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The partial differential equations governing compressible boundary layer flow problems cannot be solved as it is, many authors have solved these problems by reducing to ode’s. Falkner-Skan transformations will reduce the governing partial differential equations in to two non-linear partial differential equations. These equations are solved by HAM and the convergence of this is studied by using the Domb Sykes plot. The effect of suction and injection are studied on the velocity and temperature distribution and are depicted in a graph. It is also observed that for large values of suction and injection flow separation exists in boundary layer region. Pade approximation is also applied to HAM series solution which helped us to identify the singularities. Convergence is verified by plotting h curve for all the three cases suction, injection, and no suction for both velocity and temperature. Keywords-Compressible boundary layer flow, Homotopy analysis method, Domb Sykes plot, Pade approximations, h-curve, Region of convergence, Suction, Injection, Falkner-Skan transformations, Flow separation. Study Of Compressible Fluid Flow In Boundary Layer Region By Homotopy Analysis Method 029 0, = )] , ( [ y x u N (1) where ) , ( y x u is an unknown function, x and y are two independent variables. Liao [17] in his work in 1997 introduced a non zero auxiliary parameter h to construct a two-parameter family of equations and it is called as zeroth-order deformation equation   )], : , ( [ = ) , ( ) : , ( ) (1 0 q y x qhN y x u q y x L q(2) where ) : , ( q y x  is an unknown function, 0  h is an auxiliary parameter which provides us a convenient way to guarantee the convergence of homotopy series solution, q is the embedding parameter, L is an auxiliary linear operator and ) , ( 0 y x u is an initial guess. When 0 = q , we have   0, = ) , ( 0) : , ( 0 y x u y x L   (3) According to the linear property of L i.e 0 = (0) L (Theorem-4.17) [18] and using the fact that ) , ( 0 y x u satisfy the initial conditions which is shown in [19], [20] it is obvious that ), , ( = 0) : , ( 0 y x u y x  (4) When 1 = q , we have 0, = )] : , ( [ q y x hN  (5) here 0  h , we will get an equivalent equation which is exactly same as the original equation. Then the Maclaurin series solution is obtained by , ) , ( ) , ( = ) : , ( 1 = 0 m m m q y x u y x u q y x(6) 0, = at ) : , ( ! 1 = ) , ( q q q y x m y x u m m

Study of compressible fluid flow in boundary layer region by homotopy analysis method