Thermal Mass

Mass in thermal systems

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Libraries:
Simscape / Foundation Library / Thermal / Thermal Elements

Description

The Thermal Mass block represents a thermal mass that reflects the ability of a material, or a combination of materials, to store internal energy. The mass of the material and its specific heat characterize this property. The thermal mass is described by

$$Q=c\cdot m\frac{dT}{dt},$$

where:

• Q is the heat flow.

• c is the specific heat of the mass material.

• m is the mass.

• T is the temperature.

• t is time.

The Mass type parameter lets you specify whether the thermal mass stays constant or varies during simulation:

• Constant — The thermal mass is constant during simulation.

• Variable — The thermal mass can vary during simulation. If you select this option, the Mass parameter in the block dialog is replaced by the Minimum mass parameter and a high-priority Mass variable, and the block has two physical signal input ports: Mdot, which specifies the change in the thermal mass, and Tin, which specifies the temperature of incoming mass. The signal value at port Tin has no effect when the thermal mass is constant or decreasing.

Use the Variable option to model systems where the mass changes but the geometric effects remain negligible, such as a washing machine being filled, heated, and then emptied with a varying amount of liquid per cycle.

By default, the block has one thermal conserving port. Because the block positive direction is from the port towards the block, the heat flow is positive if it flows into the block.

In some applications, it is customary to display mass in series with other elements in the block diagram layout. To support this use case, the Number of graphical ports parameter lets you display a second port on the opposite side of the block icon. The two-port variant is purely graphical: the two ports have the same temperature, so the block functions the same whether it has one or two ports. The block icon changes depending on the value of the Mass type and Number of graphical ports parameters.

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.

If you set the Mass type parameter to Variable, use the high-priority Mass variable to specify the initial thermal mass value.

Examples

House Heating System

Model a simple house heating system. The model contains a heater, thermostat, and a house structure with four parts: inside air, house walls, windows, and roof.

• Open Model

Motor Thermal Circuit

How the thermal behavior of a brushless servomotor can be simulated using a lumped parameter model. Heat generated due to power losses in the stator iron stack, stator winding and rotor is represented by three heat flow sources: stator iron losses (Q_Iron), winding power losses (Q_Wind), and magnetizing and eddy current rotor losses (Q_Rotor). The losses were recorded during a motor typical cycle simulation and stored in the motor_losses.mat file. The motor thermal circuit is built of thermal conductances, thermal masses, and convective heat transfer blocks, which reproduce heat paths in the motor parts: winding, stator iron, motor case, rotor, front and rear bearing plates, and motor mounting flange. The motor exchanges heat with the atmosphere through the case-atmosphere, flange-atmosphere, and rear plate-atmosphere contacts. The ambient conditions are simulated with the ideal temperature source set to 300 K.

• Open Model

Ports

Input

Mdot — Mass control signal, kg/s

physical signal

Input physical signal that specifies the change in thermal mass. Use the high-priority Mass variable to specify the initial thermal mass value.

Dependencies

To enable this port, set the Mass type parameter to Variable.

Tin — Temperature of incoming mass, K

physical signal

Input physical signal that specifies the temperature of incoming mass. The signal value at port Tin has no effect when the signal at port Mdot is less than or equal to 0.

Dependencies

To enable this port, set the Mass type parameter to Variable.

Conserving

M — Port that connects mass to circuit

thermal

Thermal conserving port that connects the mass to the physical network.

The port name is not visible in the block icon, but you can see this name in the underlying source file by clicking the Source code link in the Description tab of the block dialog box.

N — Second graphical port

thermal

Second thermal conserving port that lets you connect the mass in series with other elements in the block diagram. This port has the same temperature as port M, therefore the difference between the one-port and two-port block representations is purely graphical.

The port name is not visible in the block icon, but you can see this name in the underlying source file by clicking the Source code link in the Description tab of the block dialog box.

Dependencies

To enable this port, set the Number of graphical ports parameter to 2.

Parameters

Mass type — Specify whether thermal mass can change during simulation

Constant (default) | Variable

Select whether the thermal mass can change during simulation:

• Constant — The thermal mass is constant during simulation.

• Variable — The thermal mass can vary during simulation. Use this option to model systems where the mass changes but the geometric effects remain negligible, such as a washing machine being filled, heated, and then emptied with a varying amount of liquid per cycle.

Mass — Constant mass

1 kg (default) | positive scalar

Mass value. The mass is constant during simulation.

Dependencies

To enable this parameter, set the Mass type parameter to Constant.

Specific heat — Specific heat of the material

447 J/(K*kg) (default) | positive scalar

Specific heat of the material.

Minimum mass — Minimum acceptable mass

1e-6 kg (default) | positive scalar

The minimum thermal mass value. The block issues an error if the thermal mass falls below this value during simulation.

Dependencies

To enable this parameter, set the Mass type parameter to Variable.

Number of graphical ports — Number of visible ports

1 (default) | 2

How to connect the block to the rest of the circuit:

• 1 — The block has one conserving port that connects it to the thermal circuit. When the block has one port, attach it to a connection line between two other blocks.

• 2 — Selecting this option exposes the second port, which lets you connect the block in series with other blocks in the circuit. Because the two ports have the same temperature, the block functions the same as if it had one port.

Extended Capabilities

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

Version History

Introduced in R2007b

R2023a: Use variable thermal mass

The block includes the Mass type parameter, which lets you specify whether the thermal mass stay constant or varies during simulation. In previous releases, the thermal mass could only be constant.