Heat transfer and binary diffusion in variable property free convection flows

Abstract

Variable property free convection stagnation flow and free convection on a vertical flat plate are analyzed for the case of simultaneous momentum, heat and binary mass transfer with thermodynamic coupling. The helium-air and hydrogen-air systems are considered in detail. A simplified general treatment of diffusion thermo effects is developed and applied to obtain approximate but accurate expressions for evaluating heat-transfer rates and adiabatic wall temperatures. This method shows why the driving force based on ( T w − T aw ) can be used to correlate heat-transfer results for situations where diffusion thermo is important. It is significant that the method also provides a simple error estimate for the correlation obtained by using the adiabatic wall temperature. It is found that free convection stagnation flow and free convection on a vertical plate are very similar in nature when compared on the proper basis. This seems interesting since, in the vertical plate case one employs the boundary-layer approximations whereas the stagnation flow represents an exact solution of the Navier-Stokes equations. A correlation of the σ function, which enables one to calculate heat-transfer rates for both free convection configurations studied here, both hydrogen and helium mixtures with air, and over the range of T w / T e in which diffusion thermo is important, is given and appears to be accurate enough for almost all engineering purposes.