Unsteady mixed convection flow over a vertical slender cylinder under the combined effects of buoyancy force and thermal diffusion with injection/suction has been studied where the slender cylinder is inline with the flow. The unsteadiness is introduced by time dependent free stream velocity of the fluid. The effect of surface curvature is also taken into account, especially for the applications such as wire and fiber drawing, where accurate predictions are desired. The governing boundary layer equations along with the boundary conditions are first converted into dimensionless form by a non similar transformation, and then resulting system of coupled nonlinear partial differential equations is solved by an implicit finite difference scheme in combination with the quasilinearization technique. The effects of various parameters on velocity, temperature profiles, on skin friction coefficient and heat transfer rate at the wall are reported in the present study.

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