Page 92 - Modelling in Transport Phenomena A Conceptual Approach

72 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

Simplification of Eq. (2) yields
F(L) = L - 1.99 L4I5 + 1.13 = 0 (3)
The length of the heater can be determined from Eq. (3) by wing one of the
numerical methods for root finding given in Section A.Y.2 in Appendix A. The
iteration scheme for the Newton-Raphson method, Eq. (A. 7-18), becomes

in which the derivative of the function F(L) is
dF
- = 1 - 1.592 L-lI5 (5)
dL
Assuming L4I5 L, a starting value can be estimated as L1 = 1.14141. Therefore,
0.05930
L2 = 1.14141 + - = 1.24914
0.55044
0.00152
L3 = 1.24914 + - = 1.25205
0.52272
0
L4 = 1.25205 + - = 1.25205
0.52201
Since L3 = Lq, the length of the plate is approximately 1.25 m. Now, it is necessarg
to check the validity of the second assumption:

Re - (1'25)(13) = 7.4 x lo5 + Checks!
- 21.95 x

Example 4.3 A water storage tank open to the atmosphere is 12m in length and
6m in width. The water and the surrounding air are at a temperature of 25OC,
and the relative humidity of the air is 60%. If the wind blows at a velocity of
2 m/ s along the long side of the tank, what is the steady rate of water loss due to
evaporation from the surface?
Solution
Physical properties

For air at 25 "C (298 K) : v = 15.54 x m2/ s
Diflwion coeficient of water (A) in air (B) at 25OC (298K) :

3/2
= (2.88 x (ii:) - = 2.79 x 10-5~2/~