Page 284 - Modelling in Transport Phenomena A Conceptual Approach

264 CHAPTER 8. STEADY h4ICROSCOPIC BALANCES WTHOUT GEN.

Analysis
The variation of the thermal conductivity with temperature can be estimated as

k = 42 + (-) 49 - 42 (T - 30)
60 - 30
= 35 $- 0.233T
The heat transfer rate is estimated from Eq. (A) in Table 8.3 with R1 = 10cm,
R2 = 15cm, TI = 60°C and T2 = 30°C :
r Ti

60
-
- (35 + 0.233 T) dT = 42,291 W

8.2.2.2 Transfer rate in terms of bulk fluid properties
The use of Eq. (8.2-29) in the calculation of the heat transfer rate requires surface
values TI and T2 be known or measured. In common practice, the bulk tempera-
tures of the adjoining fluids to the surfaces at R = R1 and R = R2, i.e., TA and
TB, are known. It is then necessary to relate TI and T2 to TA and TB.
The heat transfer rates at the surfaces R = R1 and R = R2 are expressed in
terms of the heat transfer coefficients by Newton's law of cooling as

-
Q = A~(~A)(TA Ti) = A2(h~)(T2 - TB) (8.2-34)
The surface areas A1 and A2 are expressed in the form

A1 = 27rR1L and A2 = 2nR2L (8.2-35)

Equations (8.2-29) and (8.2-34) can be rearranged in the form

(8.2-36)

(8.2-37)

(8.2-38)

Addition of Eqs. (8.2-36)-(8.2-38) gives

(8.2-39)