Page 297 - Modelling in Transport Phenomena A Conceptual Approach

8.2. ENERGY TRANSPORT WITHOUT CONVECTION 277

For a rectangular volume element of thickness Ax, width Ay and length Az, as
shown in Figure 8.23, Q. (8.2-1) is expressed as

(8.2-60)

From Table C.4 in Appendix C, the components of the conductive flux are given
bY m
qz=-k- (8.2-61)
6X
(8.2-62)

aT
q, = -IC- (8.263)
a2
Substitution of Eqs. (8.261)-(8.2-63) into Eq. (8.260) gives the governing equation
for temperature as

1 E d2T I d2T -o]
6x2 + zp 622 (8.264)

The boundary conditions associated with Eq. (8.2-64) are

(8.2-65)

(8.2-67)
m
at y=W -- (8.2-68)
-0
6Y
at z=O T=T, (8.2-69)
(8.2-70)

where T, is the temperature of the fluid surrounding the fin.