The laminar free convection problem for a flat plate which is placed vertically in air is treated, taking into account the variation of properties of air which depends on temperature. Previously the author solved the same problem by perturbation theory using ε=(T
0-T
1)/T
2 as a small parameter, where T
0 and T
1 are the absolute Temperatures of the surface and the surrounding air, respectively. In this reports the regorous solution for larger value of ε(=2.0 and 4.0) by successive approach method is presented. The film coefficient can be expressed as follows : α=α
ε=0(1-0.055ε) 0<ε<4.0
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