Thermal simulation with air gap

[marco_41]

Dear all,

I´m relatively new to Fusion 360, although I used Inventor in the past. I want to estimate / simulate the heating of a small diameter capillary that is located in a larger capillary. The larger capillary is heated by direct contact to a hot copper block. Between the inner and outer capillary there´s some air gap of some microns.

As a test I made a simple project with two cyclinders. The one with a smaller diameter (cyclinder 1) is held at 100°C (via "applied temperature") and I want to simulate the temperature of a larger diameter cyclinder (cylinder 2, height = 1mm) when there´s a gap of 1 mm in between the two cylinders. I followed two approaches which give different results.

In approach 1 cyclinder 1 and 2 are in direct mechanical contact.  I edited the contact manually and set it to "bonded" with lambda = 26 W/m^2K (because 26 W/m^2 K =0.026 W / m K * 1 mm, where 0.026 W / m K is the thermal conductivity of air). Cyclinder 2 is thermically connected to the surrounding  (air, T= 20°C) by convection with 10 W / m^2K. The temperature of cyclinder 2 for (1) is shown in the picture below and is ~29°C.

In approach 2 Cylinder 1 and 2 are separated mecahnically by 1 mm and there´s another body in between with an height of 1 mm. I assigned the physical properties of air to that body. Both, the air body and the larger cyclinder are cooled by convection with 10 W / m^2K. All contacts between the 3 bodies are set up automatically, so there´s direct thermal contact if I understand correctly. The final tempeature of cyclinder 2 is now close to 100°C.

Does anyone know what´s the best approach to solve this problem and why these two simulation differ that much? Maybe I´m completely wrong and none of the two makes any sense. I´m aware that Fusion can´t model convective heating, but as a first approximation I can assume the air to be static.

Thanks for your help!

[marco_41]

Just bringing this up again, cause noone replied.

[jscott6SWZG]

Think your using thermal conductivity wrong.  Think of it has wm/m2k

[karol.suchon]

Hello Marc.

The air gap is a tricky one becouse the air is a tricky one in that case.

Both proposed by you solution are only partially correct.

In the first scenario, you change the air conductivity into the thermal resistance.

In a standard air gap, we will have a thermal resistance build like: Convection on the one side, the thermal resistance of heat transfer by air and convection on the second side.

If the gap is small enough the convection swirls are not able to be produced, and the velocity inside is almost zero, for little larger gaps we have a pattern of almost identical swirls which allows transferring heat more effectively(btw they look very nice), for larger gaps than them we have a standard way. So overall the resistance in the air gap depends on the thickness of that air gap if the gap is fully closed or open and the axis of heat transfer to the gravity vector.

Here you have an additional explanation of the phenomenon.

In the second approach, you tried to apply the scenario with the convection of both sides in the open environment, but it is not applied properly.

If you will compute the thermal resistance of that air gap, that will be much higher than in the first case.

So overall the first approach is better just take the value from some standard and do not threaten the fluid as solid material 🙂 The difference between simulations is connected to calculating completely different phenomena.

If something is unclear, just let me know 🙂

Best regards,

Karol

[marco_41]

Hi Karol,

thanks for the detailed description. It´s still not clear to me what´s the best approach how to simulate this.

"In the first scenario, you change the air conductivity into the thermal resistance.

In a standard air gap, we will have a thermal resistance build like: Convection on the one side, the thermal resistance of heat transfer by air and convection on the second side.

If the gap is small enough the convection swirls are not able to be produced, and the velocity inside is almost zero, for little larger gaps we have a pattern of almost identical swirls which allows transferring heat more effectively(btw they look very nice), for larger gaps than them we have a standard way. So overall the resistance in the air gap depends on the thickness of that air gap if the gap is fully closed or open and the axis of heat transfer to the gravity vector."

So, does that mean, that a very thin air gap is actually worse (for effectively transferring heat) compared to a larger air gap, because convection swirls are not formed and heat transfer from the hot to the colder part is suppressed?

"If you will compute the thermal resistance of that air gap, that will be much higher than in the first case.

So overall the first approach is better just take the value from some standard and do not threaten the fluid as solid material" In simulation 1 I didn´t model the air, it´s only two metal parts.

So, you mean the two parts should be in contact like in the first simulation and I should adjust the thermal conductance of the contact? What do you mean with "do not threaten the fluid as solid material"?

Thanks,

Marco

[karol.suchon]

I read my post once again and it could be very unclear 🙂

I do not think that they are a larger gap which has lower resistance than a smaller one, I will probably need to look into some book abou the heat and mass transfer, but that is a difference between the solid and fluid thermal resistance. Solidbody thermal resistance is a linear function of the thickness ( standard cartesian coordinates system) with the fluid gap thermal resistance does not increase that much with a thickness of that gap. Two times larger fluid gap could have almost the same thermal resistance as the smaller one. That is what I was meaning by:

"do not threaten the fluid as solid material"

I will also add some explanation about the difference between the results, after reading what I wrote once again I have a problem understanding what I wrote 😛

In the first scenario, you applied thermal resistance as:

 R=AirConductivity thermal resistance

In the second scenario you probably want to apply:

R= Convection Resistance Hot Side+AirConductivity thermal resistance(by adding air body)+Convection Resistance Cold side

So the thermal resistance is much higher than in the first scenario. 

The AirConductivity thermal resistance is the same in both scenarios just applied in a different way.

BTW the convection resistance should be applied as a contact between the fluid and solid body.

So, you mean the two parts should be in contact like in the first simulation and I should adjust the thermal conductance of the contact? 

Exactly, the thermal gap has its own resistance depending on the depth and location of the gravity vector so there is no reason to add the air body to the solid body simulation.

BR

Karol