General solution of Casson fluid past a vertical plate subject to the time dependent velocity with constant wall temperature

Unsteady free convection flow of Casson fluid over an unbounded upright plate subject to time dependent velocity U o f ( t ) with constant wall temperature has been carried out. By introducing dimensionless variables, the general solutions are obtained by Laplace transform method. The solution corresponding to Newtonian fluid for γ → ∞ is obtained as a limiting case. Exact solutions corresponding to (i) f ( t ) = f H ( t ) , (ii) f ( t ) = f t a , a > 0 (iii) f ( t ) = f H ( t ) c o s ( ω t ) are also discussed as special cases of our general solutions. Expressions for shear stress in terms of skin friction and the rate of heat transfer in the form of Nusselt number are also presented. Velocity and temperature profiles for different parameters are discussed graphically.