| Abstract: | Numerical solutions are obtained for the equations of a uniform compressible boundary layer with variable physical properties in the vicinity of a stagnation point with different principal curvatures in the presence of an injected gas with the same properties as the incident flow. The results of the numerical solutions are approximated for the heat flux in the form of a relation that depends on the variation of the product of viscosity and density   across the boundary layer and on the ratio of the principal radii of curvature.Using the concepts of effective diffusion coefficients in a multicomponent boundary layer, previously introduced by the author in [1], and the generalized analogy between heat and mass transfer in the presence of injection, together with the numerical solutions obtained, it is always possible, even without additional solutions of the boundary-layer equations, to derive final formulas for the heat fluxes in a flow of dissociating gas of arbitrary chemical composition, provided that we make the fundamental assumption that all recombination reactions take place at the surface.By way of example, formulas are given for the heat transfer to the surface of a body from dissociating air, regarded as a five-component mixture of the gases O, N, NO, O2, N2, and from a dissociating mixture of carbon dioxide and molecular nitrogen of arbitrary composition, regarded as an eleven-component mixture of the gases O, N, C, NO, C2, O2, N2, CO, CN, C3, CO2.In the process of obtaining and analyzing these solutions it was found that, in computing the heat flux, a multicomponent mixture can be replaced with an effective binary mixture with a single diffusion coefficient only when the former can be divided into two groups of components with different (but similar) diffusion properties. In this case the concentrations of one group at the surface must be zero, while the diffusion flows of the second group at the surface are expressible, using the laws of mass conservation of the chemical elements, in terms of the diffusion flows of the first. Then the single effective diffusion coefficient is the binary diffusion coefficient D(A,M), where A relates to one group of components and M to the other.In view of the small amount of NO(c(NO) < 0.05), the diffusion transport of energy in dissociated air maybe described with the aid of a single binary diffusion coefficient D(A, M)(A=O, N, M=O2, N2, NO). However even in the case of complete dissociation into O and C atoms at the outer edge of the boundary layer, the diffusion transport of energy in dissociated carbon dioxide can not be described accurately enough by means of a model of a binary mixture with a single diffusion coefficient, since the diffusion properties of the O and C atoms are distinctly different. |
