How To Use Shell Meshing For Thermal Studies

I could make this blog post real short: For convection, double “h”; for radiation, double “f” (or avoid the surface-to-ambient option); and for conduction layers, use Solid meshing.

Instead, how about a little explanation?

SolidWorks Simulation gives you the ability to assign thermal loads and boundary conditions to your models and predict resultant temperatures. As any good engineer knows, there are 3 modes of heat transfer: conduction, convection, and radiation. As any good Simulation user knows, there are two ways to mesh a thin part: Solid, and Shell. Is it possible to use Shell mesh with all modes of heat transfer? How do the thermal boundary conditions work?

The challenge is when you select a face in SolidWorks, it only computes its area once. Yet in some situations you might need to double the effective area. How?

Let’s look at the modes of heat transfer one at a time:

Conduction

The Shell mesh has an imagined thickness. So conduction is solved along the plane of the Shell based on its imagined cross-section. No problem. However, if you have a sandwich of a thin material with conduction through its thickness, you’ll need to model it with a Solid mesh (or use a Thermal Resistance Contact Set).

SolidWorks Simulation does not compute the temperature difference from one side of the thickness to the other for a Shell mesh. Nor does it consider conduction between two Shell meshes whose nodes do not touch. This is NOT true of how Shell meshes are treated in a Static analysis (where the imagined thickness IS considered for computing contact).

Convection

Heat transfer out of (or into) the faces of the model due to motion of a fluid is represented by Convection boundary conditions (“Thermal Loads”). It’s the engineer’s responsibility to input an assumed “h” value for the convection coefficient (Flow Simulation can calculate “h” for you if you’re stumped).

Here’s the formula which governs convection, in case you’ve forgotten it:

Q = hA(T₂-T₁)

And here’s the tricky bit: When you apply Convection in SolidWorks to a Shell, it only counts that area once. Which is fine if you have a Shell on the outside of an enclosure, cooling into the room for example. But, if you have a Shell mesh representing, say, a cooling fin that has convection on BOTH SIDES, then you’re not getting any credit for the OTHER side of the selected face! And multiple Thermal Loads on the same face do not add.

Simple. In order to fake having twice the selected face area (A), just double your convection coefficient (h)! Or, more generally:

Q₁ + Q₂ = h₁A(T₂-T₁) + h₂A(T₂-T₁) = (h₁+h₂)A(T₂-T₁) = (2h₁)A(T₂-T₁)

If you don’t believe me, make up your own test case to prove me right.

Radiation

Now it gets harder, for two reasons. First of all, radiation goes by the difference of the fourth powers, like this:

Q = σεfA (T₂⁴-T₁⁴)

Forget about s right now. It’s just a constant named after a famous scientist. The values we can play with are the emissivity (ε) and view factor (f). We can try to use a similar trick as for convection, for a similar reason: we need to double the right-hand side of the equation to make up for the area only being counted once instead of twice. If you’re using a view factor or emissivity less than 0.5, you’re OK. But if these values are higher, you’re not allowed to double them because SolidWorks will force you to keep these inputs between 0.0 and 1.0 (where they’re supposed to be).

So we’ll need another trick. We can’t simply double T₂ to try to get twice the delta temp, because of the fourth power relationship. But there’s hope.

SolidWorks has two options for applying a Radiation boundary condition: surface-to-ambient, or surface-to-surface. With surface-to-ambient, you need to input your own view factor. So if your ε*f is above 0.5, you’re out of luck. But if you choose surface-to-surface, SolidWorks calculates the view factors internally for you, and IT DOES IT CORRECTLY.

That’s right. For the surface-to-surface option, BOTH sides of the shell mesh will be evaluated to determine where that radiant energy is going to shine. No tricks needed!

And here’s the coup-de-grace. Within the surface-to-surface option, there is an option to assume an “open system”. If you check that box, SolidWorks will assume any leftover view factor is radiated to ambient. And yes! If you select a single face as surface-to-surface in an open system, it acts just like a surface-to-ambient with view factor of 1. If you need a different view factor, just scale down your emissivity!

Summary

To simulate a thermal boundary condition on BOTH sides of a Shell mesh: For convection, double “h”; for radiation, double “f” or “ε“ or “ε*f“ (or use the surface-to-surface option); and for conduction use a Solid mesh unless the heat just travels along through the elements.