Flux-Matching Conditions at a Surface

Heterogeneous reactions at a gas-surface interface affect the mass and energy balance at the interface, and thus have an important influence on the boundary conditions in a chemically reacting flow simulation. The convective and diffusive mass fluxes of gas-phase species at the surface are balanced by the production (or destruction) rates of gas-phase species by surface reactions. This relationship is 

Here the are the gas-phase mole fractions, the K are the gas-phase mass fractions, W is the mean molecular weight of the gaseous mixture, Dkj is the ordinary multicomponent diffusion coefficient matrix, and the Dj are the thermal diffusion coefficients. 

In nonreacting, continuum fluid mechanics the fluid velocity normal to a solid wall is zero, which is a no-slip boundary condition. However, if there are chemical reactions at the wall, then the velocity can be nonzero. The so-called Stefan flow velocity occurs 

The expression for the Stefan velocity is easily obtained from the interfacial mass balance (Eq. 11.123) by summing over all Kg species and noting that the mass fractions must sum to one, 

Heat release or consumption by surface reactions contributes to the energy balance at a gas-surface interface. Diffusive and convective fluxes in the gas phase are balanced by thermal radiative and chemical heat release at the surface. This balance is stated as 

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