# Download Fluid Dynamics Transactions. Symposium–Jabona–September 1961 by W. Fiszdon (Eds.) PDF By W. Fiszdon (Eds.)

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Example text

4) and if along the surface ό the kinematic condition is fulfilled unx + vny + wnz = 0, where h{nX9ny9nz)— normal to the surface c5 Fig. 1 (the normal component of flow velocity disap­ pears). 8c) is admissible. 2). In our case: £i = (r-fi'fl 0. 0), h2 = (0, -A'f» 0). 2') x = x, y = y, z = φ {x, y), a = A (x, j ) . The tangent vectors to the manifold 9£ 2 have the form: Sx = (1, 0; φχ, Az), 4 Sy = (0, 1, (pyt Ay) We assume that

Sn), differentiable and '-^Φ 0. ,sn) are continuously M. 1) will have a solution only if the inequality m ^ n is satisfied. 1). , J n - l ) ... , Sn-\). The following theorem will be true: Theorem 2. 5) h e [//, i i , . . , w is satisfied. , n, u = shv°(u0) + w0 through all points of the manifold °Ιίη-\· This will be the only one solution. e. 1). In particular cases this region may be very small. Nevertheless, Theorem 2 allows, for given problems, to find the maximal region of existence of the solution.

4. Boundary Layer with Chemical Reactions in Equilibrium Chemical reactions occur in a high temperature boundary layer. These reactions depend not only on the dissociation of oxygen and nitrogen of the air and creation of nitric oxide but in practice in these conditions an interaction with the surface A. A. Dorotnitsyn 68 of the body always takes place. For this reason, to the usual boundary layer equations we must add not only the equations of diffusion of different components and the equations of the chemical kinetics but also the boundary conditions become more compli­ cated.