Approximate heat transfer coefficients based on variable thermophysical properties for laminar flow over a uniformly heated flat plate

New heat transfer coefficient approximations are developed for forced laminar flow over a uniformly heated flat plate at zero incidence angle. The development is based on solving the variable property boundary layer equations using a variable property similarity transform that incorporates an adjustable similarity scaling constant. The scaling constants value is iteratively adjusted until the scaled temperature gradient-at-the-wall value is equal to the small temperature difference value. The resulting scaled profiles are nearly congruent. The congruency scaling constant is then approximated in terms of simple functions of the kinematic viscosity and the Prandlt number evaluated at the plate and free stream temperatures. The approximate scaling constants are used to form new approximations for the heat transfer coefficient. The new approximate coefficients are compared to traditional coefficients for four gases and six liquid flows covering the range 0.5 < Pr < 3,000 with large temperature differences.