Explicit balance equations for simple cases

In chapter 5 we showed that the dusty gas model flux relations could be solved (fjite easily at the limit of Knudsen diffusion control, when they reduce to the form given in equation (5.25), namely 

Equations (12,13) and (12,14) together then provide (n+ 1) partial differential equations in the unknowns c, T. They may be solved subject Co boundary conditions specified at the pellet surface at all times, and Initial conditions specified throughout the interior of the pellet at one particular time. 

Equations (12.13) and (12.14) may be approximated by rather simple equations in most conditions of physical interest. This is possible because of the relatively large value of the thermal conductivity of the solid matrix, which has two important consequences. First, the conductive enthalpy flux, represented by the second term on the left hand side of 

With these simplifying assumptions equations (12 13) and (12.14) reduce to 

Apart from the Knudsen limit equations (12.12), the only other reasonably compact solution of the dusty gas model equations is that given by equations (5.26) and (5.27), corresponding to binary mixtures. Consequently, if we are to study anything other than the Knudsen limit, attention will 

---