# Study of Heat Recovery Equipment for Building Applications

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}O

_{3}-water nanofluids has been conducted to assess their impact on the efficiency of cross-flow microheat exchangers, revealing notable enhancements in heat transfer capabilities [32,33,34,35,36]. Furthermore, the incorporation of heat exchangers into intricate systems, such as solar thermal heat pump hybrid systems, has been subjected to modeling in order to enhance energy preservation in buildings. This analysis underscores the significance of heat exchangers in sustainable energy alternatives [37].

^{®}Design Suite software. The results suggest that the ML-OHPHE could effectively serve as a passive heat transfer device for HVAC heat recovery [40].

## 2. Materials and Methods

#### 2.1. Overall Heat Transfer Coefficient and Plate Heat Exchanger Calculation

^{2}surface area. The plate’s thickness was 5.5 mm. Plate thickness is not a usual one, but we considered it to test the model limitations under very different conditions.

^{3}]; ${\mathrm{V}}_{\mathrm{a}1}$ and ${\mathrm{V}}_{\mathrm{a}2}$ are the volumetric flows for both fluids [m

^{3}/s]; ${\mathrm{c}}_{{\mathrm{p}}_{\mathrm{a}1}}\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{c}}_{{\mathrm{p}}_{\mathrm{a}2}}$ are the fluids’ heat capacity at mean temperature [J/(kg·K)]; ${\mathrm{T}}_{\mathrm{a}1\mathrm{i}\mathrm{n}}\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{T}}_{\mathrm{a}1\mathrm{o}\mathrm{u}\mathrm{t}}$ the inlet and outlet temperature for primary fluid [K]; ${\mathrm{T}}_{\mathrm{a}2\mathrm{i}\mathrm{n}}\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{T}}_{\mathrm{a}2\mathrm{o}\mathrm{u}\mathrm{t}}$ the inlet and outlet temperature for secondary fluid [K]; U is the overall heat transfer coefficient [W/(m

^{2}·K)]; S is the total surface of all thermally effective plates [m

^{2}]; $\u2206{\mathrm{T}}_{\mathrm{l}\mathrm{o}\mathrm{g}}$ is the logarithmic mean temperature difference [K], calculated for counter-flow arrangements.

^{2}·K). The plate’s characteristics depend on the manufacturer we considered the following for our study: stainless steel plates, each having a 0.2 m

^{2}surface area and a 5.5 mm thickness.

^{2}].

_{h}(Equation (3)), channel flow area, flow rates (obtained from Equation (1)), and thermodynamic fluid properties at their mean temperature are used to calculate the first flow speed and the heat transfer coefficient.

_{hot fluid}and h

_{cold fluid}are the heat transfer coefficients for hot and cold fluid (W/m

^{2}K), ${\mathsf{\delta}}_{\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}}$ is the plate thickness (m), ${\mathsf{\lambda}}_{\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}}$ is the thermal conductivity of the plate material (W/m K), ${\mathrm{R}}_{\mathrm{f}\mathrm{o}\mathrm{u}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{c}\mathrm{o}\mathrm{l}\mathrm{d}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}}$ and ${\mathrm{R}}_{\mathrm{f}\mathrm{o}\mathrm{u}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{h}\mathrm{o}\mathrm{t}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}}$ are the fouling resistance on cold and hot sides (m

^{2}K/W). For our calculus, the fouling was neglected on both sides.

#### 2.2. Heat Exchanger Simulation in Matlab/Simulink

- Cell
_{i,1}, which describes fluid 1 temperature variation, is noted with “T_{a1}”. Fluid 1 is the one with the highest temperature. This cell is placed in the fluid 1 zone, with forced convection heat transfer being considered.

^{3}]; ${\mathrm{V}}_{\mathrm{a}1}$ is the primary fluid volumetric flow [m

^{3}/s]; ${\mathrm{c}}_{{\mathrm{p}}_{\mathrm{a}1}}$ is the primary fluid’s heat capacity at mean temperature [J/(kg·K)]; ${\mathrm{T}}_{\mathrm{a}1}\mathrm{i}\mathrm{s}$ the cell i,1 temperature for primary fluid [K]; ${\mathrm{T}}_{\mathrm{a}1\mathrm{i}\mathrm{n}}$ is the cell

_{i,1}inlet temperature for primary fluid [K]; h

_{T1}is the heat transfer coefficient for primary fluid [W/(m

^{2}·K)], ${\mathrm{A}}_{\mathrm{s}}$ is cell

_{i,1}heat surface [m

^{2}], ${\mathrm{T}}_{1}$ is the cell

_{i,2}temperature [K]; ${\mathrm{w}}_{\mathrm{a}1}$ is the primary fluid mass flow [kg/s].

- Cell i,2, which describes the plate temperature variation on the side of fluid 1, is noted with “T
_{1}”. Half of this cell dimension in the heat transfer rate direction is placed in the fluid 1 zone, and the other half is in the plate thickness. The plate thickness is, as presented in Figure 1, “2δ_{x}”. Each elementary cell has a “ δ_{x}” thickness. The thickness of the cell is its dimension in the heat transfer rate direction. Heat transfer inside this cell is obtained by forced convection in the fluid layer and conduction in the metal layer.

^{3}]; “ δ

_{x}” cell’s thickness [m]; ${\mathrm{c}}_{{\mathrm{p}}_{\mathrm{m}}}$ is the metal’s heat capacity [J/(kg·K)]; ${\mathrm{T}}_{1}$ is the cell

_{i,2}temperature [K]; ${\mathsf{\lambda}}_{\mathrm{m}}$ is the metal’s thermal conductivity [W/(m·K)]; ${\mathrm{T}}_{2}$ is the cell

_{i,3}temperature [K]; h

_{T1}is the heat transfer coefficient for primary fluid [W/(m

^{2}K)]; ${\mathrm{T}}_{\mathrm{a}1}\mathrm{i}\mathrm{s}$ the cell

_{i,1}temperature for primary fluid [K].

- Cell i,3, which describes the plate temperature variation at its half thickness, is noted with “T
_{2}”. The entire cell is made of metal, so heat transfer by conduction is considered.

^{3}]; “ δ

_{x}” cell’s thickness [m]; ${\mathrm{c}}_{{\mathrm{p}}_{\mathrm{m}}}$ is the metal’s heat capacity [J/(kg·K)]; ${\mathrm{T}}_{2}$ is the cell

_{i,3}temperature [K]; ${\mathsf{\lambda}}_{\mathrm{m}}$ is the metal’s thermal conductivity [W/(m·K)]; ${\mathrm{T}}_{1}$ is the cell

_{i,2}temperature [K]; ${\mathrm{T}}_{3}\mathrm{i}\mathrm{s}$ the cell

_{i,4}temperature [K].

- Cell i,4, which describes the plate temperature variation on the side of fluid 2, is noted with "T
_{3}." Half of this cell dimension in the heat transfer rate direction is placed in the fluid 2 zone, and the other half is in the plate thickness. Heat transfer inside this cell is obtained by forced convection in the fluid layer and conduction in the metal layer.

^{3}]; “ δ

_{x}” cell’s thickness [m]; ${\mathrm{c}}_{{\mathrm{p}}_{\mathrm{m}}}$ is the metal’s heat capacity [J/(kg·K)]; ${\mathrm{T}}_{3}$ is the cell

_{i,4}temperature [K]; ${\mathsf{\lambda}}_{\mathrm{m}}$ is the metal’s thermal conductivity [W/(m·K)]; ${\mathrm{T}}_{2}$ is the cell

_{i,3}temperature [K]; h

_{T2}is the heat transfer coefficient for secondary fluid [W/(m

^{2}K)]; ${\mathrm{T}}_{\mathrm{a}2}$ is the cell

_{i,1}temperature for secondary fluid [K].

- Cell i,5, which describes fluid 2 temperature variation, is noted with “T
_{a2}”. Fluid 2 is the one with the lowest temperature. This cell is placed in the fluid 2 zone; forced convection heat transfer is being considered.

^{3}]; ${\mathrm{V}}_{\mathrm{a}2}$ is the secondary fluid volumetric flow [m

^{3}/s]; ${\mathrm{c}}_{{\mathrm{p}}_{\mathrm{a}2}}$ is the secondary fluid’s heat capacity at mean temperature [J/(kg·K)]; ${\mathrm{T}}_{\mathrm{a}2}\mathrm{i}\mathrm{s}$ the cell

_{i,5}temperature for secondary fluid [K]; h

_{T2}is the heat transfer coefficient for secondary fluid [W/(m

^{2}K)]; ${\mathrm{A}}_{\mathrm{s}}$ is cell

_{i,5}heat surface [m

^{2}],${\mathrm{T}}_{3}$ is the cell

_{i,4}temperature [K]; ${\mathrm{w}}_{\mathrm{a}2}$ is the secondary fluid mass flow [kg/s]; ${\mathrm{T}}_{\mathrm{a}2\mathrm{i}\mathrm{n}}$ is the cell

_{i,5}inlet temperature for secondary fluid [K].

^{2}surface area. The plate’s thickness was 5.5 mm. According to the values presented, the heat transfer coefficient by convection for fluid one was calculated to be equal to 12,090 W/m

^{2}K, and the heat transfer coefficient by convection for fluid two was equal to 10,238 W/m

^{2}K. The calculated parameters were used in Matlab/Simulink in order to verify the differences between the two calculation methods.

_{1}” temperature from the 3rd level of modeling in Matlab/Simulink.

## 3. Results and Discussion

## 4. Model Validation with Experimental Data

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Block diagram corresponding to the 2nd level of modeling in Matlab/Simulink for a 1-cell model.

**Figure 3.**Block diagram corresponding to the 3rd level of modeling in Matlab/Simulink, T

_{1}equation.

**Figure 4.**Block diagram corresponding to the 2nd level of modeling in Matlab/Simulink, 3 consecutive cells from the 50-cell model.

**Figure 5.**All temperature variation occurs after the 1st cell (

**left side**) and after the 50th cell (

**right side**).

**Figure 6.**Heat flow rate for a cold fluid as a function of its heat transfer coefficient and outlet temperature of 40 °C, 45 °C, and 50 °C.

Parameter | Hot Fluid | Cold Fluid |
---|---|---|

Fluids | Wastewater | Cooling water |

Mass flow rates (kg/s) | 2.88 | 2.01 |

Inlet temperature (°C) | 104 | 60 |

Outlet temperature (°C) | 90 | 80 |

Specific heat (J/g K) | 4.21 | 4.19 |

Viscosity (s/m^{2}) | 0.284 × 10^{−6} | 0.415 × 10^{−6} |

Thermal conductivity (W/m K) | 0.6836 | 0.6676 |

Density (kg/m^{3}) | 955.4 | 977.7 |

Nusselt (-) | 195 | 168.7 |

Heat transfer coefficient (W/m^{2} K) | 12,090 | 10,238 |

Parameter | Value | U.M. |
---|---|---|

Plate material | Stainless Steel | (-) |

Thermal conductivity of plate material | 17 | W/m K |

Plate surface | 0.2 | m^{2} |

Plate thickness | 5.5 | mm |

Plate height | 989 | mm |

Plate width | 242 | mm |

Plate material density | 7850 | kg/m^{3} |

Plate material-specific heat | 0.49 | J/g K |

Chevron angle | 60 | degrees |

Enlargement factor | 1.19 | - |

Effective number of plates | 10 | - |

**Table 3.**Modeled values and calculated errors with respect to the values given by the design theme for outlet temperatures of the two fluids and heat transfer rates.

Parameter | 1 Cell | 10 Cells | 20 Cells | 30 Cells | 40 Cells | 50 Cells | Reference |
---|---|---|---|---|---|---|---|

t_{a1} out [°C] | 95.99 | 93.12 | 92.29 | 91.74 | 90.6 | 90.37 | 90 |

t_{a2} out [°C] | 71.54 | 75.68 | 76.87 | 77.66 | 79.31 | 79.64 | 80 |

Relative error for t_{a1} out [%] | −6.66 | −3.47 | −2.54 | −1.93 | −0.67 | −0.41 | |

Relative error for t_{a2} out [%] | 10.58 | 5.40 | 3.91 | 2.93 | 0.86 | 0.45 | |

(t_{a1} in–t_{a1} out) [°C] | 8.01 | 10.88 | 11.71 | 12.26 | 13.4 | 13.63 | 14 |

(t_{a2} out–t_{a2} in) [°C] | 11.54 | 15.68 | 16.87 | 17.66 | 19.31 | 19.64 | 20 |

ø1 [kW] | 97.1 | 131.9 | 142.0 | 148.7 | 162.5 | 165.3 | 169.7 |

ø2 [kW] | 97.1 | 131.9 | 141.9 | 148.6 | 162.5 | 165.2 | 168.3 |

Relative error for ø1 [%] | 42.8 | 22.3 | 16.4 | 12.4 | 4.3 | 2.6 | |

Relative error for ø2 [%] | 42.3 | 21.6 | 15.7 | 11.7 | 3.4 | 1.8 |

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**MDPI and ACS Style**

Popescu, L.L.; Popescu, R.S.; Catalina, T.
Study of Heat Recovery Equipment for Building Applications. *Buildings* **2023**, *13*, 3125.
https://doi.org/10.3390/buildings13123125

**AMA Style**

Popescu LL, Popescu RS, Catalina T.
Study of Heat Recovery Equipment for Building Applications. *Buildings*. 2023; 13(12):3125.
https://doi.org/10.3390/buildings13123125

**Chicago/Turabian Style**

Popescu, Lelia Letitia, Razvan Stefan Popescu, and Tiberiu Catalina.
2023. "Study of Heat Recovery Equipment for Building Applications" *Buildings* 13, no. 12: 3125.
https://doi.org/10.3390/buildings13123125