# Thermocouple

Model sensor that converts thermal potential difference into electrical potential difference

Sensors

## Description

The Thermocouple block represents a thermocouple using the standard polynomial parameterization defined in the NIST ITS-90 Thermocouple Database [1].

For thermocouples Type B, E, J, K (t<=0 degC), N, R, S or T, the voltage E across the device in mV is

`$E\left(mV\right)={c}_{0}+{c}_{1}t+...+{c}_{n}{t}^{n}$`

where:

• ci is the ith element of the Coefficients [c0 c1 ... cn] parameter value.

• t is the temperature difference in degrees Celsius between the temperature at the thermal port A and the Reference temperature parameter value.

### Note

The equation for voltage across the device as a function of temperature difference is defined in mV. The units of the voltage across the actual device is V.

For thermocouples Type K (t>=0 degC), the equation contains an additional exponential term:

`$E\left(mV\right)={c}_{0}+{c}_{1}t+...+{c}_{n}{t}^{n}+{a}_{0}{e}^{{a}_{1}{\left(t-{a}_{2}\right)}^{2}}$`

where a0, a1, and a2 are additional coefficients, required only by the Type K thermocouple, defined by the Coefficients [a0 a1 a2] parameter value.

The following equation describes the thermal behavior of the block:

`$Q={K}_{d}{t}_{c}\frac{dT}{dt}$`

where:

• T is the temperature at port A.

• Q is the net heat flow into port A.

• Kd is the Dissipation factor parameter value.

• tc is the Thermal time constant parameter value.

• dT/dt is the rate of change of the temperature.

To model the thermocouple in free space:

1. Connect the thermocouple to the B port of a Simscape™ Convective Heat Transfer block.

2. Connect the A port of the Convective Heat Transfer block to a Simscape Ideal Temperature Source block whose temperature is set to the ambient temperature.

3. Set the Area parameter of the Convective Heat Transfer block to an approximate area Anom.

4. Set the Heat transfer coefficient parameter of the Convective Heat Transfer block to Kd/Anom.

## Basic Assumptions and Limitations

The model is based on the following assumptions:

• The high-order polynomials this block uses are very sensitive to the number of significant figures used for computation. Use all available significant figures when specifying the Coefficients [c0 c1 ... cn] parameter.

• Coefficients [c0 c1 ... cn] are defined for use over a specified temperature range.

• The maximum supported value for `n` in the Coefficients [c0 c1 ... cn] parameter is 14, that is, the vector cannot have more than 15 elements.

## Parameters

### Electrical Tab

Thermocouple model

Select one of the modeling options:

• ```Type B, E, J, K (t<=0 degC), N, R, S or T``` — This option is equivalent to the block functionality in previous releases.

• `Type K (t>=0 degC)` — This option adds an exponential term to the block equations when the temperature difference is greater than 0 degrees Celsius.

Coefficients [c0 c1 ... cn]

The vector of coefficients c in the equation that describes voltage as a function of temperature. The maximum length of the vector is 15 elements. The default value is `[ 0 0 0 0 0 0 0 0 0 ]`.

### Note

You can download parameters for standard thermocouple types from the NIST database [1]. For information on how to do this, see the Simulink® Approximating Nonlinear Relationships: Type S Thermocouple example.

Coefficients [a0 a1 a2]

The vector of additional coefficients a0, a1, and a2, required only by the Type K thermocouple. This parameter is only visible when you select `Type K (t>=0 degC)` for the Thermocouple model parameter. The default value is `[ 0 0 0 ]`.

### Thermal Tab

Reference temperature

The temperature the block subtracts from the temperature at the thermal port in calculating the voltage across the device. The default value is `0` °C.

Thermal time constant

The time it takes the thermocouple temperature to reach 63% of the final temperature change when a step change in ambient temperature occurs. The default value is `1` s.

Dissipation factor

The thermal power required to raise the thermocouple temperature by one K. The default value is `0.001` W/K.

Initial temperature

The temperature of the thermocouple at the start of the simulation. The default value is `25` °C.

## Ports

The block has the following ports:

`A`

Thermocouple thermal port

`+`

Positive electrical port

`-`

Negative electrical port

## References

[1] NIST ITS-90 Thermocouple Database http://srdata.nist.gov/its90/main