
Heat Conduction Equation 199
areas are not necessarily exclusive portions of the system’s external area. The heat
balance equation for this system can be written as
QQ mC
dT
dt
GqAqAqA
phcrin out conv rad
−= ⇒+−−== mC
dT
dt
p
,
(8.72)
GqAhAT TATT mC
dT
hc rp
+− −− −=
conv ∞surr
4
() ()εσ
4
ddt
.
(8.73)
A special case of this system in which there was no volumetric heat generation and
no incoming heat ux, and radiation heat transfer was negligible or was combined
with convection heat transfer was studied in Section 8.6.1. Another interesting case
is one in which radiation heat transfer can be neglected or combined with convec-
tion heat transfer a