The Coupling of Conduction With Laminar Natural Convection From a Vertical Flat Plate With Arbitrary Surface Heating

A method has been developed for coupling conduction in a solid with natural convection in a surrounding fluid. The problem investigated is that of steady, constant-property, two-dimensional, laminar natural convection from a vertical, heat-conducting flat plate of finite thickness with an arbitrary heating distribution in its surface. Using this method it is possible to predict the variation of temperature in the plate and the velocity and temperature profiles in the boundary layer as a function of the heating distribution and the thermal properties of the plate and fluid. The equations for conduction in the plate and convection in the boundary layer are written in finite difference form, coupled through the common heat flux at the plate-fluid interface, and solved numerically by an iterative technique. Experimental corroboration of the numerical results is provided by measuring temperatures, both with thermocouples and a laser holographic interferometer, along ceramic and glass plates heated by thin film resistance heating elements vacuum deposited on their surface. The results indicate that the degree of coupling between conduction in the plate and natural convection in the fluid is greatly influenced by the plate-fluid conductivity ratio.