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lines changed Original file line number Diff line number Diff line change @@ -114,30 +114,6 @@ <h2 id="mathematicalformulation"><a name="Mathematical formulation"></a>Mathemat
114114 temperature, implemented as Dirichlet type in the finite element code.
115115 </ p >
116116
117- < p >
118- This problem has an analytical solution. Since the governing equation is \(\frac{d^2T}{dx^2} = 0\),
119- the general solution is a linear function \(T(x) = Ax + B\), where \(A\) and \(B\) are constants
120- determined by the boundary conditions:
121- </ p >
122- < ol >
123- < li >
124- At \(x=0\): \(\frac{dT}{dx} = -\frac{h}{k}(T-T_{in})\)
125- </ li >
126- < li >
127- At \(x=W\): \(T(W) = T_0\)
128- </ li >
129- </ ol >
130- < p >
131- Solving these equations for our specific values (\(\frac{h}{k} = 1\) m< sup > -1</ sup > , \(T_{in} = 25\) °C,
132- \(T_0 = 5\) °C, and \(W = 0.15\) m), we get the analytical solution:
133- </ p >
134- < p >
135- \(T(x) \approx 23.53x + 1.47\)
136- </ p >
137- < p >
138- The numerical solution using finite elements should closely match this analytical result.
139- </ p >
140-
141117 < h2 id ="solvingwithfeascript "> < a name ="Solving with FEAScript "> </ a > Solving with FEAScript</ h2 >
142118 < p >
143119 Below is a demonstration of how to use the FEAScript library to solve this stationary heat transfer
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