Effect of Wall Conduction on Natural Convection over a Vertical Slender Hollow Circular Cylinder

Abs t rac t . An analysis is made of the laminar natural convection of incompressible fluids over a slender, hollow circular cylinder with the inner surface at a constant temperature of Tb. The temperature of the outer surface must be solved from the coupled conduction of the cylinder and the natural convection of the fluid over the cylinder. The objective of this paper is to investigate the effect of conduction on the heat transfer characteristics of the natural convection boundary layer of the fluid. A wall conduction parameter, p, is introduced which is a measure of the heat conductivities of the solid and the fluid and the thickness of the cylindrical shell. The governing differential equations, being non-similar, are solved by a finite-difference method. Numerical results are generated for a series of values o f p ' s and Prandtl numbers. The present analysis shows that the overall effect of conduction of the cylinder is to reduce the heat transfer. Any calculation of the heat transfer rate based on the assumption of a constant wall temperature overestimates this quantity. The effect increases for large values of p.