Int. J. of Appl. Math and Mech. 8 (6): 83-108, 2012. DIFFERENTIAL TRANSFORM STUDY OF HYPERSONIC LAMINAR BOUNDARY LAYER FLOW AND HEAT TRANSFER OVER SLENDER AXISYMMETRIC BODIES OF REVOLUTION O. Anwar Bég 1 , M. M. Rashidi 2 , A. Aziz 3 , and M. Keimanesh 2 1 Aerospace and Biomechanics Research, Department of Engineering and Mathematics, Sheaf Building, Rm. 4121, Sheffield Hallam University, Sheffield, S11WB, UK. 2 Mechanical Engineering Department, Bu-Ali Sina University, Hamedan, Iran. 3 Mechanical Engineering Department, Gonzaga University, Spokane, WA 99258, USA. Email:O.Beg@shu.ac.uk Received 13 April 2011; accepted 28 November 2011 ABSTRACT The hypersonic laminar compressible boundary layer heat transfer over a slender axisymmetric geometry with large injection rates and arbitrary free stream velocity variation with time, is studied using Differential Transform Method (DTM) combined with Padé approximants. Homentropic external flow is assumed and ionization effects are neglected. The governing equations are transformed and an inviscid flow solution implemented simultaneously for the pressure gradient term. The key parameters dictating the unsteady dimensionless velocity and enthalpy fields are shown to be the Prandtl number (Pr), dissipation parameter (m), pressure gradient parameter (), transverse curvature parameter (A), density-viscosity product across the boundary layer (N), injection parameter ( ), temperature law exponent () and the length scale (R). The Differential Transform Method (DTM) with Padé approximants is required to solve the two-point boundary value problem, for the steady state case. DTM alone does not attain convergence due to the infinity boundary conditions. A number of important cases are considered. Excellent correlation is achieved with the DTM-Padé solutions and Runge-Kutta shooting quadrature. The importance of large injection rates (mass transfer at the wall) in actual hypersonic aerodynamics is also discussed. Keywords: Hypersonic aerodynamics, transverse curvature, injection, boundary layers, pressure gradient, DTM, Padé approximants, Analytical-Numerical, astronautic 1 INTRODUCTION Hypersonic flows have been the subject of a number of investigations for several decades. Such flows are typically associated with very high speed aircraft and space vehicles. Viscous hypersonic boundary layer flows are an especially rich area of research. Early research in this regard was presented by Swigart (1963) who studied the hypersonic flow past a blunt body. Yasuhara (1962) studied hypersonic flow past slender bodies presenting similarity solutions for small to moderate values of transverse curvature using a linear viscosity-temperature relation. Stewartson (1964) analyzed the hypersonic flow past slender axisymmetric bodies with large transverse curvature in the presence of a strong shock wave. This analysis assumed