## Cooling with Elmer

Elmer cases by the users for the users
Antourloupe82
Posts: 19
Joined: 19 Jun 2015, 16:56
Antispam: Yes

### Cooling with Elmer

Hi all,

Let us suppose that a small cube (a = 10 cm) made of gold is placed at the ground supposed to be a semi-infinite plane medium made of wood. The small cube is enclosed (left, right and top) by a large cubic box (L = 2 m) filled with air and made of silver. This configuration represents a small cube placed at the ground of a room.

The initial temperature of the cube (Tic = 60°C) is known, the initial temperature of air in the box is known (Tia = 20°C) and also all the relevant parameters of the system (calorific capacities, heat transfer coefficients...).

I would like to calculate the temperature of the center of the cube as a function of the time Tc(t) by taken into account :

- the thermal transfer between the cube and the air (convection...)
- the thermal transfer between the bottom of the cube and the surface of the ground on which it is placed (conduction by contact...)
- the thermal transfer by radiation (cube and sides of the box).

In this problem, the boundaries of the large box are supposed isolated (q = 0 due to the thermal isolation of the room).

Up to now, I solved the problem only when the box is supposed infinite with a small cube that floats in air (cooling of a cube embedded in air) but how to set Elmer to solve the problem above ? In particular to take into account the surface on which the cube is posed ? Have you a closed model to proposed me ?

Brice (phD)

mzenker
Posts: 1936
Joined: 07 Dec 2009, 11:49
Location: Germany

### Re: Cooling with Elmer

Hi Brice,

I think the HeatSolver will be able to solve almost all aspects of your problem.
How about the temperature of the wooden floor? Can we suppose it to be constant? Then it's simply a Dirichlet BC on the bottom of the cube.
If you want to take convection in a finite volume into account, you will need to calculate air movement - I don't have any experience there, but I think searching the forum you will find some cases where this has been done.

HTH,

Matthias

Antourloupe82
Posts: 19
Joined: 19 Jun 2015, 16:56
Antispam: Yes

### Re: Cooling with Elmer

Hi Matthia,

In a first time to make simpler, I think suppose that the temperture of the wooden floor is constant due to her large calorific capacity relative to that of the cube. According to the experimental results obtained recently, the - natural - convection is not negligible in this problem and it must be taken into account by using the Newton's law q = h.(T - Text) in a first approximation, where h is the thermal coefficient between air (Text) and cube (T) for natural convection.

Indeed, it would be more correct to take into account the coupling between the heat transfer (T) and the air movement (ux, uy, uz) described by Navier-Stokes's equation. I will look at how to couple these two models in the configuration of Elmer : Heat transfer <---> NS

Also, I found this nice simulation on the web close to my problem if one remplace the active heat source on the right by a passive small cube at the center of the room. See : https://www.youtube.com/watch?v=Zr8WbV8F_5g. Unfortunately the source file of the model is not available online.

Best

Brice

mzenker
Posts: 1936
Joined: 07 Dec 2009, 11:49
Location: Germany

### Re: Cooling with Elmer

Hi Brice,

I think if you want to take into account the finiteness of the box as you said in your initial post, you will have to do some fluidics since the air might locally change its temperature Tair due to heat exchange with the cube. Also there will be heat exchange between the air and the walls of the box.
If you keep Tair = Text constant, then indeed I would use a fixed coefficient for natural convection and neglect all of the above, which brings us back to an infinite box.

HTH,

Matthias