Technical LibraryArticle: JMAG A to Z

Issue 9 Understanding Thermal from A to Z

Has everyone mastered JMAG? JMAG continues to evolve with each passing day. There may be functions in JMAG that even those who have already been using it will learn for the first time. There are also some useful procedures that are not well known yet. Why don't we aim at making operations more efficient by becoming familiar with new functions that we don't know about? In this series, I would like to introduce "Things that we should know" in JMAG, as well as some advantageous applications.

Overview
There are many people who have the impression that induction heating analysis, thermal demagnetization analysis, and thermal stress analysis are very difficult, aren't there? JMAG thermal analysis handles simple heat conduction phenomena. For this reason, material properties or conditions to be set are less compared with those for magnetic field analysis, so just understanding the meaning of that makes it possible to run an analysis easily. Coupled analyses between thermal and magnetic field, thermal and structural, and thermal and electric field are deceptively difficult, but they are nothing more than extensions of thermal analysis. Consequently, they are not terribly difficult if you can get a firm grasp of the mechanism of thermal analysis. In this issue of AtoZ, I will focus on material properties and various conditions that form the basis of thermal analysis and explain what they are so that you can feel thermal analysis and coupled analysis with heat more familiar.

Material Properties
In thermal analysis, material properties need to be specified are only three items, specific heat [J/kg/deg C], thermal conductivity [W/m/deg C], and density [Kg/m^3]. Specific Heat and Thermal Conductivity is set in the Thermal Properties tab of the Material Editor dialog box, and Density is set in the Mechanical Properties tab. (figures 1 and 2) All these material properties can be defined as the table value for Temperature Dependent and nonlinear properties can be taken into account. (fig.3) Temperature Dependency under Density is set to express a phase transformation such as density variations from metal's crystal structure changes in high temperature. In a coupled analysis between thermal and magnetic field, a model used in a magnetic field analysis is often used also in a thermal analysis as it is. Magnetic field analysis models, however, includes parts such as air regions that are not necessary in a heat conduction analysis, so they must be deleted. In such cases, just clearing the [Include This Material to Analysis] checkbox in the Material properties dialog box of the part makes it possible to delete the part. (fig.4) The part seems to be still exits in the model, but it is exempt from calculation, leading to the shorter calculation time.
Fig. 1 Thermal Properties tab of the Material Editor dialog box
Fig. 2 Mechanical Properties tab of the Material Editor dialog box
Fig. 3 Temperature dependency table of thermal conductivity.
Fig. 4 Material properties screen

Boundary Conditions
Thermal analyses are characterized by their many boundary conditions that can be set compared with other analyses. (fig.5) Below are descriptions of the meanings and their particular characteristics of boundary conditions unique to thermal analyses.
Fig. 5 Boundary conditions list of thermal analysis

Natural Boundary
Natural boundary is one of the boundary conditions that is equivalent to Neumann boundary in Finite Element Method (FEM) analysis and means "heat insulation" in thermal analysis. Heat does not conduct thorough the natural boundary face. In JMAG, natural boundary is virtually set if no boundary condition is set to the part surface. Natural boundary or periodic boundary need to be set to the crosssection when handling a partial model to reduce the analysis region.

Heat Transfer Boundary
Heat value that enters and leaves from the part surface can be controlled by setting heat transfer coefficient [W/m^2/deg C]. Specifying the heat transfer boundary makes it possible to simulate the leakage in the heat value beyond the boundary face etc. without precisely modeling the outer air or liquid beyond the boundary face. Reference temperature needs to be set in addition to the coefficient for heat transfer boundary conditions. "Reference temperature" here means the outer ambient temperature beyond the boundary face. The user can arbitrarily specify the value for the temperature and the temperature obtained from the thermal circuit mentioned below can be referred to.

Radiation Heat Transfer Boundary
This condition is set when handling heat radiation effects (heat radiation energy exchange between object surfaces). Heat radiation effects are obvious when the object has a high temperature, but it is not so remarkable under low temperature. For this reason, radiation heat transfer boundary condition is generally not set in analysis under low temperature. Setting the radiation heat transfer boundary leads to higher calculation costs such as computer memory size and calculation time according to the specified face area. Therefore, it is necessary to study the effects carefully and keep the face to be specified to the minimum. The following section explains two topics, the meaning of setting parameters and handling of the specified face in order to achieve deeper understanding of radiation heat transfer boundary.

Setting parameters for radiation heat transfer boundary
Heat value density (heat flux) that is radiated and imbibed from the face that the radiation heat transfer boundary condition is set is defined by formula (1).
I = εσF{(T+273.15)4(T0+273.15)4} .....(1)
In this formula, where I is heat flux [W/m^2], where ε is radiant parameter, where σ is StefanBoltzmann coefficient (constant), where F is configuration factor, where T is temperature [deg C] obtained from analysis, and where T0 is reference temperature [deg C], respectively. The parameters that the user can specify are radiant parameter and reference temperature. 0 to 1 is usually set for radiant parameter. In JMAG, setting the radiant parameter value for the temperature in the table makes it possible to add temperature dependency to the radiant parameter. Configuration factor is automatically calculated internally based on the positional relationship of the parts.

Handling the specified face of radiation heat transfer boundary
Heat radiation energy is exchanged via specified face of the radiation heat transfer boundary. Targets of the heat radiation energy exchange are every direction unless shielding material exists. If heat radiation energy is emitted from a radiation heat transfer boundary's specified face and another radiation heat transfer boundary's specified face is set in its translational direction, heat radiation energy is exchanged between these faces. In case a shielding material exists in the heat radiation energy's translational direction or case neither shielding materials exists nor any other radiation heat transfer boundary's specified face is set, heat radiation energy exchange does not occur but only radiation or imbibition arise. For the case just the heat is radiated from the heat source surface, it is recommended to apply heat transfer boundary conditions after converting the heat radiation to temperature dependency heat transfer coefficient in order to reduce the calculation costs. In the direction that heat radiation energy exchange arises, T0 corresponds to the temperature on the opposite specified face. On the other hand, T0 corresponds to the temperature that is previously set by the user in the direction heat radiation energy exchange does not arise. In the real phenomena, heat sometimes reaches to the back of the shielding material from multiple reflections, but multiple reflections are not taken into account in JMAG.

Conditions
Heat generation and initial temperature are the conditions that are unique to thermal analysis. The meanings of these conditions are as their name and the setting itself is not difficult, but are extremely important conditions when carrying out a coupled analysis with any analysis other than thermal analysis. The following section explains the meanings of these conditions involving coupled analysis.

Heat generation
Heat source is defined in this condition. You can set the value in total amount [W] or density [W/m^3]. For steady state analysis, it is specified by constant value, and for transient state analysis, different heat sources per analysis time can be set in the table. Loss that is obtained from magnetic field analysis or electric field analysis can also be set for heat source. Loss distribution is automatically imported as heat source distribution just by specifying the results file from magnetic field analysis or electric field analysis. Heat source can be handled in both distributions amount and total amount in the part. When distribution amount is set for heat source type, the loss distribution obtained from magnetic field analysis or electric field analysis is directly reflected as the heat source distribution of thermal analysis. Heat source distribution is compensated even when meshes are different between magnetic field analysis and thermal analysis. On the other hand, when total amount is set for heat source type, heat value is applied to the entire part as total amount, so heat source distribution in the part is uniform. When any FEM coil condition or current condition that coil is treated as a block in magnetic field analysis is set, the current distribution can become biased, sometimes leading to a biased joule loss distribution as well. In reality, however, loss arises in every single wire, so the heat source distribution is uniform. In such case, setting total amount for heat source type makes it possible to run an analysis that is realistic.

Initial temperature
The temperature just at the 0 second in analysis time is specified for this condition. This parameter must be set for transient state analysis. Different temperatures in part, face or vertex can be set for initial temperature. Also, if you have a table file called "temp file" that includes node ID and temperature information and is formatted in the type unique to JMAG, it can be imported as initial temperature. A "temp file" can also be created using MultiPurpose File Export tool that has been improved in JMAGDesigner Ver.12.1. A "temp file" based on the mesh information of the thermal analysis input data can be exported using MultiPurpose File Export tool if you have a csv file that includes the coordinate and temperature information and an input data for thermal analysis in JMAG thermal analysis (saved as jcf file).

Heat equivalent circuit
Handling the parts and local thermal phenomenon as lumped constants and analyzing the overall thermal phenomenon in one dimension using an equivalent circuit is often conducted as a simple and highspeed analysis method even today. (fig.6)
Fig. 6 Heat equivalent circuit
Heat equivalent circuits can be handled also in JMAG, and it is possible to calculate by coupling a detailed thermal analysis using the Finite Element Method (FEM) and a simple analysis using a heat equivalent circuit. Typical heat equivalent circuit component is explained below.

Thermal resistor component
This is a component that simulates the state of being difficult to transfer of heat between terminals. (fig.7). This component corresponds to a resistance in an electric circuit and is one of the frequently used one in heat equivalent circuits. Heat value Q that transfers between terminals is defined by the formula (2).
Q=1/R*(T2T1).....(2)
In this formula, where Q is heat value [W], where R is thermal resistance [deg C/W], and where T1 and T2 are terminal temperature [deg C], respectively. Thermal resistor can be defined not only as constant value but as table value for temperature dependency.
Fig. 7 Thermal resistor component

Heat transfer boundary component, equivalent temperature boundary component
These are connection components that connect a heat equivalent circuit and a finite element model. (fig.8) The temperature can be referred to between the heat equivalent circuit and finite element model to each other via these connection components. No special setting parameters are set and just selecting the item from the pulldown menu to set which heat transfer boundary condition and which equivalent temperature boundary condition refer to the terminal temperature of the boundary component. For example, these components are used when connecting the two finite element models that are located apart from each other. (fig.9) For example, air or liquid that are usually needs to be modeled exist between these separated finite element models, so it is assumed that a thermal analysis considering the flow as liquid is required. Such complicated calculation, however, takes an extremely long time and is not easy. In such case, if heat value transfer between these two models is known experientially, simulating the heat value transfer using a heat equivalent circuit and analyzing approximately is more efficient.
Fig. 8 Heat transfer boundary component and equivalent temperature boundary component
Fig. 9 Connecting the finite element models using a heat equivalent circuit

Output
This section explains the postprocess conditions to use the results from thermal analysis not as distribution amount but as average value or total value. Of course, JMAGDesigner's post feature is equipped with the function to calculate the average value or total value of distribution amount, but previously setting this kind of postprocess conditions makes it possible to streamline the postprocess. When referring to the results from the thermal analysis in a coupled analysis, a certain representative value instead of distribution amount would be sometimes suitable and this postprocess condition is vital in such case.

Average temperature
This is a condition for calculating the average temperature in the specified region. This condition is set to specify the reference temperature for the FEM coil or resistance component that temperature dependency resistance is set when coupling with a magnetic field analysis.

Heat flow amount
This is a condition for calculating the heat value that pass through the specified face. Using the JMAGDesigner's post feature makes it possible to obtain the same results by calculating surface integral for the results of the heat flux in the specified face.

In Closing
In this issue, I have introduced the meaning of the features and how to use it concerning the especially significant conditions that are frequently set in thermal analysis. I have more and more conditions that I would like to introduce, so please let me introduce them in the next issue. Be sure not to miss it.
(Masahiko Miwa)

Contents
Issue 11 Electric Field Analysis from A to Z
Issue 10 Structural Analysis from A to Z
Issue 9 Understanding Thermal from A to Z
Issue 8 Understanding Conditions from A to Z
Issue 7 Understanding Conditions from A to Z
Issue 6 Understanding Geometry Modeling from A to Z
Issue 6 Understanding Geometry Modeling from A to Z
Issue 4 Understanding Meshes from A to Z
Issue 3 Shortening Calculation Time from A to Z
Issue 2 Evaluating Results and Viewing Models from A to Z
Issue 1 Running Multiple Case Calculations from A to Z

