a small piece sourranded

.gitignore

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+.ipynb_checkpoints

main.md

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+
+
+```python
+#1 Loading functions  and modules
+from fenics import *
+import matplotlib.pyplot as plt
+T = 2.0
+num_steps = 20
+dt = T/num_steps
+rho = 7500
+Cp = 500
+k = 50
+alpha = k/(rho*Cp)
+```
+
+
+```python
+#2 Create mesh and define function space
+nx = 0.008
+ny = 0.003
+mesh = RectangleMesh(Point(0,0),Point(nx,ny),30, 30,'left')
+V = FunctionSpace(mesh, 'Lagrange', 1) #Lagrange are triangular elements
+plot(mesh)
+plt.show()
+
+```
+
+
+![png](output_1_0.png)
+
+
+
+```python
+# Boundary conditions
+u0 = Constant(100)
+def boundary(x, on_boundary):
+    return on_boundary
+
+bc = DirichletBC(V,u0, boundary)
+```
+
+
+```python
+u_n = project(1, V)
+u = TrialFunction(V)
+v = TestFunction(V)
+f = Constant(0.0)
+F = u*v*dx + alpha*dt*dot(grad(u), grad(v))*dx-u_n*v*dx
+a, L = lhs(F), rhs(F)
+```
+
+    Calling FFC just-in-time (JIT) compiler, this may take some time.
+
+
+
+```python
+u = Function(V)
+t = 0
+for n in range(num_steps):
+    t += dt
+    #u0.t = t
+    solve(a == L, u, bc)
+    c = plot(u,)
+    plt.colorbar(c)
+    plt.show()
+    u_n.assign(u)
+```
+
+    Calling FFC just-in-time (JIT) compiler, this may take some time.
+
+
+
+![png](output_4_1.png)
+
+
+
+![png](output_4_2.png)
+
+
+
+![png](output_4_3.png)
+
+
+
+![png](output_4_4.png)
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+
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+![png](output_4_5.png)
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+
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+![png](output_4_6.png)
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+
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+![png](output_4_7.png)
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+
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+![png](output_4_8.png)
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+
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+![png](output_4_9.png)
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+
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+![png](output_4_10.png)
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+
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+![png](output_4_11.png)
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+
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+![png](output_4_12.png)
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+
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+![png](output_4_13.png)
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+
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+![png](output_4_14.png)
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+
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+![png](output_4_15.png)
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+
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+![png](output_4_16.png)
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+
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+![png](output_4_17.png)
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+
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+![png](output_4_18.png)
+
+
+
+![png](output_4_19.png)
+
+
+
+![png](output_4_20.png)
+
+
+
+```python
+1E-7
+```
+
+
+
+
+    1e-07
+
+
+
+
+```python
+1e2
+```
+
+
+
+
+    100.0
+
+
+
+
+```python
+1E-7+1e2
+```
+
+
+
+
+    100.0000001
+
+
+
+
+```python
+
+```