Y e = where
7. TESTING OF SIMPLE MODEL AGAINST EXPERIMENTAL DATA FOR IDEALISED MODEL SYSTEMS
7.1 INTRODUCTION
In Chapter 4, heat and mass transfer were simulated and numerical methods were used to predict likely chilling behaviour. The numerically-predicted results were investigated to fmd the factors that influenced evaporation. Simple model, based on the numerically-predicted results, wa s developed in Chapter 5 and gave similar predictions to the numerical method. Chapter 6 described experimental methods used to collect data across a wide range of conditions for testing the simple model. In Chapter 7 the qualities of the simple model relative to the experimental results are evaluated.
7.2 EXPERIMENTAL DESIGN AND RESULTS
In Chapter 6, the different techniques to control the environmental conditions in the air tunnel
were described. The design conditions used were:
Hr
0.78, 0.9 10, 5, 10 20, 30, 40
Different Biot numbers were obtained by varying product sizes and air velocity. Since there
were two sizes of infinite cylinder and three velocities, two Biot numbers at the intermediate level (which were between 1 .3 to 1.8), one Biot number at the highest level (3.5 - 4. 1) and
another at the lowest level (0.9 - 1) were possible (Table 7.1). In total, 30 runs were carried
out as defined in Tables 6.2 - 6.4. One extra trial not in the plan, run 3 1 was conducted. The
results are listed in Tables 7.3, 7.4, and 7.5. In these Tables the run numbers listed are those
from Tables 6.2 - 6.4. Runs 5, 27, and 29 were repeated because, at the time, there was
doubt that the wetting liquid reservoir temperature was correct. Both the frrst attempt and second are reported here and used in the analysis but, as will be shown, the frrst attempt, for
runs 27 and 29 were less well modelled than the second.
7.3 HEAT TRANSFER COEFFICIENTS
As described in Chapter 6, heat transfer coefficients
(he)
were detennined by cooling the infinite cylinders in separate trials where the cloth was wetted but a thin plastic film covered the wet cloth to avoid evaporation. The analytical solutions for heat conduction were used to back-calculatehe
values from the temperature-time data in such trials. As expected, the heat transfer coefficient depended primarily on the air velocity. Nonlinear regression analysis to fit power law equations for samples of 2 sizes and the 3 kinds of wetting liquids were performed with the following results.A. The Small Infinite Cylinder (Diameter = 0.072 m.) (1) water (Figure 7. 1)
h e
= 19.52V 0.416 ..
(2) sodium chloride (Figure 7.2)
(R 2 = 0.993)
(R
2
= 0.989 )(3) potassium chloride (Figure 7.3)
(R 2
= 0.985)B. The Large Infinite Cylinder (Diameter= 0.142 m.)
(1)
water (Figure 7. 1)he
= 1 5.55 V.. O.501
(R 2 = 0.980 )(2) sodium chloride (Figure 7.2)
he
= 15.16V .. 0.457
(R 2 = 0.992 ) (7. 1) (7.2) (7.3) (7.4) (7.5)(3) potassium chloride (Figure 7.3)
(R 2
= 0.988 ) (7.6)Table 7.2 shows heat transfer coefficients and 95% confidence bounds for individual data points at the mid-range value of air velocity. The bounds were calculated assuming normally distributed errors.
Variations in the measured heat transfer coefficients could be caused by any air or excess saturated salt solution trapped between the wet cloth and the plastic film. The amount of saturated salt solution trapped might have affected the thickness of the salt layer deposited on the cloth, and the amount of solution present might have been different for different trials. Therefore some variation in
he
for the same kind of salt is possible at any air velocity. The heat transfer coefficients also depended slightly on kinds of the liquids used, probably because different salt solutions had different thermal conductivity and where deposition occured different kinds of crystal resulted. For example, NaCI crystals were coarser than KCI crystals. These effects probably explain whyhe
for the salt solutions is lower than for water. Whilst it could be argued that the differences between equations (7. 1), (7.2), and (7.3) in one group and equations (7.4), (7.5), and (7.6) in the other were not statistically significant it was decided to use the equations specific to the different wetting fluids in further analysis because there were sensible physical reasons for differences to occur, and because each equation is based on 8 - 1 1 points, a significant number.The range of air temperatures used during cooling trials was 0 to 10 °C. Although temperature affects the thermal and physical properties of air (which in turn affect Reynolds
number
(Re),
Prantl number(Pr),
and Nusselt number (Nu» , the effect of temperature (in the interested range of 0 °C to 10 °C) on the surface heat transfer coefficient through the property changes was probably negligibly small compared to uncertainties in the measurement systems e.g.Pr
changes from 0.707 at 0 °C to 0.705 at 10 °C andRe
by 6.2 % due to v (kineticviscosity). The
he
values represent the effects of both convective and radiation heat transfer at the product surface.7.4 EQUILIBRIUM TEMPERATURE ANALYSIS
At the equilibrium temperature
(Teq),
the convective cooling rate and water vaporisation rate are in balance. In Chapter 5, equations for the equilibrium temperature were derived theoretically. In this chapter, the practical existence of the equilibrium temperature is tested. In theory it takes an infinitely long time to reach an equilibrium state. In practice, the apparent steady state condition at 15 hours was used as an approximation as all runs had reached steady state within the sensivity of the measurement system in less than 15 hours. As Tables 7.3 to 7.5 show, the experimental steady state temperature(Teq,up)
closely matched the calculated equilibrium temperature(Teql',ed'
determined using equation 5. 1 1). Figures 7.4 -7.9 plot the difference between the calculated equilibrium temperature
(Teql',eJ
and the experimental steady state temperature (assumed experimental equilibrium temperature,Teq,up)
against different parameters. Figure 7.5 suggests that there may be a trend with respect to
H, but the evidence is relatively weak. Otherwise, no significant trends were noted although the spread of results was greater at low velocities. The 95% confidence bounds were -0.4 °C to +0.3 °C (Tables 7.6 and 7.7) which is of the same magnitude as the estimated measurement uncertainty. It was concluded that within the limits of the methods used for verification the model is valid and the Lewis relationship held adequately down to velocities of about 0.4
ms·l•
7.5 LINEARIZATION OF SEMI-LOG PLOTS
As expected when the product was wrapped with the plastic film (no evaporation), it was found that at the steady state condition,
Teq,e.xp
equalledTa
(e.g. Figure 7. 10). When evaporation occured, it was found thatTeq,up
>Ta
ifaw
< H, (e.g. Figure 7. 1 1)Teq,e.xp
<Ta
ifaw
> H, (e.g. Figure 7. 12)Teq,UfJ
=Ta
ifaw
= H, (e.g. Figure 7.13)When modified
Yc,up
values were calculated usingTeq,up
to replaceTa
as discussed in Chapter5 it was observed that the modified
Yc,e.xp
and the measured equilibrium temperature linearized the plots of InYc,e.xp
versusFo
sucessfully. For example Figures 7.14 - 7.16 are the results of linearization from Figures 7. 1 1 - 7.13 respectively usingTeq,up'
The jagged appearance ofthe lines at lower
Y
c,up arises from analogue to digital conversion accuracy in the data loggingsystem. The portion of the line below modified
Y
c,up = 0.70 could be best-fitted by a straightline with R2 > 0.99 for all runs. This verified that Teq satisfactorily linearised the cooling
curves.
7.6 COOLING WITH EVAPORATIVE EFFECTS
In Chapter 5, the technique to model the evaporation effect was proposed in the form of relative values of / and j for evaporation plus convection versus convection only. The experimental results and comparisons to model predictions are shown in Tables 7.3 - 7.5. In the most extreme cases, the relative rate of cooling with evaporation to convection only is about 2 to 1. In deriving the tabulated results, experimental values of fcEWJP and jcEWJP were derived from plots of In