Heat Transfer under Magnetohydrodynamics Flow of Nanofluids Past an Inclined Plate with Non Uniform Boundary Conditions

This paper deals with natural thermal convection combined with the mass transfer of nanoparticles occurring in the boundary layers of a nanofluid subjected to magnetohydrodynamics. The wall consists of an inclined plate is considered according to a temperature as well as the volume fraction of the nanoparticles varying as the power of the axial coordinate. In addition, internal heat generation/absorption is taken into account in the mathematical formulation. The governing partial differential equations based on Buongiorno's approach are transformed into a set of ordinary differential equations. The two-level method of no-similarity equations is used to achieve higher accuracy. The whole calculation procedure is implemented using a limit value problem program written according to the Matlab computer language that applies the Lobbato IIIa finite difference method. The obtained results have revealed that small variations of the boundary conditions with the axial coordinate become very significant on the local Nusselt number and the local Sherwood number for nanoparticles. Moreover, a better heat transfer has been obtained with a larger S. However, a trade-off between desired heat transfer rate and level of reduced skin friction should be scheduled.