**FEM Thermal Analysis**

FEA Thermal Analysis is at the heart of what we do here at our Singapore offices at BroadTech Engineering.

As a professional CFD company, when solving thermal engineering problems encountered during CFD consulting, our FEA simulation engineers can utilize use of a wide range of solving solutions such as

Over here at BroadTech Engineering, we focus our CFD consulting services on FEM thermal analysis techniques that are employed in conjunction with Structural FEA simulation analysis and CFD services (IL: CFD services).

**Similarity between Structural and Thermal Modeling**

The extension from a structural FEA simulation solution to a thermal FEA modeling solution is quite a natural progression as there are direct similarities between them

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**1. Conduction Considerations**

Thermal Conduction of heat happens when there is a temperature difference across the length of a component.

Factors that affect the amount of thermal heat energy transferred includes

**1. Amount of Temperature Differential**

Thermal heat energy will flow from the hotter region to the cooler region.

The larger the temperature differential the more thermal energy that is being transferred

**2. Component material Cross-Sectional Area**

The bigger the component cross-sectional dimension, the more the thermal energy that is being transferred

**3. Thermal conductivity of Component Material**

How well a material is able to conduct Thermal energy depends on its Thermal conductivity which is an inherent material property. In general, metal material (eg. Copper) is able to efficient at conducting more thermal heat energy than non-metal (eg. Ceramics)

**2. Forms of Convection Heat Transfer**

Convection heat transfer from a body surface happens by the movement of the adjacent fluid, such as gas or a Liquid medium, where the warmer fluid is usually transported away from the surface and replaced with a cooling fluid.

The actual heat transfer mechanism of the fluid motion is relatively complicated in nature where it involves a Localized conduction of thermal energy transfer which is made possible by a fluid boundary layer at the surface

Convection heat transfer relies on fluid motion, whereby the thin fluid layer adjacent to the body surface circulates away from the body surface and is immediately replaced by a fresh layer of cooler fluid.

This Convection heat transfer is dependent on function of a number of factors such as

**Basic Forms of Convective Heat Transfer**

There are Two basic forms of Convective Heat Transfer

**1. Free Convection**

In free convection scenario, the fluid is initially in a stationary condition.

Fluid circulation starts when there is an occurrence of local thermal heating.

*Notes that the orientation of the thermal heat transfer surface relative to the direction of the gravity force also makes a difference the convection heat transfer.

If a surface is vertically positioned, the effects of gravity can help in encouraging the fluid circulation. However, if the body surface is horizontal orientated, gravity does not help in the heat circulation.

**2. Forced Convection**

In a Forced convective heat transfer, the adjacent fluid is being entrained to move along by some external driving force.

Example of such a setup includes having a fan blowing across a body heat transfer surface.

This assist in providing a more energetic driven medium for the fluid to move away from the heated surface.

*Note that as the Computation of the actual convective heat transfer under forced conditions is generally more complex, a coupled Computational Fluid Dynamic (CFD) analysis can be used to give an accurate simulation model.

**3. Radiation Calculations**

The mechanism of Radiation heat transfer involves the emitting of electromagnetic waves or energy photons from the body surface of the heat source. This mechanism does not need a medium to pass through, thus allowing radiation to occur in a vacuum.

*Note that in theory, any surface which has a temperature above 0° is emitting thermal heat energy via radiation heat transfer.

At any given point in time, a typical surface is both emitting and absorbing thermal energy via radiation heat transfer with an adjacent body surface.

Factors influencing whether a specific body surface is experiencing a net cooling or heating effect includes

**View factor**

View factor is a parameter which is determined by the effective view a Panel A surface has on Panel B. This Effective view controls the travel path of the energy photons between two panels.

In practice, it can be very challenging to calculate for arbitrary surfaces, without some kind of actual ray tracing solution.

**Non-Linearity**

Heat transfer is dependent on a fourth order temperature term. This means that any heat transfer analysis including radiation effects becomes a nonlinear solution.

**Four Types of Analysis Solutions**

**1. Linear Solutions**

In a Linear analysis solution, the material thermal properties stay constant is not dependent on time or temperature.

Also for Linear solution scenarios, it is required that there is no radiation heat transfer and no presence of other nonlinear physical effects.

*As the default solution setting defined in most CFD simulation software solvers is usually nonlinear, it can sometimes be administratively confusing to define a linear solution during the initial setup of the simulation.

**2. Nonlinear Solutions**

In a nonlinear simulation modeling, where radiation is present, most simulation parameters involved can fluctuate with temperature variations.

Such physics parameters with nonlinearity properties can include

**1. Material Thermal properties**

This includes Thermal conductivity, Convective Heat transfer coefficient

**2. Thermal boundary conditions**

**3. Thermal Loading conditions**

This includes externally applied heat flux from a thermal heat source which is a function of temperature. It is important to note that a Nonlinear analysis solution requires an incremental loading approach whereby the Total thermal loading is broken down into successive steps.

**3. Steady-State Thermal Analysis**

The steady-state condition in a thermal event happens when the thermal temperature distribution and all thermal energy flows are stabilized and remain relatively constant over time.

The steady-state analysis can be easily derived by carrying out an energy balance calculation which assumes a stabilized condition.

Often times such Steady-state conditions are key for deriving the temperature distribution over component, which is then used as an input parameter to perform structural stress analysis.

**4. Transient Thermal Analysis**

In the Transient Thermal analysis the initial conditions are defined and then an incremental time stepping solving approach is implemented out base on the thermal loading and thermal boundary conditions.

The simulation calculation can be carried out through to a steady-state thermal condition, or to evaluate initial thermal shock loadings, for instance where the steady-state thermal analysis condition is not the primary concern.

One of the considerations in the transient thermal analysis, which is in many ways analogous to a transient dynamic analysis, is an accurate calculation of the time step required.

**Stability Criteria**

This time step requirement can be established by the Stability criteria, either automatically by the simulation software solver or manually controlled by the end-user.

**Adaptive Time Stepping**

The Adaptive time stepping feature included in many simulation solvers can optimize the time step by accounting with such as

Note that it is not advisable to have a Time steps with a granularity coarser than the stability limit.

**5. Thermal Strain Loading in a Stress Analysis**

In many cases, the main objective of FEM thermal analysis is to provide insights into the thermal temperature distribution for use as input in a subsequent stress analysis.

In a typical uncoupled thermal and structural simulation modeling, a steady-state temperature distribution is mapped from the thermal model to the structural model.

Mapping can either be direct mapping within the same physical mesh or interpolated between dissimilar mesh models. In either case, both mapping approach will result in thermal strains throughout the structure.

Thermal strain values vary proportionally to the change in temperature from initial conditions and are influenced by the value of the thermal expansion Coefficient.

**Free Expansion – Zero Stress**

If a physical component subjected to a uniform change in temperature is allowed to expand freely, it will result in a uniformly constant thermal strain throughout the component and result in Zero stress.

**Restrained Expansion – Thermal Stress**

when a component subjected to thermal expansion is secured at 2 points, the component is physically restrained from expanding naturally.

This mechanical strain results in Thermal strain and Thermal Stress which has a relatively more complicated thermal distribution & Mechanical boundary conditions.

Regardless of whether a Temperature dependency of a specific material is linear or nonlinear, the Material structural properties can still allow for a linear static simulation modeling and steady state thermal heat transfer.

A nonlinear static solution may need to be adopted if the thermal heat loading exceeds the Linear structural responses. In many cases, this involves occurrence of regions of material non-linear plasticity, or Physical geometric effects such as large displacement, buckling or mechanical contacts

Experienced judgment is needed here to determine whether a fully coupled solution should be adopted whereby both thermal nonlinearity and structural nonlinearity are constantly updated throughout the duration of the FEM Thermal simulation analysis.

**Accuracy & Applicability FEM Thermal Analysis Solution**

FEA simulation methodology has a certain level of inaccuracies as it fundamentally involves the discretization of a continuous response.

As the temperature distribution obtained from the thermal analysis is used as input for subsequent structural analysis

It is important to evaluate the sensitivity of that structural simulation analysis to inaccuracies in the thermal distribution.

**Structural Analysis**

The observable physical response in the Structural analysis is based on Displacement field.

Assessment of the accuracy of a Structural analysis is determined by analyzing the jump in stress values between adjacent elements and attempt to achieve a convergence.

**Thermal Analysis**

The observable thermal response in the Thermal analysis is based on temperature distribution, which is typically presented as a contour plot.

**Heat Flux**

The distributions of heat flux passing through each element are able to give us a better sense of the thermal analysis solution compared to the use of temperature distributions.

Heat flux convergence is better than a smooth temperature contour plot as an indicative guide to Accuracy and Convergence because it is similar to the stress convergence in a structural solution.

In mesh refinement analysis, the singularity is retained, but its effect is suppressed, and the overall accuracy of the heat flux distribution, is vastly improved.

**Types of Boundary condition for use in Simulation Analysis**

**1. Application of Physical Mechanical constraints**

**2. Application of equivalent pressure loading**

**Challenges of Analysis**

Although FEA Thermal analysis solutions are relatively straightforward to set up, there are some inherent challenges involves in such analysis, such as

**Types of Heat Transfer**

Fundamentally there 3 Modes of heat transfer methods that we have to consider

**1. Conduction Heat Transfer**

Heat transfer equations: Q = K A (Tupper – T lower)/L

where

Q = Heat

K = Thermal Conductivity

A = cross-sectional area

Tupper = Temperature at Hot region

Tlower = Temperature at Colder region

L = Path Length

**2. Convection Heat Transfer**

Heat transfer equations for Natural & Forced Convection from Surface: Q = h A (Tsurface – Tfree)

Q = Heat

h = Convection Coefficient

A = surface area

Tsurface = Temperature at surface

Tfree = Temperature in free stream

**3. Radiation Heat Transfer**

Heat transfer equations q = ε σ (T4 surface)

q = Heat Flux

ε = Emissivity

σ = Stefan-Boltzmann Constant

T4 surface = Temperature at Surface

The physics of each of these and implications for the FEA solution are discussed in turn.