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q
A
T 2 .
where
T1
+ T
q 2
a + b
2
k
=
( T1
−T2
) =
m ( T1
T2
)
A ∆x
∆x
−
b T 1
+ T
k a
2
m
= +
2
This means that the mean value of k (i.e., k m ) to use in
k
= ( T ) 1
−T
2 is the value of k evaluated at the linear average of T 1 and
∆x
The rate of a transfer process equals the driving force over the
q k
resistance and the equation = ( T 1
−T
2)
can be rewritten in that form
A ∆x
as:
where
R ∆x
/ kA
T −T2
T1
−T2
q = =
∆x
/ kA R
1 =
driving force
resis tan ce
= A and is the resistance in K/W.
Fig. 3.2 Heat conduction in a cylinder
Conduction Through a Hollow Cylinder
In many instances in the process industries, heat is being transferred
through the walls of a thick-walled cylinder, such as a pipe that may or may
not be insulated. Consider the hollow cylinder in Fig.3.2 with an inside radius
of r 1 , where the temperature is T 1 , an outside radius of r 2 having a temperature
of T 2 , and a length of L m. Heat is flowing radially from the inside surface to
the outside. Rewriting Fourier's law, with distance dr instead of dx,
q x
A
= −
k
dT
dr