**3.3. Results**

**3.2. Boundary conditions**

At the surface, r = R:

The drying rate, m

[28,29] as follows:

and

•

Heat and mass transfer coefficients, h and *kc*

where *<sup>X</sup>*¯ is an average moisture content and *kv* is

At the center of the sphere, r = 0

184 Wind Tunnel Designs and Their Diverse Engineering Applications

0 *<sup>w</sup>*


¶ (16)

Δhv (17)

, can be determined by the correlations found in

(19)

*wdv k k kX* = + (20)

= ×D (21)

0.5 0.33 *Nu Re Pr* = +F 2 (18)

, in Eq. (6) repre‐

*w <sup>T</sup> <sup>k</sup> r* ¶

*r* ¶

−*kd* ∂*Td* ∂ *r*

At the receding evaporation front (r = z), the moving boundary conditions are

+ *kw*

¶

( ) *<sup>d</sup> d a sr nz <sup>T</sup> k hT T q*

> ∂ *Tw* ∂ *r*

, was defined in Eqs. (5 & 6). However, in this case, *z* "

sents the distance from the droplet surface (r = R) to the receding evaporation front (r = z).

'

0.5 0.33 *Sh Re Sc* = + 2 b

where Φ and β are constants ranging from 0.6-0.7 for Re (500 -17000).

Thermal conductivity of the wet region can be evaluated according to [30] as:

*v v v D M dp k h RT dT*

= m•


A single droplet of sodium sulphate decahydrate solution was suspended from the free end of the glass nozzle at an air temperature of 75o C and an air velocity of 1 m/s. The wet-bulb tem‐ perature was 46o C. The core and surface temperatures of the droplet versus time are plotted in Figure 15. Initially, the temperatures increased rapidly because of the large difference in tem‐ perature between the drying medium and the droplet. Basically, the plot exhibited two drying periods. A short period, from time =100 - 200 s, where the surface temperature approached the wet-bulb temperature, is described as the constant rate period. The second period, or falling rate period, extended from t =200 s to the end of the experiment.

**Figure 15.** Temperature distribution profile for sodium sulphate decahydrate at air temperature of 75o C.

Figure 15 plots the predicted values of both the core and surface temperature evaluated by the developed model. Comparison of the experimental and theoretical results showed good agreement. However, actual surface temperatures were slightly higher than those predicted by the model. This probably was due to the position of the thermocouple and its reading during the experiment, as will be discussed later in more detail.

The previous experiment was repeated at an air temperature of 140o C in the same drying medium. Figure 16 shows experimental and theoretical results of a droplet of the same ma‐ terial. The experimental results showed that the constant rate period extended from time= 85 - 165 s, shorter than that observed at 75o C. The results showed both surface and core tem‐ peratures of 130o C at 900 s, at which point the droplet had dried completely. Figure 16 showed agreement between the experimental and predicted results.

**Figure 16.** Temperature distribution profile for sodium sulphate decahydrate at air temperature of 140o C.

A single droplet of a fruit juice was dried at an air temperature of 75º C and an air velocity of 1 m/s. Wet-bulb temperature was 44.5o C. The experimental results in Figure 17 show a con‐ stant rate period from time =100 - 200 s. The falling rate period can be observed after the constant period, when the temperature increased quickly.

Figure 15 plots the predicted values of both the core and surface temperature evaluated by the developed model. Comparison of the experimental and theoretical results showed good agreement. However, actual surface temperatures were slightly higher than those predicted by the model. This probably was due to the position of the thermocouple and its reading

The previous experiment was repeated at an air temperature of 140o C in the same drying medium. Figure 16 shows experimental and theoretical results of a droplet of the same ma‐ terial. The experimental results showed that the constant rate period extended from time= 85

C at 900 s, at which point the droplet had dried completely. Figure 16

C. The results showed both surface and core tem‐

C and an air velocity of

during the experiment, as will be discussed later in more detail.

showed agreement between the experimental and predicted results.

**Figure 16.** Temperature distribution profile for sodium sulphate decahydrate at air temperature of 140o C.

1 m/s. Wet-bulb temperature was 44.5o C. The experimental results in Figure 17 show a con‐

A single droplet of a fruit juice was dried at an air temperature of 75º


186 Wind Tunnel Designs and Their Diverse Engineering Applications

peratures of 130o

During the falling rate period some experimental readings represented approximate values of the actual droplet surface temperatures. The approximate values can be attributed to the fact that the droplet diameter constantly decreased with time and that caused the distance between the tip of thermocouple and the surface of droplet to grow. In other words, during some time in the experiment, a part of the end tip of the thermocouple was touching the sur‐ face of the droplet, and the remaining area of the tip was exposed to air flow. Such a behav‐ ior caused the tip of thermocouple to give an average reading for both the surface and the air flow temperatures. Good agreement was obtained between the theoretical and experi‐ mental results of the temperature profile for the fruit juice.

**Figure 17.** Temperature distribution profile for fruit juice at air temperature of 75o C.

The fruit juice droplet was dried again at an air temperature of 140o C in the same drying medium. The results (Figure 18) showed that the constant rate period was a little shorter than that at 75o C. The results showed also that both surface and core temperatures were similar and close to the air temperature at time = 1050 s. The mathematical model showed also good agreement with the experimental readings.

**Figure 18.** Temperature distribution profile for fruit juice at air temperature of 140o C.

A single droplet of organic paste was dried under similar conditions to that of the fruit juice. A plot of the core and surface temperatures of the droplet versus time is shown in Figure 19. A relatively longer period of constant drying rate, compared to those shown for sodium sul‐ phate and fruit juice, was observed. Figure 19 also showed that surface temperature in‐ creased rapidly after time = 300 s, indicating the beginning of the falling rate period. Less agreement was obtained between the model's predicted results and the experimental re‐ sults. Organic paste, which has higher thermal conductivity, forms a thicker solid crust at the outer surface compared to the other material evaluated. Therefore, a higher resistance to heat and vapor through the crust would be expected. To improve the predictions, introduc‐ tion of a correction factor is probably required in the model for those materials which have a nature similar to that of the organic paste. Figure 20 shows the experimental and theoretical results of air temperature of 140o C. Again, forming a solid crust at the outer surface led to less agreement between theoretical and experimental results. The predicted temperature dis‐ tributions were higher than the actual temperatures.

than that at 75o

also good agreement with the experimental readings.

188 Wind Tunnel Designs and Their Diverse Engineering Applications

**Figure 18.** Temperature distribution profile for fruit juice at air temperature of 140o C.

A single droplet of organic paste was dried under similar conditions to that of the fruit juice. A plot of the core and surface temperatures of the droplet versus time is shown in Figure 19. A relatively longer period of constant drying rate, compared to those shown for sodium sul‐ phate and fruit juice, was observed. Figure 19 also showed that surface temperature in‐ creased rapidly after time = 300 s, indicating the beginning of the falling rate period. Less agreement was obtained between the model's predicted results and the experimental re‐ sults. Organic paste, which has higher thermal conductivity, forms a thicker solid crust at the outer surface compared to the other material evaluated. Therefore, a higher resistance to heat and vapor through the crust would be expected. To improve the predictions, introduc‐ tion of a correction factor is probably required in the model for those materials which have a nature similar to that of the organic paste. Figure 20 shows the experimental and theoretical

C. The results showed also that both surface and core temperatures were

similar and close to the air temperature at time = 1050 s. The mathematical model showed

**Figure 19.** Temperature distribution profile for organic paste at air temperature of 75o C.

The moisture content of the droplet was determined by measuring the weight loss against time. There was no experimental technique to measure core and surface moisture content sep‐ arately; therefore, the measured moisture content of the droplet represented the average val‐ ue. The experimental results of moisture content distribution for the three samples at an air temperature of 75o C, are shown in Figure 21. The moisture content profiles clearly show the two stages of drying, the constant rate period and the falling rate period. The profiles show that the sodium sulphate decarbohydrate solution had consistently lower moisture content, as it dried faster than the other materials. The profiles also showed that forming a solid crust in the falling rate period lowered the moisture content values for all the three samples. In the case of organic paste, the change in the moisture content was more significant.

**Figure 20.** Temperature distribution profile for organic paste at air temperature of 140o C.

Obviously, crust formation, thickness and porosity have a significant effect on the moisture content and on the drying rate of the droplet. This result was also obtained by Hayder & Mumford [31] in the drying of custard and starch droplets. They observed that crust forma‐ tion was more rapid on the custard droplet, because the smaller starch granules absorbed less and left more free water in the droplet. Therefore, the crust growth and the drying rate of the starch droplets took a longer time.

Moisture distribution curves for the three samples at 140o C air temperature are plotted in Figure 22. Similar results were obtained to those observed at an air temperature of 75o C. Also, the profiles showed that the moisture content dropped to lower values compared to those at 75o C. In other words, the droplets dried faster at the higher temperature.

#### **3.4. Discussion**

As previously observed, moisture and temperature distribution profiles of various materials exhibited constant and falling drying rate periods. In the constant rate period, the tempera‐

**Figure 21.** Moisture content profile for all samples at air temperature of 75o C.

Obviously, crust formation, thickness and porosity have a significant effect on the moisture content and on the drying rate of the droplet. This result was also obtained by Hayder & Mumford [31] in the drying of custard and starch droplets. They observed that crust forma‐ tion was more rapid on the custard droplet, because the smaller starch granules absorbed less and left more free water in the droplet. Therefore, the crust growth and the drying rate

Figure 22. Similar results were obtained to those observed at an air temperature of 75o

Also, the profiles showed that the moisture content dropped to lower values compared to

C. In other words, the droplets dried faster at the higher temperature.

As previously observed, moisture and temperature distribution profiles of various materials exhibited constant and falling drying rate periods. In the constant rate period, the tempera‐

C air temperature are plotted in

C.

of the starch droplets took a longer time.

190 Wind Tunnel Designs and Their Diverse Engineering Applications

those at 75o

**3.4. Discussion**

Moisture distribution curves for the three samples at 140o

**Figure 20.** Temperature distribution profile for organic paste at air temperature of 140o C.

ture of the droplet surface was almost equal to the wet-bulb temperature. During this peri‐ od, evaporation takes place from the free liquid surface of the droplet. The constant rate period was relatively short in sodium sulphate and fruit juice samples. However, that peri‐ od was longer in the case of organic paste.

The falling rate period is characterized by formation of a partial crust on the outer surface of the droplet. This crust recedes towards the core and the surface temperature starts to in‐ crease. Vapor diffusion becomes the predominant transport process at this stage. Crust structure, thickness and porosity have a significant effect on the rate of drying. The crust thickness increases with time, hence the resistance to heat and moisture diffusion through the crust increases. Therefore, moisture content and drying rate decrease.

Some experimental readings represented approximate values of the actual droplet surface temperatures. This was attributed to the end tip of thermocouple that was giving average readings for both the surface and the air flow temperatures at the same time. It was also as‐

**Figure 22.** Moisture content profile for all samples at air temperature of 140o C.

sumed that the mechanism of the droplet drying is similar for both small and large diame‐ ters. Therefore, it is recommended that a more accurate technique for measuring droplets with small sizes and for the taking of surface temperatures be developed.

The new model predicted temperature distribution profiles for single droplets of various ma‐ terials. The predicted results showed a good agreement with the experimental data for air temperatures at 75o C and 140o C. However, the model was less accurate in the case of organic paste due to the higher thermal conductivity of the formed crust. A correction factor should be developed and taken into account for such materials. The model provides a relatively fast and efficient way to simulate drying behavior over a range of drying conditions. The model also represents a useful tool in the design and optimization of spray drying processes.

Moisture content profiles clearly showed the two stages of the drying process. In addition, the moisture profiles supported the conclusions that the crust forming in the falling rate pe‐ riod decreased both the moisture content and the drying rate.

Through the results of the experimental work and the theoretical model for a droplet drying, a significant conclusion was obtained. It has always been wrongly assumed in the literature that there is no temperature distribution within the droplet. This concept has been corrected by the current research. All experiments for the three materials used showed a clear difference be‐ tween the core and the surface temperatures of the droplet during the drying process.
