modelCocurrentHeatExchangerEquations
Information
Cocurrent heat exchanger model consist of two channels A and B, and a separating heat transfer wall in between. Fluids A and B are flowing in the channels A and B respectively. Heat exchanger is assumed to be insulated around the outside, therefore, heat transfer occurs just between the fluids A and B. Fluid B is considered as the hot fluid and fluid A is considered to be the cold fluid.
Heat exchanger mass balance equations for the fluids can be written as:
where ρ is the density of the fluid, A is the cross section and w is the mass flow rate. Density and the cross section are assumed to be constant for the fluids, hence mass flow rate is considered constant along the channels.
Heat exchanger energy balance equations are described considering a small portion l=L/(N-1) on the channels where L is the length of each channel, and N is the number of nodes on the channels. Therefore, N-1 corresponds to the number of channel and wall segments. And, there are N-1 heat flow rates and N-1 temperature variables for the wall which are considered for the segments.Energy balance equations for cocurrent heat exchanger is very similar to the equations of countercurrent heat exchanger. The difference occurs because of the flow direction of the fluid B, therefore, in cocurrent heat exchanger boundary condition of T_B is described for the first node. And, boundary condition of T_A remained again for the first node.
for j=1…N-1. Energy balance at the each wall segment is modified in terms of temperature variables of fluid B:
for j=1…N-1.
Parameters in the CounterCurrentHeatExchangerEquations:
| Parameters | Comment |
|---|---|
| L | length of the channels |
| N | number of nodes |
| wB | mass flow rate of fluid B |
| areaA | cross sectional area of channel A |
| areaB | cross sectional area of channel B |
| rhoA | density of fluid A |
| rhoB | density of fluid B |
| cpA | specific heat capacity of fluid A |
| cpB | specific heat capacity of fluid B |
| cpW | specific heat capacity of the wall |
| gammaA | heat transfer coefficient of fluid A |
| gammaB | heat transfer coefficient of fluid B |
| omega | perimeter |
| l | length of each wall segment |
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| SIunits.Length | L | length of the channels | |
| Integer | N | 2 | number of nodes |
| SIunits.MassFlowRate | wB | mass flow rate of fluid B | |
| SIunits.Area | areaA | cross sectional area of channel A | |
| SIunits.Area | areaB | cross sectional area of channel B | |
| SIunits.Density | rhoA | density of fluid A | |
| SIunits.Density | rhoB | density of fluid B | |
| SIunits.SpecificHeatCapacity | cpA | specific heat capacity of fluid A | |
| SIunits.SpecificHeatCapacity | cpB | specific heat capacity of fluid B | |
| SIunits.SpecificHeatCapacity | cpW | specific heat capacity of the wall | |
| SIunits.CoefficientOfHeatTransfer | gammaA | heat transfer coefficient of fluid A | |
| SIunits.CoefficientOfHeatTransfer | gammaB | heat transfer coefficient of fluid B | |
| SIunits.Length | omega | perimeter | |
| SIunits.Length | l | L/(N - 1) | length of the each wall segment |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| SIunits.MassFlowRate | wA | mass flow rate of fluid A | |
| SIunits.HeatFlowRate[N - 1] | QA | heat flow rate of fluid A in the segments | |
| SIunits.HeatFlowRate[N - 1] | QB | heat flow rate of fluid B in the segments | |
| SIunits.Temperature[N] | TA | temperature nodes on channel A | |
| SIunits.Temperature[N] | TB | temperature nodes on channel B | |
| SIunits.Temperature[N - 1] | TAtilde | temperature states on channel A | |
| SIunits.Temperature[N - 1] | TBtilde | temperature states on channel B | |
| SIunits.Temperature[N - 1] | TW | temperatures on the wall segments | |
| SIunits.HeatFlowRate | QtotA | total heat flow rate of fluid A | |
| SIunits.HeatFlowRate | QtotB | total heat flow rate of fluid B |