# Exhaust Manifold Thermal

**Libraries:**

Simscape /
Driveline /
Engines & Motors /
Engine Subcomponents

## Description

The Exhaust Manifold Thermal block represents the abstracted thermodynamics of a combustion engine exhaust manifold. The block integrates with the SI Combustion Cylinder block.

### Equations

The block takes exhaust gas flow from the SI Combustion
Cylinder blocks and computes the exhaust manifold temperature,
*T _{exh}*, which the block outputs at
port

**Texh**. The block calculates the output using a lumped-parameter model, such that

$${C}_{exh}{M}_{exh}\frac{d}{dt}{T}_{exh}={h}_{exh}-{h}_{x,}$$

where

*C*is the_{exh}**Heat capacity of exhaust wall**parameter.*M*is the_{exh}**Mass of exhaust wall**parameter.*h*is the heat flow at the exhaust manifold._{exh}*h*is the heat exchange between the exhaust gas and the environment._{x}

The block calculates *h _{x}* as

$${h}_{x}={S}_{exh}\left({h}_{convec}\left({T}_{exh}-{T}_{amb}\right)-{k}_{ra}\sigma \left({T}_{exh}^{4}-{T}_{amb}^{4}\right)\right),$$

where

*S*is the_{exh}**Surface area of exhaust wall**parameter.*h*is the_{convec}**Convective heat transfer coefficient for the outer side of exhaust**parameter.*k*is the_{ra}**Radiation constant**parameter.*σ*is the**Stefan-Boltzmann constant**parameter.*T*is the_{amb}**Ambient temperature**parameter.

The block finds *h _{exh}* as

$${k}_{gas}\frac{d}{dt}{h}_{exh}={h}_{in}-{h}_{exh},$$

where *k _{gas}* is the

**Time constant of exhaust heat flow**parameter, and

*h*is the instantaneous heat flow from the engine exhaust outlets to the exhaust manifold. The instantaneous heat flow is the sum of the individual instantaneous heat flows at the exhaust outlets,

_{in}*h*, such that

_{i}$${h}_{in}={\displaystyle \sum _{i=1}^{{N}_{ports}}{h}_{i}},$$

where *N _{ports}* is the

**Number of exhaust ports**parameter.

## Examples

## Ports

### Input

### Output

## Parameters

## Version History

**Introduced in R2022a**

## See Also

Spark Ignition Engine | SI Combustion Cylinder | Crankshaft | Ignition Trigger | Air Intake