Course No Course Title Credits

temperature differential T i - T o and determine what the heat flow will be. For a
cylinder with length very large compared to diameter, it may be assumed that
the heat flows only in a radial direction, so that the only space coordinate
needed to specify the system is r. Again, Fourier's law is used by inserting the
proper area relation. The area for heat flow in the cylindrical system is
A =2πrL
so that Fourier's law is written
with the boundary conditions
q
r
dT
= −k
Ar
or
dr
q r
=−2πk rL
T = T i at r = r i ,
dT
dr
T = T o at r = r o
The solution to equation
q
r
dT
= −k
Ar
is
dr
q=
k
2πL
ln( r
2
/ r1
)
( T −T
)
1
2
and the thermal resistance in this case is
R
th
ln( ro
/ ri
)
=
2πkL
The thermal-resistance concept may be used for multiple-layer
cylindrical walls just as it was used for plane walls. For the three-layer system
shown in Figure the solution is
2π
L ( T1
−T4
)
q =
ln( r2
/ r1
) ln( r3
/ r2
) ln( r4
/ r2
)
+ +
K K K
a
The thermal circuit is also shown in Figure.
B
B