Abstract
Abstract Unsteady magnetohydrodynamic natural convection flow with Newtonian heating and constant mass diffusion over an infinite vertical plate that applies an arbitrary time-dependent shear stress to a viscous optically thick fluid is studied in the presence of a heat source. Radiative effects are taken into consideration and exact solutions for the dimensionless velocity and temperature are established under Boussinesq approximation. The solutions that have been obtained, uncommon in the literature, satisfy all imposed initial and boundary conditions and can generate exact solutions for any motion problem with technical relevance of this type. For illustration, a special case is considered and the influence of pertinent parameters on the fluid motion is graphically underlined.
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