Page 27 - Design and Operation of Heat Exchangers and their Networks

14 Design and operation of heat exchangers and their networks

2.1.1 Heat transfer coefficient and overall heat transfer
coefficient

The conventional heat exchangers are of recuperative type. In a recuperative
heat exchanger, the heat transfer occurs through a separating wall (e.g., tube
wall, plate, or other interfaces) between the two fluids. It is convenient to
express the heat transfer rate per unit area (heat flux q) in terms of the heat
transfer coefficient α defined by the Newton’s law of cooling:

ð
q ¼ α t t w Þ (2.1)
in which t w is the wall temperature and t is the fluid temperature. For an
external flow, t is the temperature in the main fluid stream outside the ther-
mal boundary layer. For an internal flow, we usually use the fluid bulk tem-
perature as t, which is defined as an equilibrium temperature after an
adiabatic mixing of the fluid from a given cross section of the flow channel:
Z Z
ρuc p tdA c utdA c
A c A c
t b ¼ Z Z (2.2)
ρuc p dA c udA c
A c A c
For concision, we will omit the subscript “b” for the fluid bulk temper-
ature if it does not cause a confusion.
The value of the heat transfer coefficient strongly depends on the flow
and heat transfer patterns, wall geometry, fluid properties, and fluid velocity,
and in most cases, they are correlated experimentally. For general applica-
tions, the heat transfer coefficient is represented in a dimensionless group,
Nusselt number:
Nu ¼ αl=λ (2.3)

where l is the characteristic length and λ is the thermal conductivity of the
fluid at its reference temperature. For internal flow, we often use the hydrau-
lic diameter as the characteristic length:

d h ¼ 4A c =P (2.4)
in which A c is the cross-sectional area of flow passage and P is the wetted
perimeter. For variable cross-sectional area along the flow passage, the min-
imum cross-sectional area of the flow passage can be used to define the
hydraulic diameter:

d h ¼ 4A c,min =P (2.5)