b = velocity coefficient cp = specific heat f = nondimensional stream function K = nonequilibrium parameter Kn = Knudsen number k = thermal conductivity l = slip length M = Mach number m = flow exponent n = distance in the normal direction P = pressure Pr = Prandtl number Re = Reynolds number T = temperature U = external x velocity u = x velocity v = y velocity x = position in the flow directio...

* Correspondence: stanford. [email protected] Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa Full list of author information is available at the end of the article Abstract This article presents an improved spectral-homotopy analysis method (ISHAM) for solving nonlinear differential equations. The implementation of this new technique is show...

The Adjoint Parabolized Stability Equations (APSE) are used to predict the receptivity of boundary layers to a variety of disturbances. The method is validated through comparisons to direct solutions of the linearized Navier–Stokes (LNS) and adjoint Navier–Stokes (ANS) equations and APSE is found to accurately predict receptivity with significant gains in efficiency compared to Navier–Stokes ba...