Page 472 - Modelling in Transport Phenomena A Conceptual Approach

452 CHAPTER 10. UNSTEADY MICROSCOPIC BAL. WITHOUT GEN.

(10.2-107)

The boundary condition defined by Eq. (10.2-102) indicates that B = 0. Applica,
tion of Eq. (10.2-103) yields

A e- x2T(sin A - A cos A) = BiH A e- sin X ( 10.2- 108)

Solving for X gives
An cot A, = 1 - BiH (10.2-109)
The first five roots of Eq. (10.2109) are given as a function of BiH in Table 10.4.

'pable 10.4 The roots of Eq. (10.2-109).

0 0.000 4.493 7.725 10.904 14.066
0.1 0.542 4.516 7.738 10.913 14.073
0.5 1.166 4.604 7.790 10.950 14.102
1.0 1.571 4.712 7.854 10.996 14.137
2.0 2.029 4.913 7.979 11.086 14.207
10.0 2.836 5.717 8.659 11.653 14.687

The complete solution is

(10.2-110)
n=l
The unknown coefficients Cn can be determined from Eq. (10.2-101). The result
is

sin A, - A, cos An
An - sin An COS An (10.2-111)

Therefore, the solution becomes