# Conductive Heat Transfer

Heat transfer by conduction

**Library:**Simscape / Foundation Library / Thermal / Thermal Elements

## Description

The Conductive Heat Transfer block represents heat transfer by conduction between two layers of the same material. For a flat surface, the Fourier law describes the transfer,

$$Q=k\cdot \frac{A}{D}({T}_{A}-{T}_{B}),$$

where:

*Q*is the heat flow.*k*is the thermal conductivity of the material.*A*is the area normal to the heat flow direction.*D*is the distance between layers, that is, the thickness of material.*T*_{A}is the temperature of layer A.*T*_{B}is the temperature of layer B.

Heat conduction through a round pipe wall is

$${Q}_{cyl}=2\pi k\cdot \frac{L}{\mathrm{ln}\left(\frac{{d}_{out}}{{d}_{in}}\right)}({T}_{A}-{T}_{B}),$$

where:

*L*is the pipe length.*d*_{in}is the inner diameter.*d*_{out}is the outer diameter.

You can specify the thermal conductivity by using the **Conductivity
type** parameter:

`Constant`

— Thermal conductivity remains constant during simulation. You specify the thermal conductivity by using the**Thermal conductivity**parameter.`Variable input`

— You specify the thermal conductivity using the input physical signal at port**K**, which can vary during simulation. The**Minimum thermal conductivity**parameter specifies the lower bound for the physical signal.`Tabulated data`

— You specify the thermal conductivity by using a lookup table based on temperature. In this case, thermal conductivity can also vary during simulation.

The `Tabulated data`

option uses the average temperature of the
block to find the thermal conductivity. For planar wall geometry, the average temperature
is

$${T}_{avg}=\frac{{T}_{A}+{T}_{B}}{2}.$$

For cylindrical wall geometry, the average temperature is

$${T}_{avg}=({T}_{A}-{T}_{B})\cdot \left(\frac{{d}_{out}}{{d}_{out}-{d}_{in}}-\frac{1}{\mathrm{ln}\left(\frac{{d}_{out}}{{d}_{in}}\right)}\right)+{T}_{B},$$

which assumes that *T*_{B} is at the inside of the
cylinder.

**A** and **B** are thermal conserving ports associated
with the material layers. Because the block positive direction is from port
**A** to port **B**, the heat flow is positive if it flows
from **A** to **B**.

### Variables

To set the priority and initial target values for the block variables prior to simulation, use
the **Initial Targets** section in the block dialog box or Property
Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model.
Using system scaling based on nominal values increases the simulation robustness. Nominal
values can come from different sources, one of which is the **Nominal
Values** section in the block dialog box or Property Inspector. For more
information, see Modify Nominal Values for a Block Variable.

## Ports

### Input

### Conserving

## Parameters

## Model Examples

## Extended Capabilities

## Version History

**Introduced in R2007b**