2. Benchmark solution

2.1. Calculation method

Air mass conservation calculation

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

Classical heat equation that is treated by a thermal calculation.

2.2. Benchmark results

With the previous numerical values, we find:

and

The constants of the heat equation are then:

2.3. Uncertainty about the solution

The uncertainties are quite large since the quasi-analytical solution (the result of a thermal calculation) is an approximate solution due to the linearization of the equations.