# Heat Exchanger

Intercooler or exhaust gas recirculation (EGR) cooler

• Library:
• Powertrain Blockset / Propulsion / Combustion Engine Components / Fundamental Flow

• ## Description

The Heat Exchanger block models a heat exchanger, for example, an intercooler or exhaust gas recirculation (EGR) cooler. The inlet (port C) connects to an engine flow component (flow restriction, compressor, turbine, or engine block). The outlet (port B) connects to a volume (control volume or environment). Based on the upstream temperature, heat exchanger effectiveness, and cooling medium temperature, the block determines the heat transfer rate and downstream temperature.

For the heat exchanger effectiveness and cooling medium temperature, you can specify either a constant value or an external input. For example, if you specify a heat exchanger effectiveness that is:

• Equal to 1, the downstream temperature is equal to the cooling medium temperature.

• Equal to 0, there is no heat transfer to the cooling medium. The downstream temperature is equal to the upstream temperature.

The block assumes no pressure drop. To model pressure losses, use a Flow Restriction block.

### Equations

The Heat Exchanger block implements equations that use these variables.

 ${T}_{upstr}$ Upstream temperature ${T}_{dnstr}$ Downstream temperature ${T}_{cool}$ Cooling medium temperature ${T}_{cool,cnst}$ Constant cooling medium temperature ${T}_{cool,input}$ External input cooling medium temperature $\epsilon$ Heat exchanger effectiveness ${\epsilon }_{cnst}$ Constant heat exchanger effectiveness ${\epsilon }_{input}$ Input heat exchanger effectiveness ${c}_{p}$ Specific heat at constant pressure ${q}_{ht}$ Heat exchanger heat transfer rate ${p}_{flw,in}$ Pressure at inlet ${p}_{vol,out}$ Pressure at outlet ${T}_{vol,out}$ Temperature at outlet ${h}_{vol,out}$ Specific enthalpy at outlet ${q}_{in}$ Heat flow rate at inlet ${q}_{out}$ Heat flow rate at outlet $\stackrel{˙}{m}$ Heat exchanger mass flow rate ${T}_{flw,in}$ Temperature at inlet ${T}_{in}$ Heat exchanger inlet temperature ${T}_{out}$ Heat exchanger outlet temperature ${h}_{in}$ Inlet specific enthalpy

Heat Exchanger Effectiveness

Heat exchanger effectiveness measures the effectiveness of heat transfer from the incoming hot fluid to the cooling medium:

`$\epsilon =\frac{{T}_{upstr}-{T}_{dnstr}}{{T}_{upstr}-{T}_{cool}}$`

In an ideal heat exchanger, the downstream temperature equals the cooling temperature. The effectiveness is equal to 1.

`$\begin{array}{l}{T}_{dnstr}={T}_{cool}\\ \epsilon =1\end{array}$`

The Heat Exchanger block uses the effectiveness to determine the downstream temperature and heat transfer rate.

`$\begin{array}{l}{T}_{dnstr}={T}_{upstr}-\epsilon \left({T}_{upstr}-{T}_{cool}\right)\\ {q}_{ht}=\stackrel{˙}{m}{c}_{p}\left({T}_{upstr}-{T}_{dnstr}\right)\end{array}$`

Fluid Flow

Since the block assumes no pressure drop, ${P}_{flw,in}={P}_{vol,out}$.

The flow component connection to the heat exchanger inlet determines the direction of the mass flow. Based on the mass flow rate direction, these temperature and heat flow equations apply.

Fluid FlowMass Flow RateTemperatures and Heat Flow

Forward — From engine flow component to outlet volume

`$\stackrel{˙}{m}\ge 0$`

`$\begin{array}{l}{T}_{upstr}={T}_{flw,in}\\ {T}_{in}={T}_{upstr}\\ {T}_{out}={T}_{dnstr}\\ {q}_{out}=\stackrel{˙}{m}{c}_{p}{T}_{dnstr}\end{array}$`

Reverse — From outlet volume to engine flow component

`$\stackrel{˙}{m}<0$`

`$\begin{array}{l}{T}_{upstr}={T}_{vol,out}\\ {T}_{in}={T}_{dnstr}\\ {T}_{out}={T}_{vol,out}\\ {h}_{in}={c}_{p}{T}_{dnstr}\\ {q}_{out}=\stackrel{˙}{m}{h}_{vol,out}\end{array}$`

The block uses the internal signal `FlwDir` to track the direction of the flow.

### Power Accounting

For the power accounting, the block implements these equations.

Bus Signal DescriptionEquations

`PwrInfo`

`PwrTrnsfrd` — Power transferred between blocks

• Positive signals indicate flow into block

• Negative signals indicate flow out of block

`PwrHeatFlwIn`

Heat flow rate at port C

qin

`PwrHeatFlwOut`

Heat flow rate at port B

-qout

`PwrNotTrnsfrd` — Power crossing the block boundary, but not transferred

• Positive signals indicate an input

• Negative signals indicate a loss

`PwrHeatTrnsfr`

Heat transfer rate to cooling medium

-qht

`PwrStored` — Stored energy rate of change

• Positive signals indicate an increase

• Negative signals indicate a decrease

Not used

## Ports

### Input

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Bus containing the heat exchanger:

• `MassFlwRate` — Mass flow rate at inlet, $\stackrel{˙}{m}$, in kg/s

• `HeatFlwRate` — Heat flow rate at inlet, ${q}_{in}$, in J/s

• `Temp` — Temperature at inlet, ${T}_{flw,in}$, in K

• `MassFrac` — Inlet mass fractions, dimensionless.

Specifically, a bus with these mass fractions:

• `O2MassFrac` — Oxygen

• `N2MassFrac` — Nitrogen

• `UnbrndFuelMassFrac` — Unburned fuel

• `CO2MassFrac` — Carbon dioxide

• `H2OMassFrac` — Water

• `COMassFrac` — Carbon monoxide

• `NOMassFrac` — Nitric oxide

• `NO2MassFrac` — Nitrogen dioxide

• `NOxMassFrac` — Nitric oxide and nitrogen dioxide

• `PmMassFrac` — Particulate matter

• `AirMassFrac` — Air

• `BrndGasMassFrac` — Burned gas

Bus containing the heat exchanger:

• `Prs` — Pressure at outlet, ${p}_{vol,out}$, in Pa

• `Temp` — Temperature at outlet, ${T}_{vol,out}$, in K

• `Enth` — Specific enthalpy at outlet, ${h}_{vol,out}$, in J/kg

• `MassFrac` — Outlet mass fractions, dimensionless.

Specifically, a bus with these mass fractions:

• `O2MassFrac` — Oxygen

• `N2MassFrac` — Nitrogen

• `UnbrndFuelMassFrac` — Unburned fuel

• `CO2MassFrac` — Carbon dioxide

• `H2OMassFrac` — Water

• `COMassFrac` — Carbon monoxide

• `NOMassFrac` — Nitric oxide

• `NO2MassFrac` — Nitrogen dioxide

• `NOxMassFrac` — Nitric oxide and nitrogen dioxide

• `PmMassFrac` — Particulate matter

• `AirMassFrac` — Air

• `BrndGasMassFrac` — Burned gas

Heat exchanger effectiveness, ${\epsilon }_{input}$.

#### Dependencies

To create this port, set Effectiveness model to `External input`.

Cooling medium temperature, ${T}_{cool,input}$.

#### Dependencies

To create this port, set Cooling medium temperature input to ```External input```

### Output

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Bus signal containing these block calculations.

SignalDescriptionUnits

`InletTemp`

Heat exchanger inlet temperature

K

`OutletTemp`

Heat exchanger outlet temperature

K

`HeatTrnsfrRate`

Heat exchanger heat transfer rate

J/s

`PwrInfo`

`PwrTrnsfrd`

`PwrHeatFlwIn`

Heat flow rate at port C

W

`PwrHeatFlwOut`

Heat flow rate at port B

W

`PwrNotTrnsfrd`

`PwrHeatTrnsfr`

Heat transfer rate to cooling medium

W

`PwrStored`

Not used

Bus containing the heat exchanger:

• `Prs` — Pressure at inlet, ${p}_{flw,in}$, in Pa

• `Temp` — Temperature at inlet, ${T}_{in}$, in K

• `Enth` — Specific enthalpy at inlet, ${h}_{in}$, in J/kg

• `MassFrac` — Inlet mass fractions, dimensionless.

Specifically, a bus with these mass fractions:

• `O2MassFrac` — Oxygen

• `N2MassFrac` — Nitrogen

• `UnbrndFuelMassFrac` — Unburned fuel

• `CO2MassFrac` — Carbon dioxide

• `H2OMassFrac` — Water

• `COMassFrac` — Carbon monoxide

• `NOMassFrac` — Nitric oxide

• `NO2MassFrac` — Nitrogen dioxide

• `NOxMassFrac` — Nitric oxide and nitrogen dioxide

• `PmMassFrac` — Particulate matter

• `AirMassFrac` — Air

• `BrndGasMassFrac` — Burned gas

Bus containing the heat exchanger:

• `MassFlwRate` — Mass flow rate at outlet, $\stackrel{˙}{m}$, in kg/s

• `HeatFlwRate` — Heat flow rate at outlet, ${q}_{out}$, in J/s

• `Temp` — Temperature at outlet, ${T}_{out}$, in K

• `MassFrac` — Outlet mass fractions, dimensionless.

Specifically, a bus with these mass fractions:

• `O2MassFrac` — Oxygen

• `N2MassFrac` — Nitrogen

• `UnbrndFuelMassFrac` — Unburned fuel

• `CO2MassFrac` — Carbon dioxide

• `H2OMassFrac` — Water

• `COMassFrac` — Carbon monoxide

• `NOMassFrac` — Nitric oxide

• `NO2MassFrac` — Nitrogen dioxide

• `NOxMassFrac` — Nitric oxide and nitrogen dioxide

• `PmMassFrac` — Particulate matter

• `AirMassFrac` — Air

• `BrndGasMassFrac` — Burned gas

## Parameters

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Block Options

Type of model to calculate the heat exchanger effectiveness.

#### Dependencies

Selecting:

• `External input` creates the `Effct` port.

• `Constant` enables the Heat exchanger effectiveness, ep_cnst parameter.

Cooling medium temperature input.

#### Dependencies

Selecting:

• `External input` creates the `CoolTemp` port.

• `Constant` enables the Cooling medium temperature, T_cool_cnst parameter.

Block icon color:

• `Intercooler` for blue, to indicate an intercooler

• `EGR cooler hot to cold` for red to blue, to indicate EGR from hot to cold

• `EGR cooler cold to hot` for blue to red, to indicate EGR from cold to hot

Constant heat exchanger effectiveness, ${\epsilon }_{cnst}$.

#### Dependencies

To enable this parameter, select `Constant` for the Effectiveness model parameter.

Constant cooling medium temperature, ${T}_{cool,cnst}$, in K.

#### Dependencies

To enable this parameter, select `Constant` for the Cooling medium temperature input parameter.

Specific heat at constant pressure, ${c}_{p}$, in J/(kg*K).

 Eriksson, Lars and Nielsen, Lars. Modeling and Control of Engines and Drivelines. Chichester, West Sussex, United Kingdom: John Wiley & Sons Ltd, 2014.

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