Laminar mixed convection over horizontal flat plates with power-law variation in surface temperature

Abstract

An analysis is performed to study the heat transfer characteristics of laminar mixed convective boundary-layer flow over a semi-infinite horizontal flat plate with non-uniform surface temperatures. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A nonsimilar mixed convection parameter χ and a pseudo-similarity variable η are introduced to cast the governing boundary layer equations and their boundary conditions into a system of dimensionless equations which are solved numerically by a weighted finite-difference method. The mixed convection parameter χ is chosen so that χ = 0 corresponds to pure free convection and χ = 1 corresponds to pure forced convection. Numerical results are presented for Prandtl numbers of 0.1, 0.7, 7 and 100 and representative values of the exponent n for the power-law variation in wall temperature. The heat transfer results are compared with existing correlations for the uniform wall temperature case and new correlations are derived for the general case of power-law wall temperature variations. It is found that an increase in the Prandtl number and exponent value n increases the local heat transfer rate.