# Numerical Analysis of Heat Exchanger for Spray-Assisted Low-Temperature Desalination System

Authors: Amour Othman Muhunzi; Yusufu Abeid Chande Jande; Revocatus Lazaro Machunda
Journal: Journal of Energy
 (2020)

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## Abstract

A numerical study for heat exchanger for spray-assisted low-temperature desalination system is presented for an existing low-temperature desalination unit at Arusha Technical College. This is aimed at recognizing the effect of mass flow and physical parameters like tube layout (diameter and length) on the overall heat transferred and the pressure drop in the shell-and-tube heat exchanger (STHX), as well as the impact of these parameters on the heat transfer coefficient and the overdesign of the STHX. Also, the study provides a suitable mathematical model for the replacement of the current condensation unit which tends to reduce energy consumption by reducing some of the electrical components in the system. A Math CAD model was developed using the Delaware method to obtain the mentioned parameters. The results show that at 0.8 kg/s flow rate a maximum heat transfer coefficient of 23212 W/m2K is achieved in a minimum diameter of 10 mm within a maximum tube length of 1000 mm heat exchanger and the pressure drop seems to be very low in a range of 0.328-0.957 Pa from all configurations. The configuration with 1000 mm tube length and 10 mm diameter performed well on the mass flow of 0.3 kg/s-0.8 kg/s by providing a suitable overall heat transfer coefficient of 2306-2539 W/m2K, while 12.8 is a maximum overdesign coefficient achieved on 0.8 kg/s mass flow. The study results show the possibility of using STHX instead of the current condensation unit in implementing a proposed system layout with the minimum effect of energy consumption.


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## Body

## 1. Introduction

The present society demands the efficient utilization of energy and at the same time reducing environmental impact to contribute to sustainable economic development. The increase of freshwater demand is mainly caused by the development of world industries and human population growth, while potable water is one of the key resources for the existence of human beings [1]. Desalination of brackish or seawater is an important approach to solve the water resource dearth. We may categorize the desalination process as thermal and nonthermal based on energy consumption [2].Spray-assisted low-temperature phase-change desalination technique is the thermal-based method that makes no boundary upon heat and mass transfer mechanism and eliminates the contribution of mechanical energy input [3]. This technology comprises two main units to reach the freshwater, namely, evaporation unit and condensation unit [4]. Fortunately, solar energy can either be used directly or indirectly in supplying thermal energy to an evaporation unit as used in vaporization of liquid into vapor and cause steam formation [5]. However, the heat exchange process occurs in the condensation unit by exchanging steam temperature with that of cooling media (gas or liquid) and condensing the steam into liquid freshwater [6].Literature shows some of the experimental and numerical studies done by some researchers concerned with the condensation unit in different desalination systems. Alsadaie and Mujtaba [7] through the multistage flash (MSF) desalination developed a dynamic fouling model of the heat exchanger, reaction and diffusion mechanisms were included to investigate the effect of surface temperature and flow velocity, and the fouling results made a clear agreement with the literature on current studies. The cryogenic refrigeration unit embedded with multieffect desalination unit hybrid system was designed by Ghorbani et al. [8] which analyzed the thermos-economic.In adsorption desalination, Elsayed et al. [9] used an aluminum fumarate metal-organic framework in experimental observation of cooling water desorption, adsorption, and condensation. Olkis et al. [10] analyzed the performance of an adsorption heat transformer through the usage of benchmarking material silica gel in the production of freshwater together with the cooling process as done by Thu et al. [11] and achieved a performance ratio of 0.60 at the inlet temperature of 80°C. Also, silica gel was proposed by Rezk et al. [12] to be employed in solar-assisted adsorption desalination cooling for the performance maximization; the results show an improvement of 70% increase in specific cooling power, 0.961 coefficient of performance, and 6.9 m3/day/ton specific daily water production.Another study was done by Woo et al. [13] on a silica gel-based adsorption cooling cum desalination system concerned with the performance effect, operating pressure, and brine concentration. Towards eco-friendliness, David et al. [14] recovered the waste heat through the method of evaporative condenser cum thermal desalination. An experimental study was conducted by Rabhi et al. [15] on the external condenser and pin fin absorber from a modified solar still; the evaluation was based on the performance of water production and the thermal behavior.Chandrakanth et al. [16] computed the tube-side pressure drop and heat transfer area respective in the optimization of the shell and tube condenser process parameters and geometric used in thermal desalination plants. The optimum pressure drop vs. heat transfer area was concluded from the second law analysis to overcome the trade-off in between. Via stoichiometric process in the spray flash desalination system, a water level model for after condenser was constructed by Matsuda et al. [17]; the results show the proper model that could improve the system behavior.From the above literature, the flash evaporator has been reported from many theoretical and experimental studies as an essential unit in the low-temperature desalination technology. But there is no specific study that discusses the condensation unit on flash evaporation desalination technology. Moreover, currently, there is an existing low-temperature desalination unit at Arusha Technical College (ATC), which uses more energy at the condensation unit. Thus, this paper focuses on a heat exchanger design for spray-assisted low-temperature desalination, whereby the pressure drop, heat transfer coefficient, overall heat transfer coefficient, oversurface, and overdesign are the main concern. The heat exchanger is designed to reduce the level of energy consumption, allowing for a smooth working environment of the desalination unit.


## 2. Modification of Existing System Configuration

Figure1 shows a schematic of the current layout with several electric components, namely, blower, feed pump, filter with a suction fan, cooling water circulation pump, and condenser with a suction fan. These components make a high level of energy intensity. Here, saline water from the source chamber is pumped into the flash chamber via nozzles. The sprayed flash occurs and the small droplets absorb the thermal energy in the flash chamber to form steam. Steam is escaping the chamber by passing between the chamber’s walls, sucked through filter suction fan directly to the filter, then sucked by condenser suction fan and condensed, and finally stored as freshwater in a distillate reservoir. The steam is condensed when the cold water is circulated in the condenser from the water circulator tank via a second feed pump. At the same time, the condenser suction fan sucks the steam from the filter to speed up the process in which much steam is allowed to escape into the atmosphere. Both condenser and filter suction fans increase the amount of energy consumption on the system.Figure 1
The current layout of spray flash evaporation system.Figure2 shows a schematic of a proposed layout that remains with the blower and the feed pump only which may alleviate the energy consumption through the implementation of the heat exchanger as a condensation unit. Now, source water from the source chamber is pumped to evacuated tube collector through the heat exchanger then fed to a flash chamber via nozzles. As usual, the sprayed flash occurs and absorbs the thermal energy in the flash chamber to form steam. Steam escapes the chamber by passing at the top, condensed by exchanging heat with cold water from the source at the heat exchanger, and stored as a freshwater. The blower is embedded with a flash chamber to increase temperature and relative humidity [18]. The heat exchanger acts as a condenser and at the same time becomes a preheater for the incoming cold water. The evacuated tube collector (also a preheater) raises further the temperature of the feed water before it is fed into the flash chamber.Figure 2
Proposed layout of spray flash evaporation system.


## 3. Heat Exchanger

The heat exchange process takes place between two or more channels at different temperatures when fluids of the channels exchange their temperature by passing through a heat exchanger [19]. The heat exchanger is a piece of equipment that permits heat transfer and often goes together with mass transfer [20]. The equipment has been used in various industries including processing industries, power plants, and many other industries [21]. Among the several heat exchanger models, shell-and-tube heat exchangers (STHX) are the best [22] and widely used [23]. Also, it can be constructed easily in an extensive range of sizes compared to other categories [24]. A model of the shell-and-tube heat exchanger is shown in Figure 3(b).Figure 3
(a) Low-temperature evaporator in Arusha Technical College, Tanzania. (b) Shell-and-tube heat exchanger model.
(a)(b)


## 4. Methodology

Thermal conductivity, density, viscosity, and specific heat capacity of the cold and hot fluid stream were among the factors estimated in the primary stage in the STHX design as can be seen in Table1, taken from the existing evaporator which appeared in Figure 3(a). Double shell passes were taken into account, and a triangular pitch of 1.25 space between tube to tube centers was considered for the analysis. A single segmental baffle was chosen for ease of maintenance and high thermal features. U-tube (tube sheet) was used to permit a distinction of thermal expansion. Moreover, the outlet temperatures 29 and 28°C (t7 and t3) for steam and water, respectively, were assumed to control the output and easy computation as shown in Figure 3(b).Table 1
Physical parameters of steam and water were taken from the steam evaporator.
System componentsṁ(kg/s)Tinlet(°C)Toutlet(°C)ρ(kg/m3)Cp(kJ/kg K)μ(Pa s)k(W/m K)Rfouling(m2K/W)Steam0.02460290.19119140.0000110.0230.00009Water0.1-0.82528996.441790.000890.5970.00018


### 4.1. Thermal Design

The temperature difference on the tube side or that of shell side was used to define the sensible heat transfer rate of a heat exchanger. The cold and hot fluid stream loads were calculated using equation (1) as described by [25]
(1)Q=ṁfCpft3−t2=ṁgCpgt6−t7,where ṁg and ṁf are mass flow rate of steam and water, respectively, Q is heat transfer rate, Cpg and Cpf are specific heat capacity of steam and water, respectively, t3 and t2 are outlet and inlet temperature of the water, and t7 and t6 are outlet and inlet temperature of steam, respectively.Equation (2) is used to calculate the logarithmic mean temperature difference (ΔTlm) to use in estimating the true temperature difference in equation (3) by applying a correction factor (Ft) in the design of shell and tube exchangers to allow for the departure from the true countercurrent flow:
(2)ΔTlm=t6−t3−t7−t2lnt6−t3/t7−t2,(3)ΔTm=FtΔTlm.


### 4.2. Overall Heat Transfer Coefficient Assessment

To attain a preliminary appraisal for the size of the STHX, an approximate value for the overall heat transfer coefficient (Uo) is used. According to the working fluid, the range is 1500-4000 W/m2K as stated by [26]
(4)A=QUoΔTm,where A is the heat transfer area, Q is the heat transfer rate, Uo is the pilot overall heat transfer coefficient, and ΔTm is the true temperature difference.


### 4.3. Tube-Side Calculations

From the standard tube layouts, the empirical equation (6) was used to determine bundle diameter. n1 and K1 in the equation are coefficients determined by the tube layout and the number of tube passes from Table 2 for triangular pitch and square pitch, while the number of tubes (nt) was calculated by dividing the total heat transfer area (A) and the tube outer surface area (At) as shown in
(5)nt=AAt,(6)Db=dontK11/n1.Table 2
Coefficientsn1 and K1 for use in equation (10) [27].
Tube passes12468Square pitchn12.2072.2912.2632.6172.643K10.2150.1560.1580.04020.0331Triangular pitchn12.1422.2072.2852.4992.675K10.3190.2490.1750.07430.0365The heat transfer coefficient (ht) of the hot fluid stream was determined by using equation (7) [28]. It is a function of a tube inner diameter (di), tube side Prandtl number (Prt), and tube side Reynolds number (Ret). Also, nondimensional numbers like hot fluid thermal conductivity (kg), hot fluid viscosity (μg), and water viscosity (μw) are included in the equation [29].
(7)ht=kgdiRet0.8Prt0.33μgμw0.14.


### 4.4. Shell-Side Equations

The shell diameter is calculated as follows:(8)Ds=Dc+Db,(9)Dc=c1+m1Db.In the above equations,Ds is a shell diameter and Dc is a clearance between the diameter of the shell and a tube bundle diameter Db, where the values of c1 and m1 are presented in Table 3. c1 and m1 are empirical coefficients that relate to the head type designed in the STHX.Table 3
Coefficientsc1 and m1 for use in equation (9) [30].
Head typec1m1Outside packed head0.0380.0Pull through floating head0.08620.009Split ring floating head0.04460.027U-tube or fixed head0.0080.01The heat transfer coefficient (hs) on the shell side was determined from equation (10), where kf is a cold fluid thermal conductivity, de is a shell equivalent diameter, Jh is a Colburn factor, Prs is a shell side Prandtl number, and μf and μw are cold fluid and water viscosity, respectively.
(10)hs=kfdeJhPrs0.33μfμw0.14.


### 4.5. Overall Coefficient Calculations

In this, the required overall heat transfer coefficientUreq was calculated using
(11)Ureq=QπntdoltΔTm.The clean overall heat transfer coefficientUc was calculated using
(12)Uc=dohtdi+dolndo/di2k+1hs−1.IfUreq<Uc, the following step was considered.Then, the design overall heat transfer coefficient was determined through(13)Ud=dohtdi+dolndo/di2k+1hs+Rvdodi+Rf−1.IfUd≥Ureq, the next step was worthy to be carried out.Overdesign is computed in equation (14). The final design safety margin is provided by overdesign in which the required fouling compensation is represented. Oversurface deals with exchanger surface area and depends on the wall and film resistances and fouling allowance; it can be obtained through equation (15).
(14)Odes=UdUreq−1,(15)Osur=UcUreq−1.


### 4.6. Pressure Drop Calculations

#### 4.6.1. Tube-Side Pressure Drop

A pressure drop (ΔPi) of the hot fluid stream was computed as shown in equation (16), where ft is a Darcy friction factor, st is the specific gravity in the tube side, lt is the tube length, Gg is the hot fluid mass velocity, np is the number of tube passes, and di is the tube internal diameter.
(16)ΔPi=ftltGg2np7.5×1012dist.The tube entrance, exit, and return losses can be computed through(17)ΔPr=1.334×10−132np−1.5Ggst.The pressure loss (ΔPnt) in the tube side nozzles is considered through equation (18), where Gnt is a tube side nozzle mass velocity and ns is the number of tube passes.
(18)ΔPnt=2.0×10−13nsGnt2st.Equation (19) was used to evaluate the total pressure drop (ΔPt) across the hot fluid stream on the tube side as presented below:
(19)ΔPt=ΔPi+ΔPr+ΔPnt.


#### 4.6.2. Shell-Side Pressure Drop

Equation (20) was used to find the initial shell side pressure losses (ΔPo), where ss is a specific gravity in the shell side, fs is the friction factor, de is the equivalent diameter, nb is the number of the baffle, and Ds is a shell diameter.
(20)ΔPo=fsGg2Dsnb+17.5×1012dess.Also, the pressure loss in the shell side nozzles (ΔPns) was considered through equation (21), where Gns is a shell side nozzle mass velocity and ns is the number of tube passes.
(21)ΔPns=2.0×10−13nsGns2ss.Then, the net pressure drop (ΔPs) across the cold fluid stream on the shell side should be computed by summing the nozzle pressure loss and initial shell side pressure losses as per
(22)ΔPs=ΔPo+ΔPns.


## 4.1. Thermal Design

The temperature difference on the tube side or that of shell side was used to define the sensible heat transfer rate of a heat exchanger. The cold and hot fluid stream loads were calculated using equation (1) as described by [25]
(1)Q=ṁfCpft3−t2=ṁgCpgt6−t7,where ṁg and ṁf are mass flow rate of steam and water, respectively, Q is heat transfer rate, Cpg and Cpf are specific heat capacity of steam and water, respectively, t3 and t2 are outlet and inlet temperature of the water, and t7 and t6 are outlet and inlet temperature of steam, respectively.Equation (2) is used to calculate the logarithmic mean temperature difference (ΔTlm) to use in estimating the true temperature difference in equation (3) by applying a correction factor (Ft) in the design of shell and tube exchangers to allow for the departure from the true countercurrent flow:
(2)ΔTlm=t6−t3−t7−t2lnt6−t3/t7−t2,(3)ΔTm=FtΔTlm.


## 4.2. Overall Heat Transfer Coefficient Assessment

To attain a preliminary appraisal for the size of the STHX, an approximate value for the overall heat transfer coefficient (Uo) is used. According to the working fluid, the range is 1500-4000 W/m2K as stated by [26]
(4)A=QUoΔTm,where A is the heat transfer area, Q is the heat transfer rate, Uo is the pilot overall heat transfer coefficient, and ΔTm is the true temperature difference.


## 4.3. Tube-Side Calculations

From the standard tube layouts, the empirical equation (6) was used to determine bundle diameter. n1 and K1 in the equation are coefficients determined by the tube layout and the number of tube passes from Table 2 for triangular pitch and square pitch, while the number of tubes (nt) was calculated by dividing the total heat transfer area (A) and the tube outer surface area (At) as shown in
(5)nt=AAt,(6)Db=dontK11/n1.Table 2
Coefficientsn1 and K1 for use in equation (10) [27].
Tube passes12468Square pitchn12.2072.2912.2632.6172.643K10.2150.1560.1580.04020.0331Triangular pitchn12.1422.2072.2852.4992.675K10.3190.2490.1750.07430.0365The heat transfer coefficient (ht) of the hot fluid stream was determined by using equation (7) [28]. It is a function of a tube inner diameter (di), tube side Prandtl number (Prt), and tube side Reynolds number (Ret). Also, nondimensional numbers like hot fluid thermal conductivity (kg), hot fluid viscosity (μg), and water viscosity (μw) are included in the equation [29].
(7)ht=kgdiRet0.8Prt0.33μgμw0.14.


## 4.4. Shell-Side Equations

The shell diameter is calculated as follows:(8)Ds=Dc+Db,(9)Dc=c1+m1Db.In the above equations,Ds is a shell diameter and Dc is a clearance between the diameter of the shell and a tube bundle diameter Db, where the values of c1 and m1 are presented in Table 3. c1 and m1 are empirical coefficients that relate to the head type designed in the STHX.Table 3
Coefficientsc1 and m1 for use in equation (9) [30].
Head typec1m1Outside packed head0.0380.0Pull through floating head0.08620.009Split ring floating head0.04460.027U-tube or fixed head0.0080.01The heat transfer coefficient (hs) on the shell side was determined from equation (10), where kf is a cold fluid thermal conductivity, de is a shell equivalent diameter, Jh is a Colburn factor, Prs is a shell side Prandtl number, and μf and μw are cold fluid and water viscosity, respectively.
(10)hs=kfdeJhPrs0.33μfμw0.14.


## 4.5. Overall Coefficient Calculations

In this, the required overall heat transfer coefficientUreq was calculated using
(11)Ureq=QπntdoltΔTm.The clean overall heat transfer coefficientUc was calculated using
(12)Uc=dohtdi+dolndo/di2k+1hs−1.IfUreq<Uc, the following step was considered.Then, the design overall heat transfer coefficient was determined through(13)Ud=dohtdi+dolndo/di2k+1hs+Rvdodi+Rf−1.IfUd≥Ureq, the next step was worthy to be carried out.Overdesign is computed in equation (14). The final design safety margin is provided by overdesign in which the required fouling compensation is represented. Oversurface deals with exchanger surface area and depends on the wall and film resistances and fouling allowance; it can be obtained through equation (15).
(14)Odes=UdUreq−1,(15)Osur=UcUreq−1.


## 4.6. Pressure Drop Calculations

### 4.6.1. Tube-Side Pressure Drop

A pressure drop (ΔPi) of the hot fluid stream was computed as shown in equation (16), where ft is a Darcy friction factor, st is the specific gravity in the tube side, lt is the tube length, Gg is the hot fluid mass velocity, np is the number of tube passes, and di is the tube internal diameter.
(16)ΔPi=ftltGg2np7.5×1012dist.The tube entrance, exit, and return losses can be computed through(17)ΔPr=1.334×10−132np−1.5Ggst.The pressure loss (ΔPnt) in the tube side nozzles is considered through equation (18), where Gnt is a tube side nozzle mass velocity and ns is the number of tube passes.
(18)ΔPnt=2.0×10−13nsGnt2st.Equation (19) was used to evaluate the total pressure drop (ΔPt) across the hot fluid stream on the tube side as presented below:
(19)ΔPt=ΔPi+ΔPr+ΔPnt.


### 4.6.2. Shell-Side Pressure Drop

Equation (20) was used to find the initial shell side pressure losses (ΔPo), where ss is a specific gravity in the shell side, fs is the friction factor, de is the equivalent diameter, nb is the number of the baffle, and Ds is a shell diameter.
(20)ΔPo=fsGg2Dsnb+17.5×1012dess.Also, the pressure loss in the shell side nozzles (ΔPns) was considered through equation (21), where Gns is a shell side nozzle mass velocity and ns is the number of tube passes.
(21)ΔPns=2.0×10−13nsGns2ss.Then, the net pressure drop (ΔPs) across the cold fluid stream on the shell side should be computed by summing the nozzle pressure loss and initial shell side pressure losses as per
(22)ΔPs=ΔPo+ΔPns.


## 4.6.1. Tube-Side Pressure Drop

A pressure drop (ΔPi) of the hot fluid stream was computed as shown in equation (16), where ft is a Darcy friction factor, st is the specific gravity in the tube side, lt is the tube length, Gg is the hot fluid mass velocity, np is the number of tube passes, and di is the tube internal diameter.
(16)ΔPi=ftltGg2np7.5×1012dist.The tube entrance, exit, and return losses can be computed through(17)ΔPr=1.334×10−132np−1.5Ggst.The pressure loss (ΔPnt) in the tube side nozzles is considered through equation (18), where Gnt is a tube side nozzle mass velocity and ns is the number of tube passes.
(18)ΔPnt=2.0×10−13nsGnt2st.Equation (19) was used to evaluate the total pressure drop (ΔPt) across the hot fluid stream on the tube side as presented below:
(19)ΔPt=ΔPi+ΔPr+ΔPnt.


## 4.6.2. Shell-Side Pressure Drop

Equation (20) was used to find the initial shell side pressure losses (ΔPo), where ss is a specific gravity in the shell side, fs is the friction factor, de is the equivalent diameter, nb is the number of the baffle, and Ds is a shell diameter.
(20)ΔPo=fsGg2Dsnb+17.5×1012dess.Also, the pressure loss in the shell side nozzles (ΔPns) was considered through equation (21), where Gns is a shell side nozzle mass velocity and ns is the number of tube passes.
(21)ΔPns=2.0×10−13nsGns2ss.Then, the net pressure drop (ΔPs) across the cold fluid stream on the shell side should be computed by summing the nozzle pressure loss and initial shell side pressure losses as per
(22)ΔPs=ΔPo+ΔPns.


## 5. Results and Discussion

### 5.1. Effect on the Pressure Drop and the Heat Transfer Coefficient

Figures4(a)–4(c) show the pressure drop together with heat transfer coefficient variations within the STHX with the length of 600 mm, 800 mm, and 1000 mm for three different tube outer diameters of 10 mm, 12 mm, and 14 mm with 1 mm thick for each, respectively, through a given range of mass flow of 0.1-0.8 kg/s as regards the shell side. From Figures 4(a)–4(c), it can be seen that both the heat transfer coefficient and the pressure drop increase proportionally to the mass flow rate by considering the nine configurations of heat exchangers. Also, confirm that the heat transfer coefficient is much greater at any point in the range of mass flow rate compared to the pressure drop. Hence, it is noted that the diameter of 10 mm shows the greatest heat transfer coefficient of 18162, 20881, and 23212 W/m2K and the maximum pressure drop of 0.328, 0.593, and 0.957 Pa, while the diameter of 14 mm shows a minimum pressure drop of 0.117, 0.223, and 0.370 Pa and a lesser heat transfer coefficient of 13265, 15326, and 17107 W/m2K in the length of 600 mm, 800 mm, and 1000 mm, respectively.Figure 4
Pressure drop and heat transfer coefficient versus mass flow rate: (a) 600 mm length, (b) 1000 mm length, (c) 800 mm length, and (d) maximum heat transfer coefficient and minimum pressure drop among all configurations.
(a)(b)(c)(d)Figure4(d) illustrates the variation of all minimum pressure drop (blue) which appears in the tube with a diameter of 14 mm versus the cold fluid stream mass flow rate in the shell side for the three different tube length exchangers. The results show that the tube configuration with a minimum length (600 mm) has a minimum pressure drop of 0.117 Pa corresponding to the rest of the configurations. Figure 4(d) also shows the results of the variation of the maximum heat transfer coefficient (black) which appears in the tube with a diameter of 10 mm versus cold stream mass flow rate in the shell side for the three different tube length exchangers; thus, the tube configuration with a maximum length of 1000 mm portrays maximum heat transfer coefficient of 23212 W/m2K compared to the rest of the configurations.


### 5.2. Effect on the Overall Heat Transfer Coefficient

Figures5(a)–5(c)) express the effect of mass flow rate on the overall heat transfer coefficients of design heat transfer coefficient (Ud) and clean heat transfer coefficient (Uc) within the STHX with the length of 600 mm, 800 mm, and 1000 mm for three different tube outer diameters of 10 mm, 12 mm, and 14 mm, respectively, with 1 mm thick for each. The results for both Ud and Uc coefficients demonstrate that when the cold fluid flows over the whole surface of the shell were varied, Ud and Uc increase constantly at any rate regardless of the difference in the tube configuration throughout the study. On the other hand, Uc is shown to increase twice or more than Ud when there is an increase in mass flow in the shell side. This is due to the significant effect of the fouling factor of the working fluids. However, the increase in mass flow and sustaining the temperatures keep Ud and Uc rising proportionally; the design coefficient is used rather than the clean coefficient based on the interest of overdesign. The highest and smallest values of Ud appeared in 10 and 14 mm tube diameter, respectively.Figure 5
Overall heat transfer coefficient versus mass flow rate: (a) 600 mm length, (b) 800 mm length, (c) 1000 mm length, and (d) design overall heat transfer coefficient among all configurations.
(a)(b)(c)(d)Figure5(d) illustrates Ud which appears through all-tube configurations. The result shows that the tube configuration with a maximum length (1000 mm) has maximum Ud compared to the other configurations. Moreover, it can be seen that as the length of the tube increases with a decrease in diameter the maximum Ud is achieved. To provide the required rate of heat transfer, the value of Ud should be greater than or equal to the value of the required coefficient, Ureq. The results show that the suitable mass flow of 0.3-0.8 kg/s with a range of 2306-2539 W/m2K can be selected for the proper design of the exchanger as shown in Figure 6(d).Figure 6
Oversurface and overdesign versus mass flow rate: (a) 600 mm length, (b) 800 mm length, (c) 1000 mm length, and (d) overdesign among all configurations.
(a)(b)(c)(d)


### 5.3. Effect on the Oversurface and Overdesign

Figures6(a)–6(c) demonstrate the oversurface (Osur) and overdesign (Odes) changes when designing the STHX with the length of 600 mm, 800 mm, and 1000 mm for three different tube outer diameters of 10 mm, 12 mm, and 14 mm with 1 mm thick for each, respectively, through a given range of 0.1-0.8 kg/s. Since Ureq is much smaller than Uc, Osur appeared to increase in the range of 19.2-463.3 as the mass flow increases. Odes were shown to increase slightly from negative value on 0.1-0.3 kg/s to a positive value on 0.4-0.8 kg/s in a range of -33.9-12.8.Since engineers do recognize that there will be uncertainties on the data provided and that there may be times when the feedstock will not exactly match up to what was originally specified, a certain amount of conservatism will be required just to achieve satisfactory performance despite unforeseen circumstances. Figure6(d) clarifies the possibility of designing the suitable STHX by displaying the greatest values of Odes which mostly appeared in the smallest tube diameter (10 mm) to all three tube length configurations with a total of nine samples. However, Odes is a negative value at a low mass flow rate of 0.1-0.3 kg/s specifically to the configurations of length 600 mm and 800 mm. Conversely, as mass flow increases from 0.4 to 0.8 kg/s, Odes becomes a positive value. Hereafter, the configuration with tube length 1000 mm performed well even from the mass flow of 0.3 kg/s compared to other configurations.


## 5.1. Effect on the Pressure Drop and the Heat Transfer Coefficient

Figures4(a)–4(c) show the pressure drop together with heat transfer coefficient variations within the STHX with the length of 600 mm, 800 mm, and 1000 mm for three different tube outer diameters of 10 mm, 12 mm, and 14 mm with 1 mm thick for each, respectively, through a given range of mass flow of 0.1-0.8 kg/s as regards the shell side. From Figures 4(a)–4(c), it can be seen that both the heat transfer coefficient and the pressure drop increase proportionally to the mass flow rate by considering the nine configurations of heat exchangers. Also, confirm that the heat transfer coefficient is much greater at any point in the range of mass flow rate compared to the pressure drop. Hence, it is noted that the diameter of 10 mm shows the greatest heat transfer coefficient of 18162, 20881, and 23212 W/m2K and the maximum pressure drop of 0.328, 0.593, and 0.957 Pa, while the diameter of 14 mm shows a minimum pressure drop of 0.117, 0.223, and 0.370 Pa and a lesser heat transfer coefficient of 13265, 15326, and 17107 W/m2K in the length of 600 mm, 800 mm, and 1000 mm, respectively.Figure 4
Pressure drop and heat transfer coefficient versus mass flow rate: (a) 600 mm length, (b) 1000 mm length, (c) 800 mm length, and (d) maximum heat transfer coefficient and minimum pressure drop among all configurations.
(a)(b)(c)(d)Figure4(d) illustrates the variation of all minimum pressure drop (blue) which appears in the tube with a diameter of 14 mm versus the cold fluid stream mass flow rate in the shell side for the three different tube length exchangers. The results show that the tube configuration with a minimum length (600 mm) has a minimum pressure drop of 0.117 Pa corresponding to the rest of the configurations. Figure 4(d) also shows the results of the variation of the maximum heat transfer coefficient (black) which appears in the tube with a diameter of 10 mm versus cold stream mass flow rate in the shell side for the three different tube length exchangers; thus, the tube configuration with a maximum length of 1000 mm portrays maximum heat transfer coefficient of 23212 W/m2K compared to the rest of the configurations.


## 5.2. Effect on the Overall Heat Transfer Coefficient

Figures5(a)–5(c)) express the effect of mass flow rate on the overall heat transfer coefficients of design heat transfer coefficient (Ud) and clean heat transfer coefficient (Uc) within the STHX with the length of 600 mm, 800 mm, and 1000 mm for three different tube outer diameters of 10 mm, 12 mm, and 14 mm, respectively, with 1 mm thick for each. The results for both Ud and Uc coefficients demonstrate that when the cold fluid flows over the whole surface of the shell were varied, Ud and Uc increase constantly at any rate regardless of the difference in the tube configuration throughout the study. On the other hand, Uc is shown to increase twice or more than Ud when there is an increase in mass flow in the shell side. This is due to the significant effect of the fouling factor of the working fluids. However, the increase in mass flow and sustaining the temperatures keep Ud and Uc rising proportionally; the design coefficient is used rather than the clean coefficient based on the interest of overdesign. The highest and smallest values of Ud appeared in 10 and 14 mm tube diameter, respectively.Figure 5
Overall heat transfer coefficient versus mass flow rate: (a) 600 mm length, (b) 800 mm length, (c) 1000 mm length, and (d) design overall heat transfer coefficient among all configurations.
(a)(b)(c)(d)Figure5(d) illustrates Ud which appears through all-tube configurations. The result shows that the tube configuration with a maximum length (1000 mm) has maximum Ud compared to the other configurations. Moreover, it can be seen that as the length of the tube increases with a decrease in diameter the maximum Ud is achieved. To provide the required rate of heat transfer, the value of Ud should be greater than or equal to the value of the required coefficient, Ureq. The results show that the suitable mass flow of 0.3-0.8 kg/s with a range of 2306-2539 W/m2K can be selected for the proper design of the exchanger as shown in Figure 6(d).Figure 6
Oversurface and overdesign versus mass flow rate: (a) 600 mm length, (b) 800 mm length, (c) 1000 mm length, and (d) overdesign among all configurations.
(a)(b)(c)(d)


## 5.3. Effect on the Oversurface and Overdesign

Figures6(a)–6(c) demonstrate the oversurface (Osur) and overdesign (Odes) changes when designing the STHX with the length of 600 mm, 800 mm, and 1000 mm for three different tube outer diameters of 10 mm, 12 mm, and 14 mm with 1 mm thick for each, respectively, through a given range of 0.1-0.8 kg/s. Since Ureq is much smaller than Uc, Osur appeared to increase in the range of 19.2-463.3 as the mass flow increases. Odes were shown to increase slightly from negative value on 0.1-0.3 kg/s to a positive value on 0.4-0.8 kg/s in a range of -33.9-12.8.Since engineers do recognize that there will be uncertainties on the data provided and that there may be times when the feedstock will not exactly match up to what was originally specified, a certain amount of conservatism will be required just to achieve satisfactory performance despite unforeseen circumstances. Figure6(d) clarifies the possibility of designing the suitable STHX by displaying the greatest values of Odes which mostly appeared in the smallest tube diameter (10 mm) to all three tube length configurations with a total of nine samples. However, Odes is a negative value at a low mass flow rate of 0.1-0.3 kg/s specifically to the configurations of length 600 mm and 800 mm. Conversely, as mass flow increases from 0.4 to 0.8 kg/s, Odes becomes a positive value. Hereafter, the configuration with tube length 1000 mm performed well even from the mass flow of 0.3 kg/s compared to other configurations.


## 6. Conclusion

A heat exchanger model for a low-temperature desalination system was established through the influence tube length and diameter, mass flow rate on pressure drop, heat transfer coefficient, overall heat transfer coefficient, oversurface, and overdesign. After making a deep analysis of these heat transfer parameters, the following summarized conclusions were obtained.(i)
Both the heat transfer coefficient and the pressure drop increase proportionally to the mass flow rate among all nine configurations of heat exchangers. But the pressure drop is noticed to be very low 0.328-0.957 Pa for all studied configurations that will lower the pumping power(ii)
The clean overall heat transfer coefficient increases twice or more to that of the design coefficient when there is an increase in mass flow in the shell side due to the effect of the fouling factor(iii)
The maximum design coefficient is achieved by increasing the tube length with a decrease in diameter. Also, the mass flow of 0.3-0.8 kg/s is suitable for the proper design of exchanger in the present study(iv)
The configuration with the 1000 mm length and 10 mm diameter which provides high heat transfer is recommended to work with a maximum flow rate of 0.8 kg/s to achieve a maximum heat transfer coefficient of 23212 W/m2K, while 12.8 is a maximum overdesign coefficient achieved on 0.8 kg/s mass flow(v)
Therefore, the implementation of the proposed layout will ensure less energy consumption in the system. Hence, an experimental study is recommended to be done to compare the results obtained by the present mathematical model



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*Source: 8844433-2020-11-16.xml*