Natural Convection Along Slender Vertical Cylinders With Variable Surface Temperature

Abstract

Natural convection in laminar boundary layers along slender vertical cylinders is analyzed for the situation in which the wall temperature Tw(x) varies arbitrarily with the axial coordinate x. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a nonsimilar transformation and the resulting system of equations is then solved by a finite difference method in conjunction with the cubic spline interpolation technique. As an example, numerical results were obtained for the case of Tw(x) = T∞ + axn, a power-law wall temperature variation. They cover Prandtl numbers of 0.1, 0.7, 7, and 100 over a wide range of values of the surface curvature parameter. Representative local Nusselt number as well as velocity and temperature profiles are presented. Correlation equations for the local and average Nusselt numbers are also given.