Page 384 - Modelling in Transport Phenomena A Conceptual Approach

364 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

which indicates that the bulk fluid temperature varies exponentially with the axial
direction as shown in Figure 9.10.

Z
Figure 9.10 Variation of the bulk temperature with the axial direction for a
constant wall temperature.

Evaluation of Eq. (9.3-19) over the total length, L, of the pipe gives

(9.3-22)

where
l
(h) = 'i; L hdz (9.3-23)
If Eq. (9.3-22) is solved for TboUt, result is
the

(9.3-24)

Equation (9.3-24) can be expressed in terms of dimensionless numbers with the
help of Eq. (3.45), i.e.,

(9.3-25)

The use of Eq. (9.3-25) in Eq. (9.3-24) gives

(9.3-26)

As an engineer, we are interested in the rate of heat transferred to the fluid,
i.e.,

Q = * eP(Tbout Tbi,) = m eP [(Tw - Tbi,) - (Tw - Tb,,,)] (9.3-27)
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