11 "The diffusion equation\n",
12 "======================\n",
15 " \\partial_t T =d\\triangle T +\\frac{ \\Phi+\\lambda_{sf}(T_f-T)}{\\rho c_p}\n",
18 "- $T$ the main unknown is the solid temperature field\n",
19 "- $\\rho$ is the solid density assumed constant and possibly set by the user\n",
20 "- $c_p$ is the solid specific heat, possibly set provided by the user and assumed constant\n",
21 "- $\\lambda$ is the solid thermal conductivity possibly set provided by the user\n",
22 "- $d=\\frac{\\lambda}{\\rho c_p}$ is the solid diffusivity\n",
23 "- $\\lambda_{sf}$ is the fluid-solid heat transfer coefficient provided by the user\n",
24 "- $\\Phi$ is the heat source term if explicitely known\n",
25 "- $T_f$ is the fluid temperature field provided by the user\n",
27 "The class [DiffusionEquation](../../Models/inc/DiffusionEquation.hxx) implementing a scalar diffusion equation for the temperature in a solid. The default values for $\\rho, c_p, \\lambda$ are those of Uranium oxyde at $900 K$. \n",
30 "\\subpage ExampleDiffusionEqPage \"Here are C and Python example scripts\"\n",
35 "<IPython.core.display.Markdown object>"
39 "output_type": "display_data"
43 "from IPython.display import display, Markdown\n",
44 "display(Markdown('DiffusionEq.md'))"
50 "display_name": "Python 2",
59 "file_extension": ".py",
60 "mimetype": "text/x-python",
62 "nbconvert_exporter": "python",
63 "pygments_lexer": "ipython2",