Page 285 - Modelling in Transport Phenomena A Conceptual Approach

8.2. ENERGY TRANSPORT WITHOUT CONVECTION 265

or,

+- (8 2-40}
Al(hA) ALMk A2(hB)
in which the terms in the denominator indicate that the resistances are in series.
The electrical circuit analogy for this case is given in Figure 8.16.

1
TA ------e TB

Figure 8.16 Electrical circuit analogy for Eq. (8.2-40).

In the literature, Eq. (8.2-40) is usually expressed in the form

= AIUA(TA - TB) = &UB(TA - TB) (8.2-41)
where the terms UA and UB are called the overall heat transfer coefficients. Com-
parison of Eq. (8.2-41) with Eq. (8.2-40) gives UA and UB as

(8.2-42)

and

(8.2-43)

Example 8.7 Consider a cylindrical pipe of length L with inner and outer radii
of R1 and R2, .respectively, and investigate how the rate of heat loss changes (1s a
function of insulation thickness.
Solution

The immediate reaction of most students after reading the problem statement is
“What’s the point of discussing the rate of heat loss as a function of insulation
thickness? Adding insulation thickness obviously decreases the rate of heat loss.”