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).

- 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 ?

Thank you for your help.

Brice (phD)