From 312fdf97c1ea0a747221eb491884bfa558b14b2e Mon Sep 17 00:00:00 2001
From: Shuang Chen <gechenshuang88@gmail.com>
Date: Mon, 1 Mar 2021 14:52:50 +0100
Subject: [PATCH] [HC/docu] fixed the input parameter typo and equation format
errors
---
.../heatconduction/BHE_array_benchmark.md | 26 +++++++++++--------
1 file changed, 15 insertions(+), 11 deletions(-)
diff --git a/web/content/docs/benchmarks/heatconduction/BHE_array_benchmark.md b/web/content/docs/benchmarks/heatconduction/BHE_array_benchmark.md
index 58bf38dbb2a..d9fb7bb7905 100644
--- a/web/content/docs/benchmarks/heatconduction/BHE_array_benchmark.md
+++ b/web/content/docs/benchmarks/heatconduction/BHE_array_benchmark.md
@@ -50,12 +50,12 @@ In this model, the quad element was adopted to compose the mesh. The initial tem
| Parameter | Symbol | Value | Unit |
| -------------------------------- |:------------ | -------------------:| ----------------:|
-| Soil thermal conductivity | $\lambda$ | 1.720 | $Wm^{-1}K^{-1}$ |
+| Soil thermal conductivity | $\lambda$ | $2.0$ | $Wm^{-1}K^{-1}$ |
| Soil heat capacity | $\rho c$ | $2.925\times10^{6}$ | $J^{-3} mK^{-1}$ |
| Ground thermal diffusivity | $\alpha$ | $5.7\times10^{-7}$ | $Wm^{-1}K^{-1}$ |
-| Initial subsurface temperature | $T_0$ | 10 | $^{\circ}C$ |
-| Heat extraction rate of the BHE | $q$ | 35 | $W/m$ |
-| Diameter of the BHE | $D$ | 0.15 | $m$ |
+| Initial subsurface temperature | $T_0$ | $10$ | $^{\circ}C$ |
+| Heat extraction rate of the BHE | $q$ | $35$ | $W/m$ |
+| Diameter of the BHE | $D$ | $0.15$ | $m$ |
{{< img src="../BHE_array_benchmark_figures/figure_1.png" >}}
@@ -65,15 +65,19 @@ Different meshes were adopted to analyse the impact of mesh density on the numer
\begin{equation}
\begin{split}
- \Delta = {\rm{ }}a{r_b}\ \hspace{6mm}
- a = \left\{ \begin{array}{l}
- 4.81 \hspace{2mm} for\hspace{2mm} n=4\\
- 6.13 \hspace{2mm} for\hspace{2mm} n=6\\
- 6.16 \hspace{2mm} for\hspace{2mm} n=8
- \end{array}\right.
- \label{eq_4}
+ \Delta = {\rm{ }}a{r_b},\ \hspace{6mm}
\end{split}
\end{equation}
+with
+\begin{equation*}
+ a = 4.81 \hspace{2mm} for\hspace{2mm} n=4,
+\end{equation*}
+\begin{equation*}
+ a = 6.13 \hspace{2mm} for\hspace{2mm} n=6,
+\end{equation*}
+\begin{equation*}
+ a = 6.16 \hspace{2mm} for\hspace{2mm} n=8.
+\end{equation*}
where $r_b$ is the BHE radius. n denotes the number of surrounding nodes. n =Â 8 is typical for a squared grid meshes. In this study, the BHE diameter is assumed to be 0.15Â m. Based on equation (4) the optimal element size should be set to approximately 0.5Â m.
--
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