2. Reference solution#

2.1. Calculation method used for the reference solution#

We have a simple analytical solution, since it involves exhibiting a harmonic function and adjusting the associated source in each domain:

in field 1: \(T(x,y,z)=T({A}_{1})+{x}^{2}+{y}^{2}+{z}^{2}\), (in the original frame \({A}_{1}\)),
in field 2: \(T(x,y,z)=T({A}_{2})+\frac{1}{2}{x}^{2}+{y}^{2}+{z}^{2}\), (in the original frame \({A}_{2}\)).

From this we deduce the values of \({s}_{1}\) and \({s}_{2}\),, \({s}_{1}=-6.\), \({s}_{2}=–\mathrm{5.W}/{m}^{3}\).

Temperatures at the points on planes \({B}_{1}{F}_{1}{G}_{1}{C}_{1}\) and \({A}_{2}{E}_{2}{H}_{2}{D}_{2}\)

Analytical solution.