Mathematical modelling of boundary layer flow and heat transfer in forced convection

Abstract

A mathematical model for the boundary layer flow and heat transfer in forced convection is developed. Boundary layer is a narrow region of thin layer that exists adjacent to the surface of a solid body where the effects of viscosity are obvious, manifested by large flow velocity and temperature gradient. The concept of boundary layer was first introduced by Ludwig Prandtl (1875-1953) in 1905. The derivation of both velocity and temperature boundary layer equations for flow past a horizontal flat plate and semi-infinite wedge are discussed. The velocity and temperature boundary layer equations are first transformed into ordinary differential equations via a similarity transformation. The differential equations corresponding to the flow past a horizontal flat plate and a semi-infinite wedge are nonlinear and known respectively as the Blasius and the Falkner-Skan equation. The approximate solutions of these equations are obtained analytically using a series expansion, namely the Blasius series and an improved perturbation series using the Shanks transformation. The solutions presented include the velocity and temperature profiles, the skin friction and the heat transfer coefficient.