.ThermoSysPro.WaterSteam.HeatExchangers.StaticWaterWaterExchanger

Information

## 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](modelica://ThermoSysPro.WaterSteam.HeatExchangers.DynamicWaterWaterExchanger).  
In addition to the [dynamic model](modelica://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.   
   
![modelica://ThermoSysPro/UsersGuide/Documentation/ThermoSysPro.WaterSteam.HeatExchangers.StaticWaterWaterExchanger.svg](modelica://ThermoSysPro/UsersGuide/Documentation/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.  
    

Revisions