[web/benchmark] Added a description of HeatTransportInStationaryFlow

web/content/docs/benchmarks/hydro-thermal/HeatTransportInStationaryFlow.md

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+project = "Parabolic/HT/HeatTransportInStationaryFlow/HeatTransportInStationaryFlow.prj"
+author = "Wenqing Wang"
+title = "One dimensional heat transport in stationary flow"
+date = 2020-12-14T08:00:32+01:00
+weight = 153
+
+[menu]
+  [menu.benchmarks]
+     parent = "hydro-thermal"
++++
+
+## Problem description
+We consider one dimensional heat transport in stationary flow in a porous medium.
+ This benchmark was first introduced as an exercise of
+ [Geoenergy Modeling I – Geothermal Processes in Fractured Porous Media](https://www.opengeosys.org/books/geoenergy-modeling-i/)
+ for [OGS 5](https://github.com/ufz/ogs5).
+
+## Numerical setting
+ The size of the domain is 1 m in the horizontal direction.
+  The material properties of fluid are:
+
+| Property               | Value | Unit        |
+|------------------------|-------|-------------|
+| Density                | 1000  | kg/m^3      |
+| Viscosity              | 1.e-3 | Pa⋅s        |
+| Specific heat capacity | 4182  | J/K/kg      |
+| Thermal conductivity   | 0.6   | W/(m⋅K)     |
+
+The material properties of porous medium are:
+
+| Property               | Value | Unit        |
+|------------------------|-------|-------------|
+| Density                | 2850  | kg/m^3      |
+| Specific heat capacity | 0  | J/K/kg      |
+| Thermal conductivity   | 0   | W/(m⋅K)     |
+
+The intrinsic permeability is 1.e-11 m^2. Since the flow equation is steady state,
+ the porosity $n$ is not applied in that equation. We set $n=1$
+ in order to use the specific heat capacity and the thermal conductivity of fluid
+ as the effective ones.
+
+The initial boundary conditions are <em>T(0)=</em>0 °C and
+  <em>p(0)=</em>1.e+5 Pa.
+
+At the left boundary, a constant temperature of <em>T=</em>1 °C
+ and a constant pressure of <em>p=</em>1.01e+5 Pa are prescribed.
+ At the right boundary condition, there is no heat flux and the pressure is
+ set as the initial one. The pressure boundary conditions lead to a
+ stationary flow with a velocity of 1.e-5 m/s.
+
+The time duration is 5.e+4 s. A fixed time step size of 250 s is used
+ for the temporal discretization.
+
+This example is also set as one of the benchmarks of
+ [ThermoHydroMechanics (THM)](https://gitlab.opengeosys.org/ogs/ogs/-/blob/master/Tests/Data/ThermoHydroMechanics/Linear/HeatTransportInStationaryFlow/HeatTransportInStationaryFlow.prj)
+ and ThermoRichardsMechanics (TRM), respectively.
+ In order to provide a reference result for the same benchmark of
+ THM and TRM, a 2D domain of 1 m $\times$ 0.1 m is used, which
+ is discretized into 3$\times$39 quadrilateral elements.
+
+## Result
+
+The temperature distribution  at <em>t=</em>  5.e+4 s together with the mesh is
+ illustrated in the following figure:
+{{< img src="../heat_transport_in_stationary_flow_domain.png" >}}
+
+The temperature  profile at <em>t=</em>  5.e+4 s along a horizontal line in the
+  2D domain is given in the following figure:
+{{< img src="../heat_transport_in_stationary_flow_profile.png" >}}
+