Page 336 - Mechanical Engineers' Handbook (Volume 4)

5 Use of Computers in Thermal Design of Process Heat Exchangers 325

wall temperature. Because of the variation of physical properties between the wall and the
bulk of the fluid, heat transfer coefficients depend on the wall temperature. Likewise, the
wall temperature depends on the relative values of the heat transfer coefficients of each fluid.
Wall temperatures on each side of the surface can be estimated by the following equations:

U
T w, hot T hot o (T hot T cold )
h hot
U o
T w, cold T cold (T hot T cold )
h cold

It is assumed in the above equations that the heat transfer coefficient on the inside surface
is corrected to the outside area. Convergence on the true wall temperature can be done in
several ways. Figure 18 shows a possible convergence scheme.

Pressure Balance Loops
These convergence loops are needed whenever the equations to be solved are implicit with
respect to velocity. The two most frequent cases encountered in heat exchanger design are
(1) flow distribution and (2) natural circulation. The first case, flow distribution, is the heart
of the shell and tube heat exchanger shellside flow calculations, and involves solution for
the fraction of flow across the tube bundle, as opposed to the fraction of flow leaking around
baffles and bypassing the bundle. Since the resistance coefficients of each stream are func-
tions of the stream velocity, the calculation is reiterative. The second case, natural circulation,
is encountered in thermosiphon and kettle reboilers where the flow rate past the heat transfer
surface is a function of the pressure balance between the two-phase flow in the bundle, or
tubes, and the liquid static head outside the bundle. In this case the heat transfer coefficients
that determine the vaporization rate are functions of the flow velocity, which is in turn a
function of the amount of vaporization. Figure 19 shows a flow velocity convergence loop
applicable to the flow distribution case.

Assume Twall Assume velocity

Calculate Calculate
Heat Transfer velocity-dependent
Coefficients quantities
New New
Twall velocity
Calculate Twall Calculate velocity

no no
Tolerance? Tolerance?
yes yes
Results Results

Figure 18 Temperature convergence loop. Figure 19 Velocity convergence loop.