Benchmark solution
=====================


Calculation method
-----------------

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


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.. _RefImage_Object_3.svg:


.. _RefEquation 2.1-1:

                         eq 2.1-1

In which

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.. _RefImage_Object_4.svg:

denotes the enthalpy of water,

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.. _RefImage_Object_5.svg:

its mass flow,

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.. _RefImage_Object_6.svg:

the mass intake of water and

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.. _RefImage_Object_7.svg:

heat flow.

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


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.. _RefImage_Object_8.svg:


.. _RefEquation 2.1-2:

                                 Eq 2.1-2


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.. _RefImage_Object_9.svg:


.. _RefEquation 2.1-3:

                                         Eq 2.1-3


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.. _RefImage_Object_10.svg:


.. _RefEquation 2.1-4:

                                 Eq 2.1-4


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.. _RefImage_Object_11.svg:


.. _RefEquation 2.1-5:

                                     Eq 2.1-5


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is the thermal diffusion coefficient,

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is the hydraulic diffusion coefficient,

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.. _RefImage_Object_14.svg:

intrinsic permeability,

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.. _RefImage_Object_15.svg:

,

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.. _RefImage_Object_16.svg:

,

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.. _RefImage_Object_17.svg:

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

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


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.. _RefImage_Object_18.svg:


.. _RefEquation 2.1-6:

                 eq 2.1-6

We ask:


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.. _RefImage_10000370000069D500002EB71819ED95FDC94958.svg:

and


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.. _RefImage_Object_19.svg:

We get


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.. _RefImage_Object_20.svg:


.. _RefEquation 2.1-7:

                             eq 2.1-7

Benchmark results
----------------------

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


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.. _RefImage_Object_21.svg:

The solution for [:ref:`éq 2.1-7 <éq 2.1-7>`] is then:


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.. _RefImage_Object_22.svg: