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Refine boundary condition descriptions and update solver configuration in HeatConduction1DWall.html and HeatConduction2DFin.html
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‎tutorials/HeatConduction1DWall.html‎

Lines changed: 69 additions & 18 deletions
Original file line numberDiff line numberDiff line change
@@ -96,14 +96,17 @@ <h2 id="mathematicalformulation"><a name="Mathematical formulation"></a>Mathemat
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within common engineering components like house walls.
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</p>
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<img src="../assets/HeatConduction1DWall.png" width="150" />
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<img src="../assets/HeatConduction1DWall.png" width="100" />
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<p>
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The above schematic illustrates the problem domain and outlines the associated boundary conditions. In
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particular, a convection boundary condition, implemented as Robin type, is applied at the inner side of
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the wall (\(x = 0\)). Morevover, at the outer side of the wall (\(x = W\), where \(W\) is the width of
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the wall), we apply a constant temperature (\(T_0\)) boundary condition, implemented as Dirichlet type
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in the finite element code.
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the wall (\(x = 0\)). The latter is expressed as \(\frac{dT}{dx}|_{x=0}=-{\frac{h}{k}}(T-T_{in})\),
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where \(h\) is the heat transfer coefficient, \(k\) the thermal conductivity and \(T_{in}\) is the
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internal temperature. We assume here that \({\frac{h}{k}}\) = 1 m<sup>-1</sup> and \(T_{in}\) = 25
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&deg;C. At the outer side of the wall (\(x = W\), where \(W\) = 0.15 m, is the width of the wall), we
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apply a constant temperature (\(T_0\) = 5 &deg;C) boundary condition, implemented as Dirichlet type in
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the finite element code.
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</p>
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<h2 id="solvingwithfeascript"><a name="Solving with FEAScript"></a>Solving with FEAScript</h2>
@@ -120,6 +123,60 @@ <h2 id="solvingwithfeascript"><a name="Solving with FEAScript"></a>Solving with
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. . .
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&lt;/head&gt;</pre
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>
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<p>
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We should then define the problem parameters, such as the solver type, the geometry configuration, and
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the boundary conditions. This is performed using JavaScript objects directly in the HTML file:
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</p>
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<pre class="prettyprint">
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&lt;body&gt;
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. . .
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&lt;script type="module"&gt;
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// Import the FEAScript library
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import { FEAScriptModel, plotSolution, printVersion } from "https://feascript.github.io/FEAScript-core/src/index.js";
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window.addEventListener("DOMContentLoaded", (event) => {
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// Print FEAScript version
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printVersion();
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// Create a new FEAScript model
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const model = new FEAScriptModel();
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// Set solver configuration
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model.setSolverConfig("solidHeatTransferScript");
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// Define mesh configuration
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model.setMeshConfig({
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meshDimension: "1D",
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elementOrder: "linear",
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numElementsX: 10,
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maxX: 0.15,
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});
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// Define boundary conditions
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model.addBoundaryCondition("0", ["convection", 1, 25]);
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model.addBoundaryCondition("1", ["constantTemp", 5]);
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// Set solver method
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model.setSolverMethod("lusolve");
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// Solve the problem and get the solution
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const { solutionVector, nodesCoordinates } = model.solve();
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// Plot the solution as a 1D line plot
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plotSolution(
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solutionVector,
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nodesCoordinates,
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model.solverConfig,
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model.meshConfig.meshDimension,
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"line",
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"solutionPlot"
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);
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});
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&lt;/script&gt;
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. . .
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&lt;/body&gt;</pre
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>
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<h2 id="results"><a name="Results"></a>Results</h2>
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@@ -162,22 +219,19 @@ <h2 id="results"><a name="Results"></a>Results</h2>
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// Set solver configuration
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model.setSolverConfig("solidHeatTransferScript");
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// Set solver method
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model.setSolverMethod("lusolve");
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// Define mesh configuration
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model.setMeshConfig({
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meshDimension: "1D",
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elementOrder: "linear",
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numElementsX: 10,
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maxX: 1,
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maxX: 0.15,
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});
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// Define boundary conditions
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model.addBoundaryCondition("0", ["constantTemp", 100]);
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model.addBoundaryCondition("1", ["constantTemp", 50]);
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model.addBoundaryCondition("0", ["convection", 1, 25]);
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model.addBoundaryCondition("1", ["constantTemp", 5]);
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// Set solver method (optional) - 'lusolve' uses LU decomposition
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// Set solver method
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model.setSolverMethod("lusolve");
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// Solve the problem and get the solution
@@ -212,22 +266,19 @@ <h2 id="results"><a name="Results"></a>Results</h2>
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// Set solver configuration
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model.setSolverConfig("solidHeatTransferScript");
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// Set solver method
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model.setSolverMethod("lusolve");
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// Define mesh configuration
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model.setMeshConfig({
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meshDimension: "1D",
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elementOrder: "linear",
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numElementsX: 10,
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maxX: 1,
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maxX: 0.15,
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});
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// Define boundary conditions
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model.addBoundaryCondition("0", ["constantTemp", 100]);
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model.addBoundaryCondition("1", ["constantTemp", 50]);
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model.addBoundaryCondition("0", ["convection", 1, 25]);
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model.addBoundaryCondition("1", ["constantTemp", 5]);
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// Set solver method (optional) - 'lusolve' uses LU decomposition
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// Set solver method
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model.setSolverMethod("lusolve");
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// Solve the problem and get the solution

‎tutorials/HeatConduction2DFin.html‎

Lines changed: 3 additions & 12 deletions
Original file line numberDiff line numberDiff line change
@@ -140,9 +140,6 @@ <h2 id="solvingwithfeascript"><a name="Solving with FEAScript"></a>Solving with
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// Set solver configuration
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model.setSolverConfig("solidHeatTransferScript");
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// Set solver method
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model.setSolverMethod("lusolve");
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// Define mesh configuration
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model.setMeshConfig({
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meshDimension: "2D",
@@ -159,7 +156,7 @@ <h2 id="solvingwithfeascript"><a name="Solving with FEAScript"></a>Solving with
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model.addBoundaryCondition("2", ["convection", 1, 20]);
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model.addBoundaryCondition("3", ["constantTemp", 200]);
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// Set solver method (optional) - 'lusolve' uses LU decomposition
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// Set solver method
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model.setSolverMethod("lusolve");
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// Solve the problem and get the solution
@@ -256,9 +253,6 @@ <h2 id="results"><a name="Results"></a>Results</h2>
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// Set solver configuration
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model.setSolverConfig("solidHeatTransferScript");
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// Set solver method
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model.setSolverMethod("lusolve");
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// Define mesh configuration
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model.setMeshConfig({
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meshDimension: "2D",
@@ -275,7 +269,7 @@ <h2 id="results"><a name="Results"></a>Results</h2>
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model.addBoundaryCondition("2", ["convection", 1, 20]);
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model.addBoundaryCondition("3", ["constantTemp", 200]);
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// Set solver method (optional) - 'lusolve' uses LU decomposition
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// Set solver method
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model.setSolverMethod("lusolve");
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// Solve the problem and get the solution
@@ -310,9 +304,6 @@ <h2 id="results"><a name="Results"></a>Results</h2>
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// Set solver configuration
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model.setSolverConfig("solidHeatTransferScript");
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// Set solver method
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model.setSolverMethod("lusolve");
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// Define mesh configuration
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model.setMeshConfig({
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meshDimension: "2D",
@@ -329,7 +320,7 @@ <h2 id="results"><a name="Results"></a>Results</h2>
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model.addBoundaryCondition("2", ["convection", 1, 20]);
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model.addBoundaryCondition("3", ["constantTemp", 200]);
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// Set solver method (optional) - 'lusolve' uses LU decomposition
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// Set solver method
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model.setSolverMethod("lusolve");
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// Solve the problem and get the solution

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