Page 188 - Mechanical Engineers' Handbook (Volume 4)

3 Radiation Heat Transfer 177

Figure 15 Temperature profiles for parallel flow and counterflow in double-pipe heat exchanger.

Cross-Flow Coefficient
In other types of heat exchangers, where the values of the overall heat transfer coefficient,
U, may vary over the area of the surface, the LMTD may not be representative of the actual
average temperature difference. In these cases, it is necessary to utilize a correction factor
such that the heat transfer, q, can be determined by
q UAF T m
Here the value of T is computed assuming counterflow conditions, i.e., T T h,i T c,i
m
1
and T T h,o T . Figures 16 and 17 illustrate some examples of the correction factor
2
c,o
F for various multiple-pass heat exchangers.
3 RADIATION HEAT TRANSFER

Heat transfer can occur in the absence of a participating medium through the transmission
of energy by electromagnetic waves, characterized by a wavelength, , and frequency, v,
which are related by c v. The parameter c represents the velocity of light, which in a
vacuum is c 2.9979 10 m/sec. Energy transmitted in this fashion is referred to as
8
o
radiant energy and the heat-transfer process that occurs is called radiation heat transfer or
simply radiation. In this mode of heat transfer, the energy is transferred through electro-
magnetic waves or through photons, with the energy of a photon being given by hv, where
h represents Planck’s constant.
In nature, every substance has a characteristic wave velocity that is smaller than that
occurring in a vacuum. These velocities can be related to c by c c /n, where n indicates
o
o