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In this article, two types of problems are investigated. The flow and heat transfer over: (1) a static flat plate (Blasius problem) and (2) a moving flat plate (Sakiadis problem) are considered. Convective boundary conditions are used to formulate the energy equation. Suitable similarity transform has been employed to reduce the governing nonlinear partial differential equations to a set of somewhat simpler nonlinear differential equations. These equations are then solved numerically by using sixth order Runge–Kutta method. Influences of different emerging parameters on both the problems are presented graphically coupled with comprehensive discussions.

In this paper, we apply a relatively new technique which is called the exp-function method to construct generalized solitary and periodic solutions of Calogero-Degasperis-Fokas (CDF) equation which plays a very important role in mathematical physics, applied and engineering sciences. The suggested algorithm is quite efficient and is practically well suited for use in these problems. Numerical results clearly indicate the reliability and efficiency of the proposed method.