Finite element computation of magnetohydrodynamic nanofluid convection from an oscillating inclined plate with radiative flux, heat source and variable temperature effects

This work describes finite element computations for radiative magnetohydrodynamic convective Newtonian nanofluid flow from an oscillating inclined porous plate with variable temperature. Heat source/sink and buoyancy effects are included in the mathematical model. The problem is formulated by employing Tiwari–Das nanofluid model, and two water-based nanofluids, copper and alumina, with spherical shaped metal nanoparticles are considered. The Brinkman and Maxwell–Garnetts models are used for the dynamic viscosity and effective thermal conductivity of the nanofluids, respectively. An algebraic flux model, the Rosseland diffusion approximation, is adopted to simulate thermal radiative flux effects. The dimensionless, coupled governing partial differential equations are numerically solved via the finite element method with weak variational formulation by imposing initial and boundary conditions with a weighted residual scheme. A grid independence study is also conducted. The finite element solutions are reduced to known previous solutions in some limiting cases of this investigation and are found to be in good agreement with published work. This investigation is relevant to electromagnetic nano-material manufacturing processes operating at high temperatures where radiation heat transfer is significant.