The hydrodynamic equations for chemically equilibrium flows of a multielement plasma with exact transport coefficients

Transformations of the equations of the first approximation of Chapman–Enskog methods and vector transport relations for mixtures of polyatomic gases

“…., N):the diffusion velocity of component i (1.11) and the total heat flux (1.12) The formulae for V i and h correspond to the "fluxes in terms of thermodynamic forces" representation. [2][3][4] Here is the partial thermal conductivity, and D ij and D Ti are the diffusion and thermal diffusion coefficients of the multicomponent mixture of molecular gases.…”

“…[2][3][4] As is usually done, [6][7][8]15 we will seek the functions T i␣ and V i␣ in the form of expansions in systems of polynomials (1.32)…”

“…For diffusion velocities V i and a heat flux q this representation is called "fluxes in terms of thermodynamic forces". [2][3][4] For gas-dynamic calculations it is more effective, however, to write d i and q in terms of T and V j . 2-4 The expressions for the diffusion thermodynamic forces d i in terms of V j and T are called the Stefan-Maxwell relations.…”

“…polynomials: the transformation of systems of linear algebraic equations for the coefficients of the expansion in Sonin polynomials 2,3 and the use of expansion in Hermite polynomials. 4 As a result, the thermodynamic forces T and d i are expressed linearly in terms of the reduced heat flux and diffusion velocities.…”

Generalized viscous shock layer equations with slip conditions on a surface in a flow field and on a head shock

“…6,14,15 The most widely known approaches for problems of external flow over a body are the model of a thin viscous shock layer, 1 the model of a full viscous shock layer, 16,17 The parabolized Navier-Stokes equations, 3 the parabolic-hyperbolic model of a viscous shock layer 8,12 , etc.…”