Heat transfer is a huge factor to consider in so many industries, including propulsion, electronics, manufacturing, and HVAC. There are three modes by which this can happen – conduction, convection, and radiation. In this blog, we will go through the basics of these modes and how we can implement them in Abaqus CAE.

## Conduction

Conduction is the process of heat transfer due to direct contact within a medium. We normally think of conduction as happening within solids, but it can happen through liquids and gases as well; however, the density of solids generally makes them the best heat conductors. One example is a cast iron pan – if you leave it on the stove for a long time, the handle will eventually get hot, even though the handle is not directly touching any heat. This is due to conduction within the pan!

The governing equation for conduction is:

Where Q is the rate of heat transfer, k is the thermal conductivity, A is the surface area, L is the thickness, T₂ is the source temperature, and T₁ is the sink temperature. Thermal conductivity is a material property – higher values mean the material is more conductive, while lower values mean the material is more insulative. This is required for any thermal finite element analysis. Some thermal conductivities are shown in the table below:

When conduction occurs between two surfaces in contact, there is usually some heat lost, depending on many factors such as surface finish, material, and contact pressure. This is known as contact conductance, or gap conductance. The conductive heat transfer between surfaces in contact can be defined as a function of the temperature differential, contact area between the surfaces, and the interface conductance value, hc. Another common term for this phenomenon is called contact resistance, which is just 1/(hcA).

One way to think about this is to think about searing a steak. If you add the steak to the pan without any oil, you won’t get as good of a sear due to the steak having uneven physical contact with the pan. Adding oil fills these microscopic gaps and increases the contact with the pan, resulting in a better sear.

## Modeling Conduction in Abaqus CAE

Conduction within parts is automatically part of any thermal analysis since thermal conductivity is a required material parameter for both steady-state and transient thermal analyses.

By default, Abaqus assigns a very high hc when surfaces are in contact or tied (to approximate a condition of matched temperature across the interface) and hc=0 when the surfaces are not in contact. This can be overridden manually as a contact property in CAE or through the *GAP CONDUCTANCE keyword.

For contact conductance between bodies, a thermal conductance property can be used. The contact conductance can be set to be a function of clearance and/or contact pressure. The user subroutine GAPCON can also be used for the greatest flexibility in defining hc.

## Convection

Convection is the process of heat transfer due to the movement of fluids. Some examples of this include air conditioning, convection currents in the Earth’s mantle, and boiling pots of water.

The governing equation for convection is:

Where Q is the rate of heat transfer, h is the convective heat transfer coefficient, A is the surface area, T₂ is the source temperature, and T₁ is the sink temperature. The heat transfer coefficient depends on many factors, including the fluid properties, surface roughness, flow type, and flow speed, just to name a few.

## Modeling Convection in Abaqus CAE

Since convection involves fluids, CFD is typically used where the temperature or movement of the fluid is important (not covered in this blog). If it’s not important to model the fluid itself, we can approximate the effect of convection on a solid body via a film condition. In a heat transfer step, a surface film condition can be added either in the interaction module in Abaqus CAE or through the keyword *SFILM. The film coefficient is equivalent to the heat transfer constant h. A sink temperature will also need to be declared.

## Radiation

Radiation is the process of heat transfer without involving a medium, instead occurring through electromagnetic waves. This can happen even in empty space – this is how we get solar energy! Every object can emit and absorb radiation; however, its effect is most prominent when the temperature differences are very large.

The governing equation for radiation is:

Where Q is the rate of heat transfer, ε is the emissivity of the object, σ is the Stefan-Boltzmann constant (5.67 x 10⁻⁸ Wm⁻²K⁻⁴), A is the surface area, T₂ is the source temperature, and T₁ is the sink temperature. Emissivity ranges from 0 to 1; perfect radiators have an emissivity of 1, while perfect reflectors have an emissivity of 0. Real life objects will fall somewhere in between, depending on factors such as surface color, surface quality, and material composition.

## Modeling Radiation in Abaqus CAE

For radiation between bodies, a radiation contact property can be used. This can be done through Abaqus CAE or through the keyword *GAP RADIATION. The required variables are the emissivity of both surfaces and the view factor as a function of clearance between the surfaces. The view factor is a fraction of how much of the total radiation emitted by the main surface is absorbed by the secondary surface.

For radiation to a body outside of the model, we can use surface radiation. The process to do this is similar to the surface film condition. The required variables are the emissivity and the ambient temperature. This can be done through Abaqus CAE or through the keyword *SRADIATE.

Finally, for radiation within enclosures, we can use cavity radiation. First, a cavity radiation property needs to be made. This will be used when defining the interaction.

The cavity can either be defined as closed (no exposure to ambient temperature) or open. This functionality can be very computationally expensive, so it’s best used in conjunction with symmetry and parallel decomposition when possible.

## Final Thoughts

The three primary forms of heat transfer are summarized here:

Conduction – Heat transferred due to direct contact within a medium

Convection – Heat transferred due to movement of fluids

Radiation – Heat transferred without a medium

All three modes of heat transfer can be accounted for in FEA. Of course, heat transfer is a lot more complicated than what I’ve been able to cover in this blog. If you’re looking for some help with your heat transfer analyses, **reach out to us today**!