Local nonsimilarity solution for vertical free convection boundary layers.

Abstract

Laminar free convection boundary layer over a vertical flat plate with an exponential variation of surface temperature in viscous fluids is analyzed using the local nonsimilarity method. The present approach takes into consideration the nonsimilarity terms appearing in the momentum and energy equations, which have been unaccounted for previously, in for example, the similarity and the local similarity methods. The governing equations are solved numerically using the Keller-box method, an efficient implicit finite difference scheme. Numerical results are presented in the form of heat transfer rates, local wall shear stress, velocity and temperature profiles. The heat transfer rates and local wall shear stress obtained show good agreement with available nonsimilar solutions. The effects of various values of transformed stream-wise coordinate $\xi$ and Prandtl numbers on velocity and temperature profiles are also presented.