Page 287 - Modelling in Transport Phenomena A Conceptual Approach
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8.2. ENERGY TRANSPORT WITHOUT CONVECTION 267
Therefore, at R3 = ki/(hB), X has the minimum value. This implies that the
rate of heat loss will reach the maximum value at R3 = R,, = ki/(hB), where
R,, is called the critical thickness of insulation. For R2 < R3 5 R,,, addition
of insulation causes an increme in the rate of heat loss rather than a decrease. A
representative graph showing the variation of the heat transfer rate with insulation
thickness is given in Figure 8.18.
R2 Rm R* R3
Figure 8.18 Rate of heat loss as a function of insulation thickness.
Another point of interest is to determine the value of R*, the point at which
the rate of heat loss is equal to that of the bare pipe. The rate of heat loss through
the bare pipe, Qo, is
On the other hand, the rate of heat loss, Q*, when R3 = R* is
Equating Eqs. (4) and (5) gives
R* can be determined from Eq. (6) for the given values of R2, (hs), and ki-
Comment: For insulating materials, the largest value of the thermal conductivity
is in the order of O.1Wlm.K. On the other hand, the smallest value of (hB) is
