Hi,
I modeled with Comsol the decrease in the temperature of a small cube whose initial temperature is Tc placed on the ground at constant temperature Ts.
Now, I would like to find my result by calculation without solving the heat equation. The situation is therefore as follows: a cube (L = 1 cm and kc = 1 W / mK) at the initial temperature Tc = 35 ° C is placed on the ground (semi-infinite plane and ks = 2 W / mK) which at a temperature of 20 ° C which is assumed to be constant. It is assumed that the sides of the cube in contact with the ambient air are insulated and that there is therefore no heat transfer by convection. There is only a transfer of heat by conduction between the side of the cube and the ground (the contact surface is 1 cm²). The cube is small enough to consider that the temperature field is uniform inside. In addition, we suppose the quasi-stationary regime.
Is there a general expression that gives the heat flow lost by the cube through the ground? Is a Newton's type relationship phi = cte (Tc - Ts) possible? If not exists a valid expression under conditions giving this flow ?
Thank you