2. Benchmark solution

2.1. Calculation method

2.1.1. Calculation of the conservation of air mass

The conservation of the mass of gas is written as:

eq 2.1.1-1

We write that the total mass of water and the total mass of air are preserved (because there is no water or gas flow at the edge) and we get:

therefore

Eq 2.1.1-2

and

Speed calculation:

Eq 2.1.1-3

since

and

and

with

Like

[éq 2.1.1-1] can then be simplified to the following form:

with

Heat equation whose result is known.

2.2. Benchmark results

With the previous numerical values, we find:

and

The constants of the heat equation are then:

2.3. Uncertainties

The uncertainties are quite large because the analytical solution is an approximate solution due to the linearization of the equations.