Page 385 - Modelling in Transport Phenomena A Conceptual Approach

9.3. HEAT TRANSFER WITH CONVECTION 365

Substitution of Eq. (9.3-22) into Eq. (9.3-27) results in

(9.3-28)

Note that h. (9.3-28) can be expressed in the form

which is identical with Eqs. (3.2-7) and (4.529).

Constant wall heat flux

Constant wall heat flux type boundary condition is encountered when electrical
resistance is wrapped around the pipe. Since the heat flux at the wall is constant,
then
(9.3-30)

Substitution of Eq. (9.3-30) into Eq. (9.3-16) gives
dTb --- - constant (9.3-31)
TDqw
--
d.2 mep
Integration of Eq. (9.3-31) gives the variation of the bulk temperature in the axial
direction as
(9.3-32)

Therefore, the bulk fluid temperature varies linearly in the axial direction as shown
in Figure 9.11.

Figure 9.11 Variation of the bulk temperature with the axial direction for a
constant wall heat flux.