Page 274 - Modelling in Transport Phenomena A Conceptual Approach

254 CHAPTER 8. STEADY MICROSCOPIC BALANCES WITHOUT GEN.

Figure 8.11 Heat transfer through a plane wall,

When the thermal conductivity and the area are constant, the heat transfer
rate is calculated from Eq. (8.2-11). The use of this equation, however, requires
the values of To and TL be known or measured. In common practice, it is much
easier to measure the bulk fluid temperatures, TA and TB. It is then necessary to
relate To and TL to TA and TB.
The heat transfer rates at the surfaces z = 0 and z = L are given by Newton's
law of cooling with appropriate heat transfer coefficients and expressed as

-
Q = A(~A)(TA -To) = A(~B)(TL TB) (8.2-14)
Equations (8.2-11) and (8.2-14) can be rearranged in the form

(8.2-15)

(8.2-16)

(8.2- 17)

Addition of Eqs. (8.2-15)-(8.2-17) gives

(8.2-18)

TA - TB I
JQ= 1 L 1 (8.2-19)

in which the terms in the denominator indicate that the resistances are in series.
The electrical circuit analogy for this case is given in Figure 8.12.