for specific cases. The present results are frequently compared with those of the classical C–P flow. Influence of operational parameters (plate movement, pressure gradient, injection–suction rate, slip length, Grashof Number, temperature ratio (between hotter to colder side) and viscous dissipation effect) on the flow and heat transfer characteristics (velocity, temperature, Nusselt number (Nu) distribution, entropy generation and Bejan Number) are investigated here. An effort is made to search singularity in the variation of Nu with some parameters, and find the parameters’ values at which the global entropy is minimally generated in the channel. Finally, a critical analysis is conducted on the individual contribution of irreversibilities due to heat flow, fluid friction and Joule heating to the total entropy generation.