Thermal Analysis

The thermal analysis module serves for solving heat transfer and thermal conduction problems. A typical goal of performing thermal analysis is finding temperature fields and heat (thermal) flux within a product's volume. AutoFEM supports two ways of formulating a thermal analysis problem:

• | Steady state – calculating temperature fields and heat flux distribution under the assumption of an infinitely long time passing after applying thermal loads. A body's temperature does not change with time in the steady state, so that an elementary body volume loses as much energy to the environment per the time unit as it gains from outside or from internal heat sources. |

• | Transient process – temperature fields calculation occurs as a function of time. The temperature field distribution pattern changes with time in the analyzed physical system, so that the study results in obtaining temperature fields at each time instant of a certain time period set forth by the user. |

Examples of a steady-state and transient thermo-dynamical processes

Details of Thermal Analysis Steps

Thermal analysis is performed in several stages. The sequence of the user's steps for putting together a study and running a thermal study of a structure is in many parts similar to algorithms of working with other study modules of AutoFEM. Therefore, we will point out in this chapter only certain details specific to thermal studies.

1. Creating Study. When creating a study, specify its type – «Termal Analysis». As in other study types, building a finite element mesh is required, for approximating the structure's geometry.

2. Applying boundary conditions. In the thermal analysis, the boundary conditions are represented by the boundary and initial temperatures, heat power sources, heat flux, and conditions of heat exchange between the model and environment – convection and radiation applied to the model.

The initial temperature is used for defining thermal loads at the initial (zero) moment of time for the transient thermal analysis only. All thermal loads defined without the «initial» flag are considered constant (invariable) in both the steady state and transient thermal analysis.

3. Solving. Before running calculations, the user can specify the type of a thermal analysis study being solved (the [Parameters] tab, steady-state or transient heat transfer), and, if necessary, adjust algorithms for solving systems of equations on the [Solve] tab.

4. Analysis of thermal solution results. The results of a thermal analysis are:

Temperature fields – temperature distribution over the model's volume.

Thermal gradients by the X, Y, Z axes, and the magnitude of the thermal gradient – reflect on the degree of temperature changes by the respective axes of the coordinate system.

Resulting thermal flux by the X, Y, Z axes, and the magnitude of the resulting thermal flux –show the rate of thermal energy transfer, determined from the solution to the thermal analysis study.

Magnitudes of the thermal (temperature) gradient and the resulting heat flux are determined as the square root of the sum of the squares of the respective coordinate-projected components.

Besides the mentioned results, the following reference data can be displayed in the postprocessor window:

• | Prescribed thermal flux corresponds to the specified initial parameters of thermal loads. |

• | Prescribed temperature – constant thermal loads applied to the model. |

• | Initial temperature – the initial temperature field applied to the model (for the transient thermal analysis). |

The methods for analyzing results of thermal analysis accepted in the AutoFEM Postprocessor, are in general similar to the methods of examining results in other analysis modules. Let us mention some specific Postprocessor tools, which can be used for analyzing results of transient heat transfer.

Solving a transient heat transfer study results in a large set of data, whose total number is equal to the number of time steps specified by the user. AutoFEM provides the user with a convenient visual interface for managing the entire array of data resulting from calculations. For this purpose, a «Time process» dialog panel can be called from the results viewing window's context menu, that can be used by the user to quickly switch to the desired result on the time scale.

Use of the «Time process» window for managing access to the results of a transient thermal study

Thermal Analysis Processor Settings

On the [General] tab, you can define or edit the descriptive attributes of the current study, as the name or a comment.

The [Solve] tab contains settings for solving systems of algebraic equations, with their meanings similar to the settings of the «Static analysis» study (see the respective section). Note that the «Calculate using linear element» mode can be used in most cases of thermal analysis, facilitating much faster calculations. Unlike studies in Statics, Frequency analysis and Buckling, results of temperature distribution over the model's volume achieved under the linear interpolation assumption are not much different from the respective results obtained from using a quadratic interpolation.

Before starting calculations, on the tab [Parameters] the user can indicate the type of solved thermal analysis problem: stationary (steady state mode) or non-stationary thermal conduction (transient process).

For non-stationary thermal conduction, it is necessary to specify a process duration («Total process time»), time step and initial temperature.

In the thermal analysis, controls «Initial temperature|Use preset temperature» allow the user to define as an initial temperature:

• |
initial temperature prescribed with the help of the command "AutoFEM | Loads/Restraints | Initial Temperature..."; |

• |
the default value of temperature at those finite element nodes where the initial temperature was not defined by the user. |

«Parameters» tab of the thermal analysis study parameters window

The «Use heat-task results» control allows defining the initial temperature by the results of an earlier conducted thermal analysis. This dialog item becomes accessible to the user, if there are earlier conducted thermal studies present in the model. In the drop-down list select the name of a solved thermal analysis study and, if necessary, the time instant, to which the solution pertains. Please note that certain conditions are to be met for using thermal analysis results as the initial temperature conditions:

1. Identity condition of finite element meshes in both thermal analyses. The simplest way of achieving such identity is the use of the "Copy" command available in the context menu. The sequence of steps can be, for example, as follows:

a) create a study of the "Thermal Analysis" type, generate a mesh, define boundary conditions, and run. We assume that the solved temperatures will be used for defining initial temperatures in another study of the transient thermal analysis;

b) create a study's copy using the «Copy» command;

c) define boundary conditions of a transient study in thermal analysis. On the «Parameters» tab of the study's properties, select the name of the first study and, if that's a transient analysis, the desired time step.

As a result, we have two studies of different types, but with identical finite element meshes.

2. The "Calculate using linear element" property on the "Solve" tab of the study parameters dialog should use the same settings in both studies. For example, if the first thermal analysis is done by linear elements, then the second thermal analysis based on the former thermal analysis results can also be run only by linear elements.

Note also that solving a transient heat transfer study requires more CPU time as compared to the steady state heat transfer, since in the former case the systems of algebraic equations are solved at each time step defined by the user.

The [Results] tab allows defining the result types displayable in the studies tree after finishing calculations.

«Results» tab (left) and dialog for setting results displayable by default in the studies tree (right)

Examples of Thermal Analysis Studies

Thermal Analysis of a Cooling Radiator. Steady State

Required is an evaluation of a passive cooling radiator efficiency for the semiconductor electronic device with the maximum dissipating power of 15 Watt. The permissible temperature of the microchip's body is 75°C in the operating range of ambient temperatures from 25°C to 55°C. An aluminum alloy radiator is used for cooling the device and is mounted at the top of the microchip's body. To improve heat dissipation, the body of the microchip is also made of aluminum.

Step 1. Creating «Study», meshing, and assigning material. Create a study of the «Termal Analysis» type using the command «Analysis|New Study» based on two bodies – the microchip and the radiator. Generate a finite element mesh. You also need to define parameters of the part's material. By default, calculations use material properties «From Operation», that is, the material properties are automatically obtained from the product part's solid model. This is especially convenient when a study includes bodies from different materials representing parts of assembly models. In our case, the «Aluminum» material was defined at creation of the 3D model of the radiator and the microchip, with its physical and chemical properties contained in the AutoCAD database.

Three-dimensional model of the microchip with a passive cooling radiator |
Resulting finite element mesh |

Step 2. Applying boundary conditions. Let us specify thermal loads for the model. We will apply the «Heat power» load of 15 Watt to the volume of the microchip, and define the «Convection» boundary condition on the external heat-sinking radiator surfaces with the convection parameter of 15 Watt/(m2 . °C) and ambient temperature of (25°C). We can disregard in this study the heat exchange factor of mutual and ambient radiation, since their radiation contribution is vanishingly small at the expected temperatures (tens of degrees Celsius). Upon completing the commands of building the finite element mesh and defining thermal loads, we get a calculations-ready finite element model.

Defining "Heat Power" load

Defining "Convection" load

Step 3. Running calculations and analyzing results. We will start the thermal analysis by running the command «Analysis|Solve». In the appearing dialog of the study's properties, set the «Steady state» option on the [Parameters] tab. Use the «Calculate using linear element» mode on the [Solve] tab to speed up the calculations.

The list of calculation results is displayed in the «Studies» window, and can be accessed by the context menu in the calculation results window. The maximum temperature according to the heat and analysis results is 39,1°C at the convection temperature equal to 25°C. We will then edit the convection temperature using the «Edit» command of the studies tree context menu, setting the operational ambient temperature to its upper limit (55°C), and then rerun calculations. We will obtain the maximum temperature of the microchip equal to 69.1°C. The conclusion is the radiator does fulfill the required temperature condition for the device in the entire specified range of the device's operational temperatures. The study is complete.

Temperature fields in the radiator under the convection temperature of 25°C

Calculating the Time of Heating up the Cooling Radiator. Transient Mode

Let us estimate the time required for the device to reach a steady thermal state. To do this, let's run a transient thermal analysis of the «microchip+radiator» system.

Step 1. Creating study's copy. We will create a copy of the original study in a steady-state thermal analysis using the «Copy» command of the studies tree context menu. On the [General] tab of the study's properties, change the study name to «Heating».

Step 2. Defining parameters of transient analysis. On the [Parameters] tab of the thermal analysis properties, set the «Transient» mode. Define the time analysis parameters – the modeling time of 30 minutes and the modeling step of 0.5 minutes. We will use the uniform ambient temperature (25°C) as the initial model temperature.

Defining calculation parameters of transient heat analysis – time and initial temperature

Step 3. Running calculations and analyzing results. After the completion of calculations, you can examine results at each time step. To view such results, we use a floating «Time process» bar that allows the user to quickly switch to the time instant of interest using a slider. With the help of these tools we determine that a nearly complete heating of the radiator will occur after approximately 26 minutes.

Result of thermal analysis at time 1590 sec (26 min.)

Calculating Time of Cooling down the Cooling Radiator. Transient Mode

Now, let's evaluate the time required for the device-cooling radiator to cool down after an extended work.

Step 1. Creating study's copy. Adjusting boundary conditions. Let's create a copy of the original study of the steady-state thermal analysis. Adjust the boundary conditions of this study: the «Heat power» load will be deleted.

Step 2. Defining parameters of transient analysis. Set the «Transient» mode on the tab of the thermal analysis properties. Define time analysis parameters – the modeling time of 30 minutes, the modeling step of 0.5 minutes. Let's use the result from the previous steady-state radiator evaluation as the initial model temperature.

Setting up study parameters for calculating cooling process

(transient heat transfer)

Step 3. Analyzing calculation results. Let's run calculations and analyze the results. Using the «Time process» bar, we can determine that nearly complete cooling of the radiator will occur in approximately 26 minutes after turning the device off.

Device cooling calculation.

Temperatures distribution at 1590 seconds of the calculation time