A Theoretical Analysis of Laminar Forced Flow and Heat Transfer About a Rotating Cone

Abstract

The present paper presents analytically a method of attack on the problem of laminar forced flow and heat transfer about a rotating cone. The nonsimilar nature of the general problem requires that separate consideration be given to a slow rotating cone and a fast rotating cone, depending on the relative magnitude of the rotating speed with respect to the free-stream velocity. The Mangler transformation first reduces the problem of a slow rotating cone to one of wedge flow with a transverse velocity component. The problem is then solved by a perturbation scheme which uses the solution of wedge flow as the zeroth-order solution. The case of a fast rotating cone is solved by a series-expansion scheme which gives successive corrections to the zeroth-order solution, i.e. the solution of a rotating disk in a quiescent fluid. The zeroth-order and first-order equations for both cases are given in the present work, together with the numerical results for the special case of a cone of about 107-deg cone angle. The first-order results in both cases are shown for the drag and torque coefficients, and the local Nusselt number. Higher-order results can be obtained according to the present analysis. The effect of cone angle on the flow and heat-transfer characteristics is indicated by the comparison between the results of the 107-deg cone and those of the disk, i.e., the 180-deg cone.