Page 365 - Modelling in Transport Phenomena A Conceptual Approach

9.2. ENERGY TRANSPORT WITHOUT COiWECTIOA 345

Figure 9.6 Representative temperature distributions in a rectangular wall with
constant generation.

Type I1 boundary condition
The solution of Eq. (9.2-8) subject to the boundary conditions

dT
at z=O -k-=qo
dz (9.2-15)
at x=L T=TL
is given by

(9.2-16)

Note that when R = 0, Eq. (9.2-16) reduces to Eq. (G) in Table 8.2. Further
simplification of Eq. (9.2-16) depending on whether k and/or 8 are constant are
given below.
R Case (i) k = constant

In this case Eq. (9.2-16) reduces to
k (T - TL) = [lz!R(u) du] dz + qoL (1 - i) (9.2-17)

When !R = 0, Eq. (9.2-17) reduces to Eq. (H) in Table 8.2.

W Case (ii) k = constant; !R = constant
In this case Eq. (9,216) reduces to
?I2 L2
+
T=TL+- 2k [1- (323 y (1 - ;) (9.2-18)