{ "cells": [ { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "The diffusion equation\n", "======================\n", "\n", "$$\n", " \\partial_t T =d\\triangle T +\\frac{ \\Phi+\\lambda_{sf}(T_f-T)}{\\rho c_p}\n", "$$\n", "where\n", "- $T$ the main unknown is the solid temperature field\n", "- $\\rho$ is the solid density assumed constant and possibly set by the user\n", "- $c_p$ is the solid specific heat, possibly set provided by the user and assumed constant\n", "- $\\lambda$ is the solid thermal conductivity possibly set provided by the user\n", "- $d=\\frac{\\lambda}{\\rho c_p}$ is the solid diffusivity\n", "- $\\lambda_{sf}$ is the fluid-solid heat transfer coefficient provided by the user\n", "- $\\Phi$ is the heat source term if explicitely known\n", "- $T_f$ is the fluid temperature field provided by the user\n", "\n", "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", "\n", "\n", "\\subpage ExampleDiffusionEqPage \"Here are C and Python example scripts\"\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import display, Markdown\n", "display(Markdown('DiffusionEq.md'))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 2 }