A general analysis has been developed to study the flow and heat transfer characteristics of an unsteady laminar mixed convection on a continuously moving vertical slender cylinder. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a nonsimilar transformation and the resulting system of nonlinear coupled partial differential equations is then solved by an implicit finite difference scheme in combination with the quasilinearization technique. © 2005 Elsevier Ltd.