wall_bc.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:1508340f29e20e00734d55c0a64508ad892b64122f3ac96d65f7fc4917ff4421"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy as sy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rho_b,rho_i,D_i,D_b,Y_b,Y_s,h,Y_1,dx = sy.symbols(\"rho_b rho_i D_i D_b Y_b Y_s h Y_1 dx\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "flux_cond = sy.Eq(rho_b*D_b*h*(Y_b-Y_s) ,rho_i * D_i *(Y_s -Y_1)/dx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "flux_cond"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "D_b*h*rho_b*(Y_b - Y_s) == D_i*rho_i*(-Y_1 + Y_s)/dx"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol = sy.solve(flux_cond,Y_s,dict=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "[(D_b*Y_b*dx*h*rho_b + D_i*Y_1*rho_i)/(D_b*dx*h*rho_b + D_i*rho_i)]"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "flux  = rho_i*D_i*(Y_s-Y_1)/dx"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "flux.subs({Y_s:sol[0]}).simplify()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "D_b*D_i*h*rho_b*rho_i*(-Y_1 + Y_b)/(D_b*dx*h*rho_b + D_i*rho_i)"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol[0]\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "(D_b*Y_b*dx*h*rho_b + D_i*Y_1*rho_i)/(D_b*dx*h*rho_b + D_i*rho_i)"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}