2. Benchmark solution

2.1. Calculation method

We start from the energy equation [éq 3.1.3-1] from document [R7.01.11], which in this case gives:

eq 2.1-1

In which

denotes the enthalpy of water,

its mass flow,

the mass intake of water and

heat flow.

Given the assumptions made, it is easy to see that:

Eq 2.1-2

Eq 2.1-3

Eq 2.1-4

Eq 2.1-5

is the thermal diffusion coefficient,

is the hydraulic diffusion coefficient,

intrinsic permeability,

,

,

are respectively the density, the viscosity and the calorific heat at constant pressure of water.

By reporting [éq 2.1-2], [éq 2.1-3], [éq 2.1-4], and [éq 2.1-5] in [éq 2.1-1] we find:

eq 2.1-6

We ask:

and

We get

eq 2.1-7

2.2. Benchmark results

In order to obtain the steady state more quickly, coefficients such as:

The solution for [éq 2.1-7] is then: