Heat Exchanger

Intercooler or exhaust gas recirculation (EGR) cooler

Libraries:
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.

$T_{u p s t r}$	Upstream temperature
$T_{d n s t r}$	Downstream temperature
$T_{c o o l}$	Cooling medium temperature
$T_{c o o l, c n s t}$	Constant cooling medium temperature
$T_{c o o l, i n p u t}$	External input cooling medium temperature
$ε$	Heat exchanger effectiveness
$ε_{c n s t}$	Constant heat exchanger effectiveness
$ε_{i n p u t}$	Input heat exchanger effectiveness
$c_{p}$	Specific heat at constant pressure
$q_{h t}$	Heat exchanger heat transfer rate
$p_{f l w, i n}$	Pressure at inlet
$p_{v o l, o u t}$	Pressure at outlet
$T_{v o l, o u t}$	Temperature at outlet
$h_{v o l, o u t}$	Specific enthalpy at outlet
$q_{i n}$	Heat flow rate at inlet
$q_{o u t}$	Heat flow rate at outlet
$\dot{m}$	Heat exchanger mass flow rate
$T_{f l w, i n}$	Temperature at inlet
$T_{i n}$	Heat exchanger inlet temperature
$T_{o u t}$	Heat exchanger outlet temperature
$h_{i n}$	Inlet specific enthalpy

Heat Exchanger Effectiveness

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

$ε = \frac{T_{u p s t r} - T_{d n s t r}}{T_{u p s t r} - T_{c o o l}}$

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

$\begin{array}{l} T_{d n s t r} = T_{c o o l} \\ ε = 1 \end{array}$

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

$\begin{array}{l} T_{d n s t r} = T_{u p s t r} - ε (T_{u p s t r} - T_{c o o l}) \\ q_{h t} = \dot{m} c_{p} (T_{u p s t r} - T_{d n s t r}) \end{array}$

Fluid Flow

Since the block assumes no pressure drop, $P_{f l w, i n} = P_{v o l, o u t}$ .

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 Flow	Mass Flow Rate	Temperatures and Heat Flow
Forward — From engine flow component to outlet volume	$\dot{m} \geq 0$	$\begin{array}{l} T_{u p s t r} = T_{f l w, i n} \\ T_{i n} = T_{u p s t r} \\ T_{o u t} = T_{d n s t r} \\ q_{o u t} = \dot{m} c_{p} T_{d n s t r} \end{array}$
Reverse — From outlet volume to engine flow component	$\dot{m} < 0$	$\begin{array}{l} T_{u p s t r} = T_{v o l, o u t} \\ T_{i n} = T_{d n s t r} \\ T_{o u t} = T_{v o l, o u t} \\ h_{i n} = c_{p} T_{d n s t r} \\ q_{o u t} = \dot{m} h_{v o l, o u t} \end{array}$

Fluid Flow

Mass Flow Rate

Temperatures and Heat Flow

Forward — From engine flow component to outlet volume

$\dot{m} \geq 0$

$\begin{array}{l} T_{u p s t r} = T_{f l w, i n} \\ T_{i n} = T_{u p s t r} \\ T_{o u t} = T_{d n s t r} \\ q_{o u t} = \dot{m} c_{p} T_{d n s t r} \end{array}$

Reverse — From outlet volume to engine flow component

$\dot{m} < 0$

$\begin{array}{l} T_{u p s t r} = T_{v o l, o u t} \\ T_{i n} = T_{d n s t r} \\ T_{o u t} = T_{v o l, o u t} \\ h_{i n} = c_{p} T_{d n s t r} \\ q_{o u t} = \dot{m} h_{v o l, o u t} \end{array}$

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			Description	Equations
`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	q_in
		`PwrHeatFlwOut`	Heat flow rate at port B	-q_out
	`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	-q_ht
	`PwrStored` — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease		Not used

Examples

Build Conventional Vehicle Model

Build a vehicle with an internal combustion engine using the conventional vehicle reference application.

Ports

Input

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C — Inlet mass flow rate, heat flow rate, temperature, mass fractions
two-way connector port

Bus containing the heat exchanger:

MassFlwRate — Mass flow rate at inlet, $\dot{m}$ , in kg/s
HeatFlwRate — Heat flow rate at inlet, $q_{i n}$ , in J/s
Temp — Temperature at inlet, $T_{f l w, i n}$ , 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

B — Outlet volume pressure, temperature, enthalpy, mass fractions
two-way connector port

Bus containing the heat exchanger:

Prs — Pressure at outlet, $p_{v o l, o u t}$ , in Pa
Temp — Temperature at outlet, $T_{v o l, o u t}$ , in K
Enth — Specific enthalpy at outlet, $h_{v o l, o u t}$ , 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

Effct — Heat exchanger effectiveness
`scalar`

Heat exchanger effectiveness, $ε_{i n p u t}$ .

Dependencies

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

CoolTemp — Cooling medium temperature
scalar

Cooling medium temperature, $T_{c o o l, i n p u t}$ .

Dependencies

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

Output

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Info — Heat exchanger data
bus

Bus signal containing these block calculations.

Signal			Description	Units
`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
	`PwrTrnsfrd`	`PwrHeatFlwOut`	Heat flow rate at port B	W
	`PwrNotTrnsfrd`	`PwrHeatTrnsfr`	Heat transfer rate to cooling medium	W
	`PwrStored`		Not used

C — Inlet flow pressure, temperature, enthalpy, mass fractions
two-way connector port

Bus containing the heat exchanger:

Prs — Pressure at inlet, $p_{f l w, i n}$ , in Pa
Temp — Temperature at inlet, $T_{i n}$ , in K
Enth — Specific enthalpy at inlet, $h_{i n}$ , 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

B — Outlet volume mass flow rate, heat flow rate, temperature, mass fractions
two-way connector port

Bus containing the heat exchanger:

MassFlwRate — Mass flow rate at outlet, $\dot{m}$ , in kg/s
HeatFlwRate — Heat flow rate at outlet, $q_{o u t}$ , in J/s
Temp — Temperature at outlet, $T_{o u t}$ , 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

Effectiveness model — Model type for heat effectiveness
`Constant` (default) | `External input`

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 — Specify type
`Constant` (default) | `External input`

Cooling medium temperature input.

Dependencies

Selecting:

External input creates the CoolTemp port.
Constant enables the Cooling medium temperature, T_cool_cnst parameter.

Image type — Icon color
`Intercooler` (default) | `EGR cooler hot to cold` | `EGR cooler cold to hot`

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

Heat exchanger effectiveness, ep_cnst — Effectiveness
`0.7` (default) | `scalar`

Constant heat exchanger effectiveness, $ε_{c n s t}$ .

Dependencies

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

Cooling medium temperature, T_cool_cnst — Temperature
`300` (default) | `scalar`

Constant cooling medium temperature, $T_{c o o l, c n s t}$ , in K.

Dependencies

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

Specific heat at constant pressure, cp — Specific heat
`1005` (default) | `scalar`

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

References

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2017a

Heat Exchanger

Description

Equations

Power Accounting

Examples

Build Conventional Vehicle Model

Ports

Input

C — Inlet mass flow rate, heat flow rate, temperature, mass fractions two-way connector port

B — Outlet volume pressure, temperature, enthalpy, mass fractions two-way connector port

Effct — Heat exchanger effectiveness scalar

Dependencies

CoolTemp — Cooling medium temperature scalar

Dependencies

Output

Info — Heat exchanger data bus

C — Inlet flow pressure, temperature, enthalpy, mass fractions two-way connector port

B — Outlet volume mass flow rate, heat flow rate, temperature, mass fractions two-way connector port

Parameters

Effectiveness model — Model type for heat effectiveness Constant (default) | External input

Dependencies

Cooling medium temperature input — Specify type Constant (default) | External input

Dependencies

Image type — Icon color Intercooler (default) | EGR cooler hot to cold | EGR cooler cold to hot

Heat exchanger effectiveness, ep_cnst — Effectiveness 0.7 (default) | scalar

Dependencies

Cooling medium temperature, T_cool_cnst — Temperature 300 (default) | scalar

Dependencies

Specific heat at constant pressure, cp — Specific heat 1005 (default) | scalar

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

C — Inlet mass flow rate, heat flow rate, temperature, mass fractions
two-way connector port

B — Outlet volume pressure, temperature, enthalpy, mass fractions
two-way connector port

Effct — Heat exchanger effectiveness
`scalar`

CoolTemp — Cooling medium temperature
scalar

Info — Heat exchanger data
bus

C — Inlet flow pressure, temperature, enthalpy, mass fractions
two-way connector port

B — Outlet volume mass flow rate, heat flow rate, temperature, mass fractions
two-way connector port

Effectiveness model — Model type for heat effectiveness
`Constant` (default) | `External input`

Cooling medium temperature input — Specify type
`Constant` (default) | `External input`

Image type — Icon color
`Intercooler` (default) | `EGR cooler hot to cold` | `EGR cooler cold to hot`

Heat exchanger effectiveness, ep_cnst — Effectiveness
`0.7` (default) | `scalar`

Cooling medium temperature, T_cool_cnst — Temperature
`300` (default) | `scalar`

Specific heat at constant pressure, cp — Specific heat
`1005` (default) | `scalar`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.