Laminar Natural Convection

The problem of laminar, natural convection flow over a vertical f rus tum of a cone is treated in this paper. The thermal boundary condition at the wall include both the constant wall temperature and the constant wall heat flux cases. The governing differential equations are solved by a combinat ion of quasilinearization and finitedifference methods. Numerical solutions are obtained for a range of Prandtl numbers . The solutions are found to approach to the solutions for a full cone if the flow is far downst ream or the radius of the cross-section at the leading edge is very small. Introduction In a recent study of the effect of slenderness on the natural convection flow over a slender frustum of a cone [1, 2], the authors found that the problem of natural convection flow over a frustum of a cone without transverse curvature effect (i.e., large cone angles when the boundary layer thickness is small compared with the local radius of the cone) has not been treated in the literature, even though the problem for a full cone has been treated quite extensively [3-11] . It is therefore the purpose of this paper to present an analysis of this problem (see Fig. 1) when the thermal boundary condition on the wall is constant either in the wall temperature or in the wall heat flux. The physical model and the coordinate system are shown in Figure 1. Similar to the analysis of the natural convection flow over a slender circular cylinder by Sparrow and Gregg [12], the boundary layer is 409 Applied Scientific Research 35 (1979) 409-421. All rights reserved. Copyright © 1979 Martinus Nijhoff Publishers, The Hague~Boston~London. 410 T. Y. NA AND J. P. CHIOU