Page 28 - Design and Operation of Heat Exchangers and their Networks

Basic thermal design theory for heat exchangers 15

For complicated geometry, especially for compact heat transfer surfaces,
we can also define d h as
d h ¼ 4V=A (2.6)

where V is the fluid volume in the flow passage and A is the heat
transfer area.
The Nusselt number (Nu) strongly depends on the Reynolds number
(Re), which is a ratio of inertial forces to frictional forces. According to
its value, we can know whether a flow is laminar, or undergoes a transition
to turbulent flow, or is fully turbulent. The transition from laminar flow to
turbulent flow can be distinguished by the critical Reynolds number Re cr .
For the fluid flow in a straight circular tube, Re cr ¼2300. For Re<Re cr , the
flow is laminar. If Re>Re cr , the flow is in a transition region and may
4
become turbulent. When Re>10 , the flow is fully turbulent.
In the laminar flow region, the heat transfer and pressure drop will be
influenced by the form of channels and heating or cooling boundary con-
ditions. Two typical boundary conditions are as follows: uniform wall
temperature denoted by the subscript “T” and uniform heat flux denoted
by the subscript “H” for uniform heat flux in both flow direction and
peripheral direction (thin-wall duct) and “H1” for constant heat flux in
the flow direction and uniform peripheral wall temperature (thick-wall
duct), respectively. The Nusselt number for fully developed laminar flow
in a circular tube with uniform wall temperature can be analytically obtained
as 3.6567935, and that under the uniform heat flux condition is 48/11
(Shah and London, 1978), 12% higher than the former. The real boundary
condition in heat exchangers might lie between these two values. If we were
not sure which one is more suitable, we would like to take the value for
uniform wall temperature for a conservative design of the heat exchanger.
The inlet conditions also affect the heat transfer and pressure drop char-
acteristics. When a fluid enters the tube or when it is heated (or cooled)
beginning from the inlet cross section, the velocity or temperature boundary
layer will form and develop along the wall until the boundary layer fills the
entire flow channel. Therefore, at the entrance, the local heat transfer coef-
ficient and frictional pressure drop are high and then decrease with the
increase of the boundary layer thickness. For short heat exchangers,
the entrance effects should be taken into account. Three cases have been
considered: (1) thermally developing and hydrodynamically developed lam-
inar flow, (2) thermally and hydrodynamically developing laminar flow,
and (3) thermally and hydrodynamically developed laminar flow.