Hypersonic stagnation-point boundary layers with massive blowing in the presence of a magnetic field

Abstract

The effect of massive blowing rates on the steady laminar hypersonic boundary-layer flow of an electrically conducting fluid in the stagnation region of an axisymmetric body with an applied magnetic field has been studied. The governing equations have been solved numerically by combining the implicit finite-difference scheme with the quasi-linearization technique. It is observed that the effect of massive blowing rates is to remove the viscous layer away from the boundary, whereas the effect of the magnetic field is just the opposite. It is also found that the velocity overshoot increases with blowing rates and also with magnetic field. The effect of the variation of the density-viscosity product across the boundary layer is strong only when the blowing rate is small, but for the massive blowing rate the effect is negligible.

Effect of large blowing rates on the compressible boundary layer flow at the stagnation point of a rotating sphere

“…The coupled nonlinear ordinary differential equations governing the flow have been solved by two different methods, namely, the method of matched asymptotic expansion and the implicit finite-difference scheme with nonuniform step size in combination with the quasilinearization technique. The particular cases of the present results have been compared with those of Kubota and Fernandez [4], Liu and Nachtsheim [7], Liu and Chiu [81, Krishnaswamy and Nath [9], and Libby [12].…”

“…Furthermore, Eqs. (8), (10), and (11) for 2 = 0, co = 1 reduce to those of Libby [12] if we apply the following transformations: (8), (10), and (11) reduce to those of Krishnaswamy and Nath [9] when we put M = 0 and fl = 0.5 in their equations. The local skin friction coefficients in the longitudinal and tangential directions are given by…”

“…The effect of large blowing rates on the steady compressible laminar boundary layer flow in the stagnation region of two-dimensional and axisymmetric bodies has been considered by Kubota and Fernandez [4], Kassoy [5], Garett et al [6], Liu and Nachtsheim [7], Liu and Chiu [8], and Krishnaswamy and Nath [9]. Methods adopted in the above investigations include the method of matched asymptotic expansion [4], [5], matrix method [6], backward shooting [7] and the finite-difference scheme with nonuniform grid size in combination with the quasilinearization technique [8], [9].…”

“…The backward shooting method takes long computing time which increases as the blowing rate increases. The implicit finite-difference scheme with nonuniform step size in combination with the quasilinearization technique is found to be highly efficient for large blowing problems [8], [9]. Vigdorovich and Levin [10] have presented a review of literature on large blowing problems.…”

“…Methods adopted in the above investigations include the method of matched asymptotic expansion [4], [5], matrix method [6], backward shooting [7] and the finite-difference scheme with nonuniform grid size in combination with the quasilinearization technique [8], [9]. The method of matched asymptotic expansion is an approximate method whose accuracy can be checked by comparing the results with those of an exact (numerical) method.…”