الفهرس 
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Abstract
In this thesis the group theoretic method is used to analyze the problem of laminar boundary layer free convection on vertical surfaces immersed in isothermal fluid. Two geomctries are considered: the vertical flat plate and the vertical cilcolar cylinder.
The application.of two - parameter transformation group reduces the system of governing partial differential equations with the boundary conditions to a system of ordinary differential equations with the appropriate boundary conditions. All possible classes of surface temperature distributions which yield this reduction are deduced. For each class the similarity representation is obtained. The system of equations is solved numerically. The boundary layer characteristics as well as the heat transfer results are obtained. The results are illustrated in figures and tables and compared with those of other authors when available.
The effect of the parameters controlling the surface temperature variation is discussed. Also the effect of the Prandtl number is confirmed.