DIFFERENTIAL TRANSFORM STUDY OF HYPERSONIC LAMINAR BOUNDARY LAYER FLOW AND HEAT TRANSFER OVER SLENDER AXISYMMETRIC BODIES OF REVOLUTION

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.

Hypersonic aerodynamics, transverse curvature, injection, boundary layers, pressure gradient, DTM, Padé approximants, Analytical-Numerical, astronautic