Prediction of the Natural Convective Heat Transfer From a Horizontal Heated Disk

Abstract

A thin-layer approximation is applied to the laminar momentum and energy equations governing the natural convection above an isothermal heated disk in air. Using the Boussinesq assumption the equations are nondimensionalized in terms of a stream function, pressure and temperature difference. The variables are expanded in a series solution and the resulting set of equations are solved numerically. The solution is cast in terms of the nondimensional radial position and the disk Grashof number. These two parameters are shown to define the outer boundary conditions which are uniquely determined from a point source solution. The outer velocity boundary condition is shown to decrease in relative magnitude as the disk Rayleigh number increases. Beyond a Rayleigh number of approximately 106 the outer flow may be ignored in calculating the disk heat transfer rate. The radial variation of the outer flow is to the – 1/5 power measured inward from the leading edge. This is a result of the scaling difference of the thin layer flow, and the outer, plume entrainment flow. The local heat transfer rate is increased by including the entrainment effects on the outer flow and varies as the Grashof number to the power (1/5–ε), where ε is a decreasing function of inward radial distance.