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In a recent paper by Makinde (Thermal Science, 2011, Vol. 15, Suppl. 1, pp.   S137-S143.) the effect of thermal buoyancy along a moving vertical plate with   internal heat generation was considered. The plate thermal boundary condition   was a convective condition with a heat transfer coefficient proportional to   x-1/2 . The fluid thermal expansion coefficient was proportional to 1-x and   the internal heat generation was assumed to decay exponentially across the   boundary layer and proportional to x-1 in order that the problem accepts a   similarity solution. In the present work, the same problem without heat   generation is considered, with constant heat transfer coefficient and   constant thermal expansion coefficient which is more realistic and has much   more practical applications. The present problem is non-similar and results   are obtained with the direct numerical solution of the governing equations.   The problem is governed by the Prandtl number, the non-dimensional distance   along the plate and a convective Grashof number, which is introduced for the   first time. It is found that the wall shear stress, the wall heat transfer   and the wall temperature, all increase with increasing distance and the wall   temperature tends to 1. The influence of the convective Grashof number is to   increase the wall shear stress and the wall heat transfer and to reduce the   wall temperature

Non-similar solutions for natural convection from a moving vertical plate with a convective thermal boundary condition