Page 292 - Modelling in Transport Phenomena A Conceptual Approach

272 CHAPTER 8. STEADY MICROSCOPIC BALANCES WTHOUT GEN.

2. The heat transfer from the ball to the fluid takes place only by conduction.

3. The thermal conductivity of the fluid is constant.
Analysis

a) The use of Eq. (B) in Table 8.5 with TI = TR, T2 = T,, R1 = R and R2 = 00
gives the rate of heat transferred from the ball to the fluid as
4~k (TR - T,)
k
Q= = ~TR (TR - T,)
1/R
b) The tempemture distribution can be obtainedfrom Eq. (0) Table 8.5 in the
of
form
T-T, -_
R
-
TR-T, T
c) The amount of heat transfed can also be calculated from Newton’s law of
cooling, Eq. (3.2-7), as
Q = 4wR2(h)(T~ - Tm) (3)
Equating Eqs. (1) and (3) leads to

Thewfore, the Nusselt number is

NU=-- (h)D
k -2 (5)

8.2.3.1 Electrical circuit analogy
Equation (B) in Table 8.5 can be rearranged in the form

(8.2-53)

R1
4~k R2
Comparison of Eq. (8.2-53) with Eq. (8.2-10) indicates that the resistance is given
bv

(8.2-54)

In order to express the resistance in the form given by Eq. (8.2-13), let us define a
geometric mean area, ACM, as
AGM = dZG

= J(4xR:) (4~R3 47rRlRz (8.2-55)
=