Page 477 - Modelling in Transport Phenomena A Conceptual Approach

10.3. MASS TRANSPORT 457

The amount of heat transferred to the sphere can be calculated as
t
Q = 47rR2(h) 1 (2'- - 2') dt (10.2-122)

Substitution of Eq. (10.2-121) into Eq. (10.2-122) gives

( 10.2- 123)

or,
-=l-exp(-3BiH7) (10.2-124)

The exact values of Q/Qo obtained from Eq. (10.2-86) are compared with the
approximate results obtained from Eq. (10.2-124) for different values of BiH in
Table 10.5. As expected, when BiH = 0.1, the approximate values are almost equal
to the exact ones. For BiH > 0.1, the use of Eq. (10.2-124) overestimates the exact
values.

Table 10.5 Comparison of Q/Qo values obtained from Eqs. (10.2-86) and
(10.2-124).

Q/Qo

Exact Approx. Exact Approx. Exact Approx.
0 0.000 0.000 0 0.000 0.000 0 0.000 0.000
1 0.255 0.259 0.1 0.229 0.259 0.01 0.157 0.259
2 0.444 0.451 0.2 0.398 0.451 0.02 0.259 0.451
3 0.586 0.593 0.3 0.530 0.593 0.03 0.337 0.593
4 0.691 0.699 0.4 0.633 0.699 0.04 0.402 0.699
5 0.770 0.777 0.5 0.713 0.777 0.05 0.457 0.777
6 0.828 0.835 0.6 0.776 0.835 0.06 0.505 0.835
7 0.872 0.878 0.7 0.825 0.878 0.07 0.548 0.878
8 0.905 0.909 0.8 0.863 0.909 0.08 0.586 0.909
9 0.929 0.933 0.9 0.893 0.933 0.09 0.620 0.933
10 0.947 0.950 1.0 0.916 0.950 0.10 0.650 0.950

10.3 MASS TRANSPORT

The conservation statement for species A is expressed as

Rate of Rate of species A ) (10.3-1)
( species A in ) - ( spR:kt ) = ( accumulation