[web] Add a description of mini-benchmark1 of FE-task force

web/content/docs/benchmarks/thermo-hydro-mechanics/heating-homogeneous-domain/index.md

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+project = ["ThermoHydroMechanics/HeatingHomogeneousDomain/hex_THM.prj"]
+author = "Wenqing Wang"
+title = "Heating of a homogeneous volume"
+date = 2023-02-10T16:12:48+01:00
+weight = 100
+image = "domain.png"
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+
+{{< data-link >}}
+This example is one of the mini-benchmarks of  FE-Modelling Task Force
+(by Andrés Alcolea et. al.). The example is aimed to simulate the coupled THM
+ processes in a fully water saturated unit cubic porous medium ($[0, 1]^3\,\text{m}^3$)
+ with a linear homogeneous temperature increment from
+ 20$^{\circ}$C to 30$^{\circ}$C in 100 days.
+
+The gravity is not considered in all balance equations.
+ Since the temperature is homogeneous, the specific heat capacity is set to zero
+ and thermal conductivity can be any non-zero number. The liquid density is
+ given as
+ $$\rho_L = \rho_0 \exp (\beta_L (p_L-p_0)+\alpha_L^T(T-T_{ref})) $$
+ with
+
+- $\rho_0=1002.6$ kg/m$^3$ the initial liquid density,
+- $\beta_L=4.5\cdot10^{-10}$ Pa the liquid compressibility,
+- $\alpha_L^T=-2.0\cdot 10^{-4} \text{ K}^{-1}$ the liquid thermal expansivity,
+- $T_{ref} = 273.15 \text{ K}$ the reference temperature.
+
+ While the liquid viscosity is defined as
+  $$\mu_L = \text{A}\exp(\text{B}/T)$$
+with  A=$2.1\cdot 10^{-6} \text{ Pa}\cdot\text{s}$, and B=1808.5 K.
+
+ The other material parameters are given below:
+
+| Property               | Value | Unit        |
+|------------------------|-------|-------------|
+| Young's modulus        | 1     | GPa         |
+| Poisson ratio          | 0.35  | -           |
+| Solid thermal expansion | $3 \cdot 10^{-6}$  |$\text{K}^{-1}$     |
+| Biot's coefficient   | 0.96111  | -     |
+| Porosity   | 0.1  | -     |
+| Intrinsic permeability |$3.0 \cdot 10^{-20}$ | m$^2$|
+
+Initially, the temperature is  $20 ^{\circ}$C, the pore pressure is
+ $2\cdot 10^6$ Pa, and all effective stress components are zero.
+
+At the boundary surfaces, there is no heat or flow flux, and the normal
+ displacement is fixed to zero.
+
+As a CTest, only 5 time steps with a fixed time step size $1.728\cdot 10^4$ s
+ are computed. If the example is run up to 50 time steps, corresponding to 100
+ days of simulation time, the variations of pressure and effective
+ stress can be obtained as that are shown in the two figures below:
+
+<figure>
+<img  src="p.png" alt="drawing" width="400"/>
+<img  src="Szz.png" alt="drawing" width="415"/>
+</figure>