Heat-Transfer from a Vertical Flat Surface by Laminar Free-Convection : The cases where the physical constants of fluids depend on the temperatures and the surface has an arbitrary temperature distribution in vertical direction

Abstract

It was studied that physical constants for what temperature should be taken in arranging the experimental data on heat-transfer coefficients. From the numerical calculations made on water and ethylene-glycol, were given the following conclusions. Prandtl number, kinematic viscosity and thermal conductivity ;(the surface temperature)-1/4 (temperature difference between the surface and the fluid). Coefficient of cubical expansion ; the mean coefficient of cubical expansion to be made up to the arithmetic mean of the surface temperature and the fluid temperature with the fluid temperature as basis. For the second problem we derived from the momentum and energy equations an ordinary differential equation, which would give a solution for any Prandtl number and an arbitrary temperature difference distribution. The equation is soluble elementarily in the case where Pr→∞. From the several examples of numerical calculations were derived the following conclusions.(1) There is no effect of Pr upon the correlation between surface temperature distribution and distribution of heat transferred.(2) When the temperature at an approximately half height is taken as a typical temperature, the total heat transferred is generally equal to the value in the case of uniform surface temperature.