*3.2. Calculation of Volume Flow Rate of Hot Water*

The hot water volume is always changed according to the demand. Therefore, the maximum volume flow rate of hot water per hour (*Vhwmax*/h) needs to be defined. Based on the make-up water volume into the system, the *Vhwmax*/h was collected for typical 10 days of the month with higher number of tourists as shown in the Figure 3. As can be seen, there is a time when *Vhwmax*/h is ranging from 16–20 pm daily. From these data, the ratio of average hot water volume flow rate per hour with its value per day was calculated as shown in the Figure 4. It can be observed that the ratio of *Vhwmax*/h at peak hour is nearly 6% from daily hot water volume which is suggested for other days in the year. Thus, from the maximum hot water volume as suggested in Table 3, *Vhwmax*/d = 94 m3/day and the above ratio of 6% at peak hour, the *Vhwmax*/h was determined such that *Vhwmax*/h = 94 <sup>×</sup> 6/100 = 5.65 m3/h.

the maximum hot water volume as suggested in Table 3, *Vhwmax*/d = 94 m<sup>3</sup>

the maximum hot water volume as suggested in Table 3, *Vhwmax*/d = 94 m<sup>3</sup>

above ratio of 6% at peak hour, the *Vhwmax*/h was determined such that *Vhwmax*/h = 94 × 6/100

above ratio of 6% at peak hour, the *Vhwmax*/h was determined such that *Vhwmax*/h = 94 × 6/100

*3.2. Calculation of Volume Flow Rate of Hot Water*

*3.2. Calculation of Volume Flow Rate of Hot Water*

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 6 of 15

= 5.65 m<sup>3</sup>

= 5.65 m<sup>3</sup>

/h.

/h.

**Figure 3.** Hourly used hot water volume for typical days with higher number of tourists. **Figure 3.** Hourly used hot water volume for typical days with higher number of tourists. **Figure 3.** Hourly used hot water volume for typical days with higher number of tourists.

The hot water volume is always changed according to the demand. Therefore, the maximum volume flow rate of hot water per hour (*Vhwmax*/h) needs to be defined. Based on the make-up water volume into the system, the *Vhwmax*/h was collected for typical 10 days of the month with higher number of tourists as shown in the Figure 3. As can be seen, there is a time when *Vhwmax*/h is ranging from 16–20 pm daily. From these data, the ratio of average hot water volume flow rate per hour with its value per day was calculated as shown in the Figure 4. It can be observed that the ratio of *Vhwmax*/h at peak hour is nearly 6% from daily hot water volume which is suggested for other days in the year. Thus, from

The hot water volume is always changed according to the demand. Therefore, the maximum volume flow rate of hot water per hour (*Vhwmax*/h) needs to be defined. Based on the make-up water volume into the system, the *Vhwmax*/h was collected for typical 10 days of the month with higher number of tourists as shown in the Figure 3. As can be seen, there is a time when *Vhwmax*/h is ranging from 16–20 pm daily. From these data, the ratio of average hot water volume flow rate per hour with its value per day was calculated as shown in the Figure 4. It can be observed that the ratio of *Vhwmax*/h at peak hour is nearly 6% from daily hot water volume which is suggested for other days in the year. Thus, from

/day and the

/day and the

Ratio of the average hot water demand hourly Ratio of the average hot water demand hourly

**Figure 4.** Ratio of average hot water volume flow rate per hour. **Figure 4.** Ratio of average hot water volume flow rate per hour. **Figure 4.** Ratio of average hot water volume flow rate per hour.

#### *3.3. Maximum Production of Hot Water Volume 3.3. Maximum Production of Hot Water Volume 3.3. Maximum Production of Hot Water Volume*

Figure 5 shows the diagram of separate hot water system. To ensure the continuous and adequate hot water supply, the hot water is always revolved in the system with the circulating hot water flow (*Vcc*) and requirement is *Vcc* > *Vhwmax*/h. The circle factor (*n*) is introduced, with = ℎ , we choose *n* = 2.75 in this study. From Table 3, the average hot water demand is *Vhwa* = 52 m<sup>3</sup> /day = 2.2 m<sup>3</sup> /h, the circular water flow can be defined *Vcc* = *Vhwa* × *n* = 6 m<sup>3</sup> /h > *Vhwmax*/h = 5.65 m<sup>3</sup> /h, that means the supplied hot water demand at peak hour will be ensured. From there, the volume flow rate of make-up water (*Vmu*) to the Figure 5 shows the diagram of separate hot water system. To ensure the continuous and adequate hot water supply, the hot water is always revolved in the system with the circulating hot water flow (*Vcc*) and requirement is *Vcc* > *Vhwmax*/h. The circle factor (*n*) is introduced, with = ℎ , we choose *n* = 2.75 in this study. From Table 3, the average hot water demand is *Vhwa* = 52 m<sup>3</sup> /day = 2.2 m<sup>3</sup> /h, the circular water flow can be defined *Vcc* = *Vhwa* × *n* = 6 m<sup>3</sup> /h > *Vhwmax*/h = 5.65 m<sup>3</sup> /h, that means the supplied hot water demand at peak hour will be ensured. From there, the volume flow rate of make-up water (*Vmu*) to the Figure 5 shows the diagram of separate hot water system. To ensure the continuous and adequate hot water supply, the hot water is always revolved in the system with the circulating hot water flow (*Vcc*) and requirement is *Vcc* > *Vhwmax*/h. The circle factor (*n*) is introduced, with *n* = *Vcc Vhwa* , we choose *n* = 2.75 in this study. From Table 3, the average hot water demand is *Vhwa* = 52 m3/day = 2.2 m3/h, the circular water flow can be defined *Vcc* <sup>=</sup> *<sup>V</sup>hwa* <sup>×</sup> *<sup>n</sup>* = 6 m3/h > *<sup>V</sup>hwmax*/h = 5.65 m3/h, that means the supplied hot water demand at peak hour will be ensured. From there, the volume flow rate of make-up water (*Vmu*) to the system is calculated, *Vmu* = *Vhwa* = *Vcc* − *Vre*, where *Vre* is the returned hot water flow rate. The temperature of returned hot water (*tre*) is decreased because of occurred heat loss along the length of tube, this range temperature is set ∆*t* = 15 ◦C. Thus, the *tre* = 55 − 15 = 40 ◦C. The heat balance equation is established at the entrance of secondary heat exchanger:

$$\mathcal{V}\_{\boldsymbol{w}} \cdot \mathbb{C}\_{\boldsymbol{p}\boldsymbol{w}}(t\_{\boldsymbol{w}\ \boldsymbol{re}} - t\_{\boldsymbol{w}\ \boldsymbol{in}2}) = \mathbb{C}\_{\boldsymbol{p}\boldsymbol{w}}(t\_{\boldsymbol{w}\ \boldsymbol{in}2} - t\_{\boldsymbol{w}\ \boldsymbol{un}}) \tag{2}$$

where, *Cpw* is the specific heat of water, the water-in temperature of secondary heat exchanger (*tw in*2), *tw mu* is the temperature of make-up water (*tmu* = 25 ◦C at the investigated resort). Thus, from Equation (2) *tw in*<sup>2</sup> = 35 ◦C.

. ( − 2

**Figure 5.** Diagram of separate hot water system. **Figure 5.** Diagram of separate hot water system.

resort). Thus, from Equation (2) *t<sup>w</sup> in*<sup>2</sup> = 35 °C.

The heat transfer rate from the exhaust gas to the water is presented by the balance equation: The heat transfer rate from the exhaust gas to the water is presented by the balance equation:

system is calculated, *Vmu* = *Vhwa* = *Vcc* − *Vre*, where *Vre* is the returned hot water flow rate. The temperature of returned hot water (*tre*) is decreased because of occurred heat loss along the length of tube, this range temperature is set *Δt* =15 °C. Thus, the *tre* = 55 − 15 = 40 °C. The heat balance equation is established at the entrance of secondary heat exchanger:

where, *Cpw* is the specific heat of water, the water-in temperature of secondary heat exchanger (*t<sup>w</sup> in*2), *t<sup>w</sup> mu* is the temperature of make-up water (*tmu* = 25 °C at the investigated

$$
\eta \cdot Q\_{\text{eg}} = Q\_{\text{hw}} = V\_{\text{hw}} \cdot \mathbb{C}\_{pw} (t\_{\text{w \, out2}} - t\_{\text{w \, in2}}) \tag{3}
$$

) = ( 2 − ) (2)

 . = ℎ = ℎ. ( 2 − 2 ) (3) where *Qhw* is the heat rate of water, *Vhw* is the maximum volume flow rate of hot water that could be produced, *Cpw* is the water specific heat (*Cpw* = 4.18 kJ/kg °C), *η* is the performance where *Qhw* is the heat rate of water, *Vhw* is the maximum volume flow rate of hot water that could be produced, *Cpw* is the water specific heat (*Cpw* = 4.18 kJ/kg ◦C), *η* is the performance of the heat exchanger (*η* = 0.9).

of the heat exchanger (*η* = 0.9). Thus, from Equation (3) the maximum volume flow rate of hot water from the fully exhaust gas is evaluated as *Vhw* = 26 m<sup>3</sup> /h at 80% load of ICE. This flow rate is larger than the flow rate of the circular hot water (*Vcc* = 6 m<sup>3</sup> /h), it means that the EGH from ICE re-Thus, from Equation (3) the maximum volume flow rate of hot water from the fully exhaust gas is evaluated as *Vhw* = 26 m3/h at 80% load of ICE. This flow rate is larger than the flow rate of the circular hot water (*Vcc* = 6 m3/h), it means that the EGH from ICE responses sufficiently to the demand of hot water at the resort.

### sponses sufficiently to the demand of hot water at the resort. *3.4. Specifications of Heat Exchanger*

*3.4. Specifications of Heat Exchanger* The specifications of two heat exchangers were designed and chosen from the parameters of exhaust gas and hot water. Firstly, the tube diameter, tube spacing, the heat transfer coefficient (*k*1), the length (*L*1) and the width (*W*1) are selected for the primary heat exchanger unit. Next, the area of heat exchanger (*F*1), number of tube rows, number of tubes are calculated followed by calculation of the resistance. If the back pressure or resistance (*Δp*1) is larger than the allowed back pressure ([*Δp*1]) then L<sup>1</sup> and W<sup>1</sup> are re-adjusted. The steps are repeated and the k<sup>1</sup> is re-tested. The specifications for which the Δp<sup>1</sup> The specifications of two heat exchangers were designed and chosen from the parameters of exhaust gas and hot water. Firstly, the tube diameter, tube spacing, the heat transfer coefficient (*k*1), the length (*L*1) and the width (*W*1) are selected for the primary heat exchanger unit. Next, the area of heat exchanger (*F*1), number of tube rows, number of tubes are calculated followed by calculation of the resistance. If the back pressure or resistance (∆*p*1) is larger than the allowed back pressure ([∆*p*1]) then *L*<sup>1</sup> and *W*<sup>1</sup> are re-adjusted. The steps are repeated and the *k*<sup>1</sup> is re-tested. The specifications for which the ∆*p*<sup>1</sup> is lower than [∆*p*1] = 3000 Pa are accepted.

Calculate the resistance though the heat exchanger:

is lower than [*Δp*1] = 3000 Pa are accepted. Calculate the resistance though the heat exchanger: The parameters of the tube and fin such as the outside diameter of the tube (*dout*1), horizontal spacing (*s*1), fin spacing (*sf*) and fin thickness (δ*f*) were selected. The vertical spacing (*s*2) is evaluated as <sup>2</sup> = √3 2 1 , the slit between two fins (*tf*) is calculated as = − , the diameter of the fin (*df*) is calculated as = <sup>1</sup> − , the height of the fin (*hf*) is calculated as ℎ = 0.5 ( − 1), number of the fin per 1 m length of tube (*nf*) is evalu-The parameters of the tube and fin such as the outside diameter of the tube (*dout*1), horizontal spacing (*s*1), fin spacing (*s<sup>f</sup>* ) and fin thickness (*δ<sup>f</sup>* ) were selected. The vertical spacing (*s*2) is evaluated as *s*<sup>2</sup> = √ 3 2 *s*1, the slit between two fins (*t<sup>f</sup>* ) is calculated as *t<sup>f</sup>* = *s<sup>f</sup>* − *δ<sup>f</sup>* , the diameter of the fin (*d<sup>f</sup>* ) is calculated as *d<sup>f</sup>* = *s*<sup>1</sup> − *t<sup>f</sup>* , the height of the fin (*hf* ) is calculated as *<sup>h</sup><sup>f</sup>* <sup>=</sup> 0.5 *d<sup>f</sup>* − *dout*<sup>1</sup> , number of the fin per 1 m length of tube (*n<sup>f</sup>* ) is evaluated as *n<sup>f</sup>* = <sup>1</sup> *sf* .

ated as = 1 The factor of the fin (CT [1]/136):

$$\varepsilon\_f = 1 + \frac{d\_f^2 - d\_{out1}^2}{2 \times d\_{in1} \times s\_f} \tag{4}$$

The area without fin per 1 m length of tube (m<sup>2</sup> ):

$$F\_0 = \pi \times d\_{out1} \times t\_f \times n\_f \tag{5}$$

The area with fin per 1 m length of tube (m<sup>2</sup> ):

$$F\_f = \frac{\pi}{2} \left(d\_f^2 - d\_{out1}^2\right) n\_f \tag{6}$$

Total the outside area of fin-tube: *F*<sup>2</sup> = *F*<sup>0</sup> + *Fc*.

The equivalent diameter of the slits between tubes and fins through which gas flow passes (CT [1]/118):

$$d\_{eqi} = \frac{F\_0 d\_{out1} + F\_f \sqrt{\frac{F\_f}{2n\_f}}}{F\_0 + F\_f} \tag{7}$$

The hot water flow rate needs to be produced (*Vhw*) is known based on the hot water demand. Based on the heat balance equation of secondary heater, the primary hot water flow (*Vhw*1) is calculated as:

$$V\_{\text{lw1}}c\_{pw1}(t\_{\text{lw}\,\,out1} - t\_{\text{lw}\,\,in1})\eta = V\_{\text{lw2}}c\_{pw2}(t\_{\text{lw}\,\,out2} - t\_{\text{lw}\,\,in2})\tag{8}$$

Based on the heat balance equation of primary heater, the exhaust gas-out temperature (*tkr*) is calculated as:

$$\mathbf{G}\_{\text{eg}}\mathbf{c}\_{\text{pg}}(\mathbf{t}\_{\text{eg}}\text{ in}\mathbf{1} - \mathbf{t}\_{\text{eg}}\text{ out}\mathbf{1})\boldsymbol{\eta} = \,\,\mathbf{V}\_{\text{hw}1}\mathbf{c}\_{\text{pw}1}(\mathbf{t}\_{\text{hw}}\,\,\text{out}\mathbf{1} - \mathbf{t}\_{\text{hw}}\,\,\text{in}\mathbf{1})\tag{9}$$

The heat transfer coefficient (*kF*2) was selected in the suitable range of *kF*<sup>2</sup> = 40–80 W/m<sup>2</sup> ·K based on common design.

Calculate the average temperature difference (∆*t*) with ∆*tmax* = *tegin*<sup>1</sup> − *thw out*<sup>1</sup> and ∆*tmin* = *tegout*<sup>1</sup> − *thw in*1:

$$\overline{\Delta t} = \frac{\Delta t\_{\text{max}} - \Delta t\_{\text{min}}}{\ln \frac{\Delta t\_{\text{max}}}{\Delta t\_{\text{min}}}} \tag{10}$$

Calculate the heat power required to heat the hot water at rate flow demand (*Qhwd*):

$$Q\_{\rm hwd} = G\_{\rm eg} c\_{p\rm eg} \left( t\_{\rm eg \ in 1} - t\_{\rm eg \ out 1} \right) \tag{11}$$

Calculate the waste heat power:

$$Q\_{\mathfrak{eg}} = \mathbb{G}\_{\mathfrak{eg}} \mathbb{c}\_{\mathfrak{pg}} \left( t\_{\mathfrak{eg}\ \hat{\mathfrak{i}}n1} - t\_{\mathfrak{air}} \right) \tag{12}$$

Calculate the waste heat recovery efficiency:

$$
\eta\_{HR} = \frac{Q\_{hwd}}{Q\_{\mathcal{eg}}} \times 100 \text{ (\%)}\tag{13}
$$

Calculate the inside (*F*1) and outside area (*F*2) of fin-tube:

$$F\_2 = \frac{Q\_{hwd}}{k\_{F2}\overline{\Delta t}} \text{ and } F\_1 = \frac{F\_2}{\varepsilon\_f} \tag{14}$$

The total length of the heat transfer tube was calculated:

$$F\_1 = \frac{F\_1}{\pi d\_{in1}}\tag{15}$$

The length of 1 tube (*L*1) was as the width of the heat exchanger as *W*<sup>1</sup> = *L*1. Numbers of rows of tube (*z*1), number of tubes in 1 row (*m*1), the height of the heat exchanger (*H*1) were evaluated as, *z*<sup>1</sup> = *W*1/*s*2, *m*<sup>1</sup> = *l*1 *z*1*L*<sup>1</sup> , *H*<sup>1</sup> = *m*1·*s*1.

The velocity of exhaust gas flow through minimum cross section was defined (CT [1]/121):

$$
\omega = \frac{\omega\_0}{1 - \left(\frac{d\_{out1}}{s\_1} + \frac{2h\omega\_f}{s\_1 s\_f}\right)}\tag{16}
$$

where *ω*<sup>0</sup> is the velocity of exhaust gas-in, *ω*<sup>0</sup> = *Geg ρ f* and *f* is the area of cross section, *f* = *L* × *W*.

From the average temperature exhaust gas (*t<sup>k</sup>* ) and *teg* = *teg in*1−*teg out*<sup>1</sup> 2 , the heat conductive coefficient (*λ*) and the viscosity (*v*) of exhaust gas were known.

The number Re of exhaust gas was calculated:

$$\text{Re}\_{\text{eg}} = \frac{\omega d\_{\text{eq}}}{\upsilon} \tag{17}$$

The resistance factor (*ξ*) for the staggered arrangement tubes with circle fins was defined (CT [1]/119):

$$\zeta\_{\uparrow}^{\tau} = 0.72 \times \text{Re}\_{\text{eg}}^{-0.245} \left( \frac{s\_1 - d\_{out1}}{s\_f} + 2 \right)^{0.9} \times \left( \frac{s\_1 - d\_{out1}}{d\_{out1}} \right)^{0.9} \times \left( \frac{d\_{\text{eq}i}}{d\_{out1}} \right)^{0.9} \times \left( \frac{s\_1 - d\_{out1}}{s\_2 - d\_{out1}} \right)^{-0.1} \tag{18}$$

The resistance of friction (∆*p<sup>f</sup>* ), the local resistance at inlet and outlet (∆*p<sup>l</sup>* ), the total resistance of the system (∆*p*) were calculated, ∆*p*<sup>1</sup> = ∆*p<sup>f</sup>* + ∆*p<sup>l</sup>* :

$$
\Delta p\_f = \xi \times \rho \times \frac{\omega^2}{2} \times z\_1 \tag{19}
$$

$$
\Delta p\_l = \xi \times \rho \times \frac{\omega^2}{2} \tag{20}
$$

The total resistance of the system (∆*p*) has to be lower than the allowable resistance in the exhaust gas system of ICE [∆*p*] = 3000 Pa. Using the design procedure explained above, the specifications of primary and secondary heat exchangers are evaluated. The type of heat exchanger selected for primary case is tube and fin type heat exchanger. The water to be heated is flowing through tubes whereas the exhaust gas is flowing around the tubes. The flow paths for water and exhaust gas are presented in Figure 6a. The tube and fins in the primary heat exchanger are made up of steel. The inner and outer diameters of tube are 27.24 mm and 34 mm, respectively and total length of tube is 4.4 m with spacing of 7 mm. The fin thickness and spacing are designed as 1 mm and 4 mm, respectively. The arrangement and dimensions of fins are depicted in Figure 6b. The summary for specifications of primary heat exchanger is shown in Table 4. Similarly, the type of heat exchanger, the heat transfer coefficient (*k*2), the area of heat exchanger (*F*2), number of tube rows, number of tubes and the resistance are calculated for the secondary heat exchanger unit. The shell and tube heat exchanger are selected for secondary circle. The water heated through the exhaust gas is passing through the shell whereas, the fresh water is circulating through the tubes. The flow patterns for both water paths are shown in Figure 7. The secondary heat exchanger comprises of 3 shell passes and 36 tubes divided equally in 3 tube passes. The outer diameter and length of tube are evaluated as 19 mm and 740 mm, respectively. The summary for specifications of secondary heat exchanger is shown in Table 5.

**Table 4.** Specifications of primary heat exchanger. Number of pass in secondary side 3 passes

**Table 4.** Specifications of primary heat exchanger.

**Table 5.** Specifications of secondary heat exchanger.

**Table 4.** Specifications of primary heat exchanger.

**Component Specification**

Material of tube and fin steel Heat conductive coefficient 46 W/m<sup>2</sup>−K Outside –tube diameter 34 mm Thickness of tube 3.38 mm Horizontal spacing 7 mm Fin spacing 4 mm Fin thickness (*δc*) 1 mm Total length of tube 4.4 m Length of 1 tube 0.5 m Fin factor 15 Resistance 1210 Pa

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 10 of 15

Heat exchanger type Liquid–gas (Figure 6a), liquid (water) flows inside the tube,

Tube type Fin–tube, staggered arrangement (Figure 6b)

**Component Specification**

**Component Specification**

Outside –tube diameter 19 mm Length of tube 740 mm Heat conductive coefficient 46 W/m2−K Number of pass in primary side 3 passes

Material of tube and fin steel Heat conductive coefficient 46 W/m<sup>2</sup>−K Outside –tube diameter 34 mm Thickness of tube 3.38 mm Horizontal spacing 7 mm Fin spacing 4 mm Fin thickness (*δc*) 1 mm Total length of tube 4.4 m

Number of tubes 36 tubes

Number of pass in secondary side 3 passes

Heat exchanger type shell–tube (Figure 7), the lower temperature wa-

Tube type Fin–tube, staggered arrangement (Figure 6b)

Heat exchanger type Liquid–gas (Figure 6a), liquid (water) flows inside the tube,

gas flows outside the tube

ter is heated by the higher temperature water.

gas flows outside the tube


**Figure 7.** Secondary heat exchanger. **Figure 7.** Secondary heat exchanger.

**Table 5.** Specifications of secondary heat exchanger.

