Abstract
To solve the thermal convection problem, the author adopted the Cowley-Levy method. The fundamental equations are equation of motion, energy equation, and equation of continuity. This method consists in the expansion of the non-linear terms to the infinite power series of the parameter. In this paper, the author converts these equations to non-dimensional form and expands the stream function and temperature. The common parameter is Grashof number denoted by the hot surface. Each term of the two sets of series must satisfy the following equations. For stream function ⊿⊿ψ_n=f_n(x.y), and for temperature ⊿θ_0=0, ⊿θ_n=n(x.y) n=1,2,……… The former is similar form to the equation of deformation of the plate under lateral load, and the latter are Laplace and Poisson's equations. Then, each term can be calculated successively. In the numerical computation the finite difference method is used. From the calculation of a few terms of each series, the radius of convergence is considered less than Gr=5,000. So, it is very unsatisfactory. In addition the pressure distribution and the local heat transfer coefficient expressed by Nusselt number, are calculated at the boundary.
