Mathematical model for velocity and temperature of gravity-driven convective optically thick nanofluid flow past an oscillating vertical plate in presence of magnetic field and radiation

Analytic expression for unsteady hydromagnetic boundary layer flow past an oscillating vertical plate in optically thick nanofluid in presence of thermal radiation and uniform transverse magnetic field is obtained. The Rosseland diffusion flux model is adopted to simulate thermal radiation effects. The momentum and energy conservation equations are made dimensionless and analytic solution is obtained using the Laplace transform. The results for velocity and temperature are obtained and plotted graphically. It is found that the velocity of the nanofluid increases with radiation parameter Nr, Grashof number Gr and time while decreases with increase in magnetic field and Prandtl number Pr. Temperature of nano-fluids increases with time while decrease with increase in Nr and Pr.