Page 52 - Mechanical Engineers Reference Book

Heat transfer 1141
tion and convection can be added to enable the heat transfer
rate to be determined in terms of the two fluid temperatures.
For a plane surface (Figure 1.63)

For a tubular surface (Figure 1.64)

It can be seen that the added resistances may be inverted to
give an overall conductance which is known as a 'U-value' or
overall heat transfer coefficient.
Figure 1.61 Conduction through a single-layer cylindrical surface For a plane surface

For a tubular surface

The heat transfer rate is then simply written
For a plane surface
Q = UA(Tf, - Tf2, where A is the area

Boundary Fluid
layer 2

14
Figure 1.152 Conduction through a multi-layer cylindrical surface
Bulk
vary considerably (Table 1.9). Although the determination of temperature
h is crucial to convection calculations it is an extremely Tf2
difficult process, and accurate prediction of convective heat
transfer is not always possible.
If we express the convection equation in a thermal res-
istance ,form suitable for plane surfaces

it can biz seen that the thermal resistance is (lih) m' K WA1. Figure 1.63 U-value for a plane surface
For tubular surfaces it is again more convenient to work per
unit length. so that
Fluid 1, Tf,
Boundary layer, h1
and the thermal resistance is (1/25-rh) m K W-' Double-layer tube
Boundary layer, h2
Table 1.9 Range of values of surface heat transfer
coefficient (W rr2 K-') Fluid 2, Ti2
Free convection Gases 0.5 to 500
Liquids 50 to 2000
Forced convection Gases 10 to 700
Liquids 100 to 10 000 L=-l_+z In (rOuter/rlnner) 1
2ar2hz
U' 2nrlhl 2nk + A
1.7.2.3 Overall heat transfer coefficients
A common heat transfer situation is a solid wall separating two
fluids. and for this problem the thermal resistances for conduc- Figure 1.64 U-value for a cylindrical surface