The Variable Fluid-Property Problem in Free Convection

Abstract An analysis is made for the variable fluid-property problem for laminar free convection on an isothermal vertical flat plate. For a number of specific cases, solutions of the boundary-layer equations appropriate to the variable-property situation were carried out for gases and for liquid mercury. Utilizing these findings, a simple and accurate shorthand procedure is presented for calculating free-convection heat transfer under variable-property conditions. This calculation method is well established in the heat-transfer field. It involves the use of results which have been derived for constant-property fluids, and of a set of rules (called reference temperatures) for extending these constant-property results to variable-property situations. For gases, the constant-property heat-transfer results are generalized to the variable property situation by replacing β (expansion coefficient) by 1/T∞ and evaluating the other properties at Tr = Tw − 0.38(Tw − T∞). For liquid mercury, the generalization may be accomplished by evaluating all the properties (including β) at this same Tr. It is worth while noting that, for these fluids, the film temperature (with β = 1/T∞ for gases) appears to serve as an adequate reference temperature for most applications. Results are also presented for boundary-layer thickness and velocity parameters.