Solution of the diffusion equation when Le

From equations (19) and (22) it can be seen that Y is simply related to T provided that the next assumption is allowed  

It is shown in Appendix E that Le = 1 is a reasonable approximation. The difference of equations (19) and (22) is dxjd — lho) dYjd ) = t — Y, which, when Le = 1, has the general solution 

Dimensionless forms for the momentum equation and the species-conservation equation 

The relation between a and the dimensionless heat release a used in Section 2.2.2 is 

By substituting equations (26), (27), and (30) into equation (25), we obtain the dimensionless form of the momentum conservation equation. 

Equation (33) is a dimensionless form of the species-conservation equation. We are entitled to indicate that f fr, cp), as defined in equation (34), is a function of r and p, because the additional variables p and T, which appear on the right-hand side of equation (34), are easily expressed in terms of t, q , and constants through equations (6) and (27). The function f (t, (p) is nonnegative over the entire range 0 r 1, in the physically acceptable range of p, and it equals zero only at r = 1, although it becomes very small (because of the exponential factor involving T) near t = 0 where T is small. 

---