For the energy equation, either the temperature, a zero-heat-flux (adiabatic), or a specified heat flux condition is specified at the solid walls. In the transformed equations, is the independent variable and the physical coordinate is a dependent variable. For the evaluation of , then, we specify as boundary conditions that at the lower boundary and at the upper boundary (the channel radius in the case of cylindrical coordinates). Notice that there is no explicit equation or boundary condition for the pressure even though it is a dependent variable. Note also that a boundary value of is specified at both boundaries even though Equation 12–16 is only a first-order equation. This apparent over-specification is resolved by the fact that there is no boundary condition for pressure.[85]

The boundary conditions for the surface species involve heterogeneous reactions. The convective and diffusive mass fluxes of gas-phase species at the surface are balanced by the production (or depletion) rates of gas-phase species by surface reactions. This relationship is

(12–21)

where the gas-phase diffusion velocities are given by Equation 12–5 or Equation 12–6 and is the surface area fraction of the m th material on the solid wall.

In nonreacting flows the fluid velocity normal and tangential to a solid wall is zero. However, if there are chemical reactions at the wall, then the normal velocity can be nonzero. This so-called Stefan flow velocity occurs when there is a net mass flux between the surface and the gas. The Stefan velocity is given by

(12–22)

This expression is easily obtained from the interfacial mass balance, Equation 12–21 , by summing over all gas-phase species and using the requirement that the mass fractions must sum to one, that is,

(12–23)

and that the sum of the diffusion fluxes must be zero.

The Surface Kinetics input includes the mass densities for all bulk species involved in a surface reaction mechanism. These densities are used to convert the surface reaction rate of production of a bulk species (in moles/cm² /sec) into a growth rate (in cm/sec) for each bulk species. The relationship is given by:

(12–24)