Effect of passive chemical reaction on turbulent dispersion.
As the injection velocity increases (decreasing values of m) the thermal layer is blown further away from the wall since T]T = Q(l/Pr m). For a sufficiently small value of m, the thermal layer will be far from the wall where the series expansion for / will not be valid. This value of m is found by rewriting Eq. (3) in terms of the variable z, the parameter Pr, and the exponent m and treating the resulting form as an asymptotic expansion for the limit Pr -+• oo; z fixed. It will follow that the major contribution from the third term in Eq. (3) will be as large as that from the second term when m = -J-. Hence, the preceding analysis is useful when -J < m < -J. Larger values of fw [i.e., fw = 0(1) but smaller than the blowoff value] are treated by using numerical calculations4 for f(tf) directly to find the value rjT) where /(rjr) = 0. Equation (2) is then transformed to the thermal layer form using z = [77 — 7jT]/5(Pr) and a Taylor series expansion for / around 77 = T]T. The derivatives necessary in the latter [/'(rjr), /"(*?T), etc.] are found from the aforementioned numerical calculations. It follows that for a physically meaningful equation 5 = Pr~1/2and + f' = 0 T(z