Buoyancy driven convection of nanofluids in an infinitely long channel under the effect of a magnetic field

In this paper, we have proposed a theoretical analysis to investigate buoyancy driven convection of nanofluids in an infinitely long channel under superimposed magnetic field. We derive closed form analytical solutions for the magnetohydrodynamic flow and temperature field under two distinctive wall boundary conditions. Proceeding further ahead, we also present an analysis for the total entropy generation due to magnetohydrodynamic fluid friction and heat transfer irreversibilities. Utilizing water based Al2O3 nanofluids, results are shown for the following range of conditions as 0 ⩽ Ha ⩽ 50, 0 ⩽ ϕ ⩽ 4% and 103 ⩽ Gr ⩽ 105. It is revealed that magnetohydrodynamic effect reduces flow strength. Likewise the case of the velocity profiles, magnetic effect reduces the magnitude of temperature distribution. Total entropy generation shows decreasing trend when the volume fraction of the nanofluids is increased. Increasing nanoparticle size results in increasing total entropy generation and the Bejan number.