From an energy balance around a heat exchanger, it is clear that the heat duties
calculated on the hot and cold sides should be equivalent. The data obtained
throughout this experiment were consistent with this assertion. This is shown in Figure
4.4. In the figure, it can be seen that the heat duties on the hot and cold sides are
equivalent (within experimental error) for all runs of the finned, double-pipe heat
exchanger. The energy balances for the runs in the other exchangers are similarly
satisfied, as seen in Tables 4.1 and 4.2.
The fact that the energy balances are satisfied allows confidence to be placed in
the data obtained throughout the experiment. This, in turn, allows confidence to be
placed in the scale-up.
Analysis of the Wilson Plots
The Wilson Plot method makes use of the fact that when the velocity of the hot
fluid in a heat exchanger is varied, the only resistance to heat transfer that changes is
the fluid coefficient, h. There are empirical correlations to determine the Nusselt number
as a function of the Reynolds number and the Prandtl number. From these correlations,
it can be shown that h v0.8 for sufficiently high fluid velocity. As such, it follows that a
plot of 1/U versus 1/v0.8 should be linear.
As seen in Figures 4.1, 4.2 and 4.3, the data obtained in this experiment are
consistent with this theory. Plots of 1/U versus 1/v0.8 for all exchangers tested in this
experiment were remarkably linear. This is evident from the coefficient of determination
(R2) values of the best fit lines. The R2 value for the high cold flow rate data in the plate
heat exchanger, for example, was 0.998. This means that 99.8 percent of the variation
in the data is accounted for in the line. As seen in Figures 4.1, 4.2 and 4.3, the other
best fit lines also have R2 values close to unity. Because the R2 values are so close to
one, confidence can be placed in the best fit lines obtained.
The exchanger with least linear Wilson Plot was the finned, double-pipe heat
exchanger. The R2 values for the high and low cold flow rate data in this exchanger
were 0.962 and 0.966 respectively. While these values are still fairly close to unity, it
may be possible to obtain better results by modifying the power to which the velocity is
raised from 0.8. However, this is outside the scope of this study.
Comparison of Heat Exchanger Types
Three different types of heat exchangers, shell and tube, plate, and finned,
double-pipe, were studied in this experiment for their feasibility for scale up. At the same
range of volumetric flow rates, the overall heat transfer coefficient of each exchanger
was determined. As seen in Tables 4.1, 4.2 and 4.3, the overall heat transfer
coefficients obtained in the plate exchanger were the highest, followed by those obtained
in the shell and tube exchanger. The overall heat transfer coefficients obtained in the
finned, double-pipe exchanger were the lowest of the exchangers...