Ch. 1 comprises the motivation to the study, the description and the historical background of the problems considered in other chapters. Ch. 2 includes all basic definitions, the governing equations and techniques that are exploited in the rest of dissertation. In ch. 3, the natural buoyancy effect on 2nd-grade fluid along a vertical plate is analyzed. The asymptotic method in conjunction with Pade´ approximation, the LNS local nonsimilarity solution method and Keller Box technique are exploited to get the solution. Study of the natural buoyancy for 2nd -grade flow along a heated vertical plate with variable heat flux is considered in ch 4. The influence of dissipation term on natural buoyancy is discussed in ch. 5 for a second grade fluid along flat vertical plate. Ch 6 is mainly composed of buoyancy flow between two expanding/contracting vertical surfaces with variable temperature on both walls. Ch 7 is to analyze the natural buoyancy of second grade fluid in a deformable channel with variable heat flux at both walls. Analytic solutions of nonlinear problem arising in chapters 6 and 7 are developed by HPM. The numerical results are also obtained using method of parallel shooting.