# StaticWaterWaterExchanger


## Copyright © EDF 2002 - 2026  
## ThermoSysPro Version 4.2  
This component model is documented in Sect. 9.6.2 of the ThermoSysPro book.   
# Static water water exchanger   
   
This static plate heat exchanger is the steady-state version of the [dynamic water water exchanger](ThermoSysPro.WaterSteam.HeatExchangers.DynamicWaterWaterExchanger).  
In addition to the [dynamic model](ThermoSysPro.WaterSteam.HeatExchangers.DynamicWaterWaterExchanger) assumptions, the specific heats and mass flow rates of both fluids are supposed constant.  


## Modelica component model  

The equations mentioned below are implemented in the component *StaticWaterWaterExchanger*, located in the *WaterSteam.HeatExchangers* sub-library.   
   
![ThermoSysPro.WaterSteam.HeatExchangers.StaticWaterWaterExchanger.svg](./icons/ThermoSysPro.WaterSteam.HeatExchangers.StaticWaterWaterExchanger.svg)  

## Nomenclature  

| Symbol| Description| Unit| Definition| Modelica name |  
| :----------------------------------- | :------------------------------------------------------------------------------------------- | :------------------------------------------- | :---------------------------------------------------------------------- | :----------- |  
| $A$| Heat exchange surface| $\mathrm{m}^{2}$| $\left(N_{\mathrm{p}}-2\right) \cdot S_{\mathrm{p}}$| S |  
| $m_{\mathrm{h}}$| Hot fluid mass flow rate| $\mathrm{kg} / \mathrm{s}$|| Qc |  
| $m_{\mathrm{c}}$| Cold fluid mass flow rate| $\mathrm{kg} / \mathrm{s}$|| Qf |  
| $N_{\mathrm{c}}$| Number of channels of each fluid| $-$| $\left(N_{\mathrm{p}}-1\right) / 2$| N |  
| $N_{\mathrm{p}}$| Number of plates| $-$|| nbp |  
| $P_{\mathrm{c}, \mathrm{i}}$ | Cold fluid pressure at the inlet| $\mathrm{Pa}$|| Ef.P |  
| $P_{\mathrm{c}, \mathrm{o}}$ | Cold fluid pressure at the outlet| $\mathrm{Pa}$|| Sf.P |  
| $P_{\mathrm{h}, \mathrm{i}}$ | Hot fluid pressure at the inlet| $\mathrm{Pa}$|| Ec.P |  
| $P_{\mathrm{h}, \mathrm{o}}$ | Hot fluid pressure at the outlet| $\mathrm{Pa}$|| Sc.P |  
| $T_{\mathrm{c}, \mathrm{i}}$ | Cold fluid temperature at the inlet| $\mathrm{K}$|| Tef |  
| $T_{\mathrm{c}, \mathrm{o}}$ | Cold fluid temperature at the outlet| $\mathrm{K}$|| Tsf |  
| $T_{\mathrm{h}, \mathrm{i}}$ | Hot fluid temperature at the inlet| $\mathrm{K}$|| Tec |  
| $T_{\mathrm{h}, \mathrm{o}}$ | Hot fluid temperature at the outlet| $\mathrm{K}$|| Tsc |  
| $U$| Global heat transfer coefficient \(internal overall heat exchange coefficient\)| $\mathrm{W} / \mathrm{m}^{2} / \mathrm{K}$ || K |  
| $W$| Thermal power exchanged between the two fluids| $\mathrm{W}$|| W |  
| $\Delta T_{1}$| Temperature difference 1| $\mathrm{K}$| For counter flow $T_{\mathrm{h}, \mathrm{i}}-T_{\mathrm{c}, \mathrm{o}}$ For parallel flow $T_{\mathrm{h}, \mathrm{i}}-T_{\mathrm{c}, \mathrm{i}}$ | DT1 |  
| $\Delta T_{2}$| Temperature difference 2| $\mathrm{K}$| For counter flow $T_{\mathrm{h}, \mathrm{o}}-T_{\mathrm{c}, \mathrm{i}}$ For parallel flow $T_{\mathrm{h}, \mathrm{o}}-T_{\mathrm{c}, \mathrm{o}}$ | DT2 |  
| $\Lambda_{\mathrm{c}}$| Friction pressure loss coefficient of the entire length of the exchanger for the cold fluid | $\mathrm{m}^{-4}$|| p_Kf |  
| $\Lambda_{\mathrm{h}}$| Friction pressure loss coefficient of the entire length of the exchanger for the hot fluid| $\mathrm{m}^{-4}$|| p_Kc |  
| $\rho_{\mathrm{c}}$| Cold fluid density| $\mathrm{kg} / \mathrm{m}^{3}$|| rhof |  
| $\rho_{\mathrm{h}}$| Hot fluid density| $\mathrm{kg} / \mathrm{m}^{3}$|| rhoc |  



## Governing equations  

### Energy balance equation \(hot fluid\)  


    
    

- Validity domain:   
   
 $\forall \dot{m}_{\mathrm{h}}$  

- Mathematical formulation:   
   
 $$W=\dot{m}_{\mathrm{h}} \cdot c_{p, \mathrm{h}} \cdot\left(T_{\mathrm{h}, \mathrm{i}}-T_{\mathrm{h}, \mathrm{o}}\right)$$  


### Energy balance equation \(cold fluid\)  


    
    

- Validity domain:   
   
 $\forall \dot{m}_{\mathrm{c}}$  

- Mathematical formulation:   
   
 $$W=\dot{m}_{\mathrm{c}} \cdot c_{p, \mathrm{c}} \cdot\left(T_{\mathrm{c}, \mathrm{o}}-T_{\mathrm{c}, \mathrm{i}}\right)$$  


### Heat exchanged between the fluid and the wall  


    
    

- Validity domain:   
   
 $\dot{m}_{\mathrm{h}} 
\neq 0, \dot{m}_{\mathrm{c}} 
\neq 0, \Delta T_{1} 
\neq 0$ and $\Delta T_{2} 
\neq 0$  

- Mathematical formulation:   
   
 $$W=U \cdot A \cdot \frac{\Delta T_{2}-\Delta T_{1}}{\ln \left(\frac{\Delta T_{2}}{\Delta T_{1}}\right)}$$  

- Comments:   
   



### Momentum balance equation \(hot fluid\)  


    
    

- Validity domain:   
   
 $\forall \dot{m}_{\mathrm{h}}$  

- Mathematical formulation:   
   
 $$P_{\mathrm{h}, \mathrm{o}}=P_{\mathrm{h}, \mathrm{i}}-\Lambda_{\mathrm{h}} \cdot \frac{\dot{m}_{\mathrm{h}} \cdot \lvert \dot{m}_{\mathrm{h}}\rvert}{N_{\mathrm{c}}^{2} \cdot \rho_{\mathrm{h}}}$$  

- Comments:   
   



### Momentum balance equation \(cold fluid\)  


    
    

- Validity domain:   
   
 $\forall \dot{m}_{\mathrm{c}}$  

- Mathematical formulation:   
   
 $$P_{\mathrm{c}, \mathrm{o}}=P_{\mathrm{c}, \mathrm{i}}-\Lambda_{\mathrm{c}} \cdot \frac{\dot{m}_{\mathrm{c}} \cdot \lvert \dot{m}_{\mathrm{c}}\rvert }{N_{\mathrm{c}}^{2} \cdot \rho_{\mathrm{c}}}$$  

- Comments:   
   


## References   
   
El Hefni, Baligh and Bouskela, Daniel (2019). [Modeling and Simulation of Thermal Power Plants with ThermoSysPro](https://link.springer.com/book/10.1007/978-3-030-05105-1), sect. 9.6.2. Springer Nature Switzerland AG.