3. Falling film heat transfer coefficient development

The idea was to modify the famous and well accepted Han and Fletcher's correlation to incorporate the different salt concentration effect and expanded to low range temperature evaporation. This will help to fill two major gaps as mentioned earlier in processes industries evaporators design.

#### 3.1 Theoretical model

The dimensionless terms such as Nusselt, Reynolds and Prandtl numbers in the Han and Fletcher's correlation are adequate to incorporate the liquid film thermal effect in heat transfer. As per steam properties table, the specific volume of steam is rapidly changes at low temperature and it might have significant effect on heat transfer. At low temperature, the generation of microbubbles at tubes surfaces rapidly detach due to low density and it agitate the thermal barrier formed by liquid film. The conventional heat transfer correlations are not able to capture this effect. The heat transfer enhancement due to micro-bubble generation and detaching is an important phenomenon at low temperature and need to be captured in heat transfer correlation for efficient evaporator design.

The basic form of Han and Fletcher's correlation is shown in Eq. (1).

$$\frac{h\_{\text{evap}} \left(\frac{\mu\_l^2}{g\rho\_l^2}\right)^{1/3}}{k\_l} = \text{Nu} = \text{0.0028} (\text{Re}\_{I'})^{0.5} (\text{Pr})^{0.85} \tag{1}$$

The constants and indices can be found from the boundary conditions of falling film evaporators. The heat supplied to the evaporator can be calculated by the energy balance of hot water circulation through the tubes as presented in Eq. (2).

$$Q\_{\rm in} = m\_{\rm ch,w} \mathbf{C} \mathbf{p}\_{\rm ch,w} \left( T\_{\rm ch,w}^{\rm o} - T\_{\rm ch,w}^{i} \right) \tag{2}$$

The overall heat transfer coefficient (Uoverall) can be calculated by using the saturation temperatures of evaporator and log mean temperature difference (LMTD) parameters as shown in Eq. (3).

Design of Industrial Falling Film Evaporators DOI: http://dx.doi.org/10.5772/intechopen.84230

$$\text{UA}\_{\text{overall}} = \frac{m\_{\text{ch},w} \text{Cp}\_{\text{ch},w} \left( T\_{\text{ch},w}^{\text{out}} - T\_{\text{ch},w}^{\text{in}} \right)}{\left\{ \frac{\left( T\_{\text{ch},w}^{\text{out}} - T\_{\text{ant}} \right) - \left( T\_{\text{ch},w}^{\text{in}} - T\_{\text{ant}} \right)}{\ln \left( \frac{\left( T\_{\text{ch},w}^{\text{out}} - T\_{\text{ant}} \right)}{\text{ch}\_{\text{b}} \cdot w} \right)} \right\}} \tag{3}$$

The Dittus-Boelter correlation can be applied to investigate the local heat transfer coefficient for falling film evaporators as shown in Eq. (4).

$$\mathbf{Nu} = \mathbf{0.023Re}^{0.25} \mathbf{Pr}^n \tag{4}$$

Now, falling film heat transfer coefficient for evaporation can be calculated by applying Eqs. (1)–(4). The material resistance is neglected due to very thin tube wall (less than 0.7 mm). Eq. (5) presents the calculation process for falling film heat transfer coefficient.

$$\frac{1}{\mathbf{UA}} = \left(\frac{1}{\mathbf{hA}}\right)\_{\text{tubeside}} + R\_{\text{wall}} + \left(\frac{1}{\mathbf{hA}}\right)\_{\text{outside}}\tag{5}$$

The unknown parameters in Eq. (5) are calculated by the planned experiments as discussed in the following sections.

#### 3.2 Experimental apparatus

The pilot facility of adsorption desalination (AD) cycle in Mechanical Engineering (ME) Department of NUS is utilized to investigate the unknown parameters for FFHTC correlation development. The AD pilot facility is shown in Figure 1.

The AD cycle has four major components such as (a) reactor beds packed with adsorbent, (b) evaporator, (c) condenser and (d) circulation pumps. In addition, there is also a conditioning facility and pre-treatment facility to perform test at an accurate conditions. The flow schematic of AD cycle is shown in Figure 2.

To investigate the falling film heat transfer coefficient, evaporator is designed with horizontal tubes arranged in staggered manner. There are four rows of tubes and each row has 12 tubes installed in four pass arrangements. The tubes are

Figure 1. Adsorption cycle pilot installed at NUS, Singapore (published with PI permission [43, 44]).

### Heat and Mass Transfer - Advances in Science and Technology Applications

#### Figure 2.

Adsorption cycle flow schematic with detailed components (published with author's permission [43, 44]).


#### Table 3.

Adsorption cycle evaporator design parameters.

fabricated with special outside and inside profile to enhance heat transfer. The design parameters of evaporator are given in Table 3.

#### 3.2.1 Experimental procedure

There are three liquid circuits in the system those are important to control and maintain for a successful experiment. Firstly, the chilled water circulation through the tubes of evaporator to maintain required saturation temperature. An accurate thyristor controlled heater is installed to control chilled water temperature within ˜ 0.15 K. A vacuum rated feed pump help to spray water from pool of evaporator below tubes bundle to the tubes surface. To maintain the liquid level in the evaporator, the evaporated quantity refluxed back from condenser as a close loop.

Secondly, the cold water supply to the adsorption bed to remove the heat of adsorption. The adsorber bed directly communicates to evaporator to adsorb the vapors and release the heat of adsorption. This heat must be removed to maintain the vapor uptake otherwise it can be drooped to very low quantity. The cooled water flow through the cooling tower on the rooftop to reject heat to the ambient.

Lastly, the heat source to the desorber bed to regenerate the adsorbent. Once the adsorber bed fully saturated, it cannot take more vapor and it has to be regenerated for next adsorption process. The hot water is circulated through the tubes of the bed to supply heat of desorption to the adsorbent. The hot water temperature is maintained either by heater or solar thermal collectors.

Design of Industrial Falling Film Evaporators DOI: http://dx.doi.org/10.5772/intechopen.84230

Since whole system is operating at sub-atmospheric pressure so it is required to remove the non-condensable gases. A vacuum pump is connected to all the major components to remove non-condensable in case on any leakage. Table 4 shows the operation parameters of AD cycle.

The system is instrumented with highly accurate sensors to extract real time data. For example, for pressure measurements, Yokogawa pressure transducers are installed. These sensors can measure 0–60 kPa (abs) with accuracy of ˜0.25%. Similarly, liquid flow is measured by KROHNE flow meters (accuracy ˜ 0.5%) and temperatures are recorded by OMEGA 10 kΩ thermistors (accuracy ˜ 0.15 K). All sensors are connected to Agilent system for data logging.


Table 4.

Experimental operational parameters of adsorption pilot.

#### Figure 3.

Micro-bubbles agitation of liquid film on evaporator tube surfaces captured by camera (published with author's permission [43, 44]).

#### Figure 4.

Conventional thermal barrier braking phenomenon due to bubble agitation (published with author's permission [43, 44]).

To capture the event of micro-bubble formation at low pressure, a high speed camera was installed on evaporator. The camera successfully captured the agitation of liquid film on tube surface due to formation and detaching of micro-bubbles as shown in Figure 3. The phenomenon of breaking the liquid thermal barrier due to film agitation is presented in Figure 4 step by step. The natural temperature gradient within liquid film on tubes surface is the major bottle neck in heat transfer. The micro-bubble generation at low temperature agitates this barrier due to low density and produce turbulence as also captured by camera. The micro-bubble, firstly agitate the liquid film and break thermal barrier that enhance heat transfer. Secondly, when it moves up due to low density, it draw heat and provide space to adjacent liquid to have direct contact with tube surface that helps faster heat transfer rates.

## 4. Results and discussion

The overall heat transfer coefficient (U) was calculated at assorted heat source and salt concentrations. The evaporator chilled water temperature was varies from 10 to 40°C and salt concentration from 35,000 to 95,000 ppm. The typical trend is presented in Figure 5 at 90,000 ppm salt concentration. The similar trend was observed at other concentration values.

The two important results can be concluded, firstly, the U values drop over 25% due to salt concentration at lower temperature but this impact is not very significant at higher temperature. This might be due to propertied change at higher temperature. Secondly, The U values are higher at lower temperature and this is due to micro-bubble generation and detaching phenomenon as described earlier. The same trend of U values at all concentrations strengthens the argument of micro-bubble enhanced heat transfer phenomenon.

#### Figure 5.

Overall heat transfer coefficient profiles at 90,000 ppm salt concentration and different chilled water temperatures (with author's permission [43, 44]).

#### Design of Industrial Falling Film Evaporators DOI: http://dx.doi.org/10.5772/intechopen.84230

The falling film heat transfer coefficient (FFHTC) values are then calculated by using the methodology presented in the earlier section and presented in Figure 6. It can be noticed that FFHTC follows the same trend as U values at assorted heat source and salt concentrations.

The noticeable point in the plot is the heat transfer coefficient values drop initially with drop in evaporator vapor space temperature and achieve minimum values at 300 K. Once the vapor space temperature dropped further down, the heat transfer values start increasing. The increasing trend is even sharper below 295 K vapor space temperature and this is because of rapid change in vapor specific volume. The vapor specific volume change can divide the evaporation processes into three categories; namely, film surface evaporation, transition and micro-bubble assisted evaporation. The sharp change in specific volume below 295 K help to generate micro-bubble that detach from tube surface immediately due to low density and agitate the thermal barrier resulting increase in heat transfer rates. This phenomenon is observed and captured for the first time and named as "microbubble assisted film evaporation".

It can be clearly noticed that micro-bubbles play an important role at low temperature to enhance the heat transfer. The traditional heat transfer coefficient correlations are not able to capture this unique phenomenon. All correlations available in the literature can only work in film surface evaporation zone. Their extrapolation to capture transition and micro-bubble assisted zone also cannot predict an accurate value and heat exchanger designed based on these values cannot perform up to the level. Hence there is an urgent need for the development of an accurate heat transfer coefficient correlation to capture these two zones for efficient heat exchanger design.

A new correlation is proposed for falling film heat transfer coefficient that can efficiently capture transition and micro-bubble assisted evaporation at assorted salt concentration. The proposed model was written in FORTRAN and fitted with experimental data conditions. All important parameters such as heat flux, flow velocity and vapor properties were also included. Most importantly, the salt concentration and vapor specific volume parameters those were missing in conventional correlations are also embedded in the proposed correlation as shown in Eq. (6) [48, 49].

#### Figure 6.

Experimental film evaporation heat transfer coefficient profiles at different saturation temperature and different salt concentrations (with author's permission [43, 44]).

$$h\_{\text{fallingfilm}} = \left\{ 0.279 \left( \frac{\mu\_l^2}{g\_\gamma \rho\_l^2 K\_l^3} \right)^{-0.333} (R\_\epsilon)^{-2.18} (P\_r)^{4.0} \left( 2.\exp\left(\frac{S}{300000}\right) - 1 \right)^{-0.45} \right\}$$

$$\cdot \left( \frac{T\_{\text{emp}}}{322} \right) \rangle + \left\{ 0.875 \left( \frac{q}{DT} \right) . \left( \frac{V\_{\text{emp}}}{52.65} \right) \right\} \tag{6}$$

The proposed correlation is applicable from 280 to 305 K saturation temperatures. It also captures the feed water concentration ranges from 35,000 to 95,000 ppm. The film Reynolds number (ReГ) ranges from 45 to 90 and Prandtl number (Pr) from 5 to 10. In proposed correlation, the first term control the thermally driven evaporation and second terms capture bubble assisted evaporation phenomenon that is missing in the conventional correlations. The proposed model results are presented in Figure 7. It can be noticed that model has good agreement with experimental results. The uncertainty of measured data is less than 5% and RMS of regressed data is 3.5%.

Conventionally, the Han and Fletcher correlation is applied in the industry for low temperature rages with its extrapolated results. The comparison of actual heat transfer values calculated by the experiments is compared with extrapolated Han and Fletcher values and it can be observed from Figure 8 that there is huge difference. The conventional Han and Fletcher correlation can only capture film evaporation zone accurately but bubble assisted evaporation is totally out of range. The unique feature of "bubble assisted evaporation" can only be captured by the proposed falling film heat transfer coefficient correlation that boost heat transfer 2–3 fold. As a result, for process industries where the saturation temperature is below 295 K, the evaporator can be compact and low cost as compared to current design. The proposed correlation is timely and important for efficient design of falling film evaporator for process industries.

#### Figure 7.

The proposed falling film heat transfer coefficient correlation with experimental results (with author's permission [43, 44]).

Design of Industrial Falling Film Evaporators DOI: http://dx.doi.org/10.5772/intechopen.84230

#### Figure 8.

Proposed falling film heat transfer coefficient compared with conventional Han & Fletcher's extrapolated values (with author's permission [43, 44]).

### 5. Summary

The horizontal falling film evaporators have many advantages over submerged and vertical tubes evaporators. Currently, there is no heat transfer correlation that can capture evaporation at low temperature especially below 295 K with different salt concentration. This is very important for efficient design of process evaporators. A horizontal tube falling film heat transfer coefficient correlation is proposed to capture effect, low temperature and salt concentration. It is demonstrated that the actual heat transfer values at low temperature can be 2–3 fold higher than the estimated values due to unique bubble-assisted evaporation phenomenon. The proposed correlation is applicable from 280 to 305 K saturation temperatures and feed water concentration ranges from 35,000 to 95,000 ppm. The uncertainty of measured data is less than 5% and RMS of regressed data is 3.5%.

#### Acknowledgements

Authors would like to thanks to KAUT and NUS for this study. The data is reproduced by the author's permission [44].

#### Nomenclature


