Series Solution of Nonlinear Partial Differential Equations Arising In Fluid Flow Problems

Abstract

This work consists of solving nonlinear PDEs arising in nanofluid flow problems in boundary newlinelayer region for different geometry. Our main aim is to obtain analytical solutions and newlinecompare them with numerical solutions. We would like to restrict ourselves to nonlinear newlinePDEs obtained in fluid flows over a flat plate with stretching sheets with/without the external newlinemagnetic field. PDEs are solved mainly by method of series solutions called homotopy newlineanalysis method (HAM) and we discuss the convergence of solution by calculating convergence newlineparameter h. Using Domb-sykes we get the radius of convergence of solution by newlinecalculating convergence of the obtained solution. newlineNonlinear Partial Differential Equations are very difficult to analyse by solving but approximate newlineanalytical solutions can be obtained by different methods such as general Power newlineseries, Homotopy analysis, Dirichlet series method etc. Fluid dynamics deals with flow newlineof fluids in potential and boundary layer region which is modelled into nonlinear partial newlinedifferential equations. These nonlinear partial differential equations can be reduced to nonlinear newlineordinary differential equations by using suitable transformations and approximate newlineanalytical solutions can be obtained. newline