{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import quad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 2000            # \n",
    "T0 = 300            # K\n",
    "σ = 5.67E-8         # W/m2K4\n",
    "H = 1.0\n",
    "k = 10\n",
    "\n",
    "Ib = σ*T**4/np.pi\n",
    "I0 = σ*T0**4/np.pi\n",
    "\n",
    "def get_q(x):\n",
    "    I1, _ = quad(lambda θ: np.cos(θ)*np.sin(θ)*\n",
    "                           (Ib-(Ib-I0)*np.exp(-k*x/np.cos(θ))), 0, np.pi/2)\n",
    "    I2, _ = quad(lambda θ: np.cos(θ)*np.sin(θ)*\n",
    "                           (Ib-(Ib-I0)*np.exp(-k*(H-x)/np.cos(θ))), 0, np.pi/2)\n",
    "    return 2*np.pi*(I1-I2)\n",
    "\n",
    "def get_Q(x):\n",
    "    I, _ = quad(lambda θ: np.sin(θ)*(np.exp(-k*x/np.cos(θ)) + np.exp(-k*(H-x)/np.cos(θ))), 0, np.pi/2)\n",
    "    return -2*np.pi*k*(Ib-I0)*I\n",
    "\n",
    "x = np.linspace(0,H,100)\n",
    "q = np.zeros(len(x))\n",
    "Q = np.zeros(len(x))\n",
    "for i in range(len(q)):\n",
    "    q[i] = get_q(x[i])\n",
    "    Q[i] = get_Q(x[i])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YTwGXmlm2c65nZKuU0cQ5t3en2h3ydrrdod4dcO/k7Yh7d8494QjhiKMn4u24QxFHOOLt1MN9X0d/Rva+jrzvdcR564QjEI5ECDuiyyL9zotEILx3m9j3jnzgM8PR+iKOvTWHotc+RlJOVgZ5WRmMyckiPyeT3KwMxuZmUZCbRUlBLgW5WYyNToV53vyC3CyK8rMpyov+zM9mwphs8rMzFSgpLN77fAz4ipn9EO860CvA0t5w8kkx3hhzdX3m1wFnDLDNFODZftbPir5fTewCM7scuBygoqJimOWKX3rCEVo6QzR39NDc2UNrZ4iWrhCtnSHaukO0dnnfrnu/bbf3hOno9r6Rd+z9Zh79ph7z7X1/38RHSmaGkWlGZoaRlWFkxPzsnf++yfquA1kZGWRkQHZGBpkZGWQa0ffLIDPT2yYr09um932yMjL2fmZWppGZkUF2hpGVmUF2prdOdmYGOZkZZGV6v2dnZpCTZeRkZpKdaWRnZZAbnXIyM8nN7n3tBU2GrqFI1HBuMq0A7gHagIXAn83sPuBy55w//0oTzDl3B3AHwMKFC0f+a6AMSjji2NXaRW1zJzubu2ho7Z262d3mTXvau2ls964HtHaF9vueGQZjo9++x+Rkkp+TRX52BnnZmYzPzyYv29tx5mV7O82cmB1oTqb3OicrI7oDtugOOTovZoednZkR3WnH7Nyjv2dnemGRHZ2fmWFkGPo2L2lhOOFzkXPuhd4X0VGv/wpcC/x0uIUNQgPeAKelfeaXArUDbFM7wPqh6PtJAMIRx47GDrbtamf7bm/q7Z20o7GDnS1de7u/xirMzWJiQQ4TxuRQWpTHrCmFjM/PYVx+NuPyvVM0hXnZFOb94xRO7yme3KwM7eRFAhRv+DQAO2NnREe9/gpwGz6Ej3Ou28zWAouBh2IWLWbgzgMrgfP6zFsMrNH1nsQLRxxVDa1srm1lc10Lb9a2sKWhla272vfexAeQnWmUj8+nfFw+xx00ifJx+ZQW5TI5evG4uCCH4oLctHjUsMhoFW/4vIZ3LeTf+szfBkwdTkFDdBPwWzNbDazA681WDtwOYGZLAZxzl0TXvx34kpndDPw3cAKwBLjQx5rTgnOObbvaWffuHtZtb2R9dROVNS109HjdYDMMpk8ay8ySAk6dNZmZJWM5cNJYKiaOobQoT/dXiIxy8YbP94BlZjYV70jndSAf+HfAty7Yzrnfm9mkaD1lwHrgLOfctugqFX3WrzKzs4D/i9cdewdwte7xGT7nHO/Ut/LSO7tY+Y43/tWutm4AxuZkMm/qOC48uoJ55UXMLivkoJICHbmIpLG4wsc5tzp6f8wtwDNA7x1aHcA/jVBtg63lNrwA7G/ZKf3MewFvJAYZpo7uMC++3cCyzTt5ftNOdjR1AjB1fD4nzyrhqAMncNSBEzhkcqGOZETkfeLucOCcWw+cHj3yOAqv2/Mq59zukSpOkk9Hd5i/bdrJ42/U8LdNO+noCVOQm8WJBxfz5dNLOOGgYg6YmK+L+SKyT0MKHzO7CfgTsKK3O7VzbhcfvHFTRhHnHK9u38NDa97jr6/X0NoVorggh/OPmsrHDitj0fSJGp5ERIZkqEc++cADQI6ZPQY8AjzlnOsY6cIkeB3dYR55rZq7V2xlc10L+dmZnDW/jPOPmsoxMybpVJqIxG2ow+tcCVxpZkcDnwSuB35nZs/hBdFfnHP1I16l+KqxvZvfvFjF0pe30djew9yyIn52/nzOPrycglw9/FZEhi/uDgfAauC70ZtLP4nXZfn2aLfnR4D7nXPVI1Sn+KCxvZtfv1jFXSu20toV4qPzSvncCTM4esZEXcMRkREVV/iY2WnAa8653c65t4FfAL8ws2LgE9EJPjjopyShnnCE367cxs3PvklzZ4iz55dx9emHMGtKYdClicgoFe85lMfwrvtUA3/Hu+l0HfC6c+43eM/LkRTw/Oad/OivG9lS38ZJhxTz3bPnMHtKUdBlicgoF2/4nAfcidfLrRs4Ffgu4MysFXiDaCjFPGtHkkhjezc/+stGHl5XzYzisfz60oWcNnuyTq+JiC/iDZ9bgS86557onWFmJ+AF0m3AROBw4JuAwifJPLOxju/86Q32tHVz9WkH86+nHUxulkYbEBH/xBs+04DNsTOccyvM7FrgUufc+cOuTEZcdyjCT5+o5K4VW5lTVsTdly1iXvm4oMsSkTQUb/gsBz6HN6ZarDfwRomWJLOjsYN/ve9V1m1v5LITpvPtj83RjaEiEph4w+dLwKrowKI3AxuAbLxRrjW8TpJZu20PX1y6hu5QhF9ddCRnH14WdEkikubivc/nzeiNpr/E6+UWwhtctBv4/MiVJ8P11IZarr5/HVPG5fGbJYs4qKQg6JJERIY1sOhbwEfNbBqwAHDAWudczUgVJ8Pz25Vb+cGjG5g/bTy/uXQhkwpygy5JRAQY3mO0AXDOvQe8NwK1yAi6c/kWrn+skjPmTObWC48kP0e92UQkeWigrlHonpe2cv1jlZw9v4xbLjiCrEx1LBCR5KK90ihz36rt/ODRDSyeW8rNCh4RSVLaM40iT7xRw3f+9AanzZ7MLy9aQLaCR0SSlPZOo8Qb7zXxbw++xpEV47nt4iM1YoGIJDWFzyhQ29TJF5a+wqSxufz3ZxeSl63gEZHkpvBJcR3dYb64dA2tnSHuvHQhJYXqTi0iyU+93VLc9Y9t5I3qJu68ZCFzyvQoBBFJDTrySWFPb6jld6u2c/mHZ3LG3NKgyxERGTSFT4qqa+7k2j++zmFTi/j6R2YFXY6IyJAofFJQJOK45sHX6OyJcMsFCzQ6tYikHO21UtC9q7ax4u1dfP/jczVQqIikJIVPitnZ0smNT27mpEOKuWDRAUGXIyISF4VPivnJY5V0hSL88BPzMLOgyxERiYvCJ4W89HYDj7y2gytOnslMnW4TkRSm8EkR3aEI3/vzeiomjuGqUw8OuhwRkWHRTaYp4p6XtrKlvo27Lluk4XNEJOXpyCcFtHaF+K8X3uGkQ4o5ddbkoMsRERk2hU8KuOvFKna3dfM13UwqIqOEwifJNbX3cMfyLSyeW8oRB4wPuhwRkRGh8Elydyx/h5bOENcsPjToUkRERozCJ4k1tHZx14qtnHN4mUasFpFRReGTxH79YhWdPWH+TUc9IjLKKHySVEd3mPtWbeej86Zo/DYRGXUUPknq4XXv0dTRw2UnzAi6FBGREZeS4WNmuWZ2q5k1mFmbmT1qZtP2s811Zub6TLV+1TwUzjnuXrGVw6YWsWj6hKDLEREZcSkZPsDNwPnAhcBJQBHwVzPb363/m4GymGl+AmuM24tvN/DWzlYuO36GBg8VkVEp5YbXMbNxwOeBy5xzz0TnfRbYBpwBPLWPzUPOuaQ82on1mxerKC7I5ZwPlQVdiohIQqTikc9RQDbwdO8M59y7QCVw/H62nWlmO8ysysweMLOZCawzLlvqW1m2uZ7PHFtBbpbGcBOR0SkVw2cKEAYa+syviy4byCpgCXAm8MXoui+Z2aSBNjCzy81sjZmtqa+vH1bRg3Xvy9vJzjQuPuZAXz5PRCQISRM+ZnZ9Px0C+k6nxPv+zrknnHMPOuded849C5yD1/5L97HNHc65hc65hSUlJfF+9KD1hCP8+bVqzphTSklhbsI/T0QkKMl0zedm4N79rLMdOBbIBIqB2MORUmD5YD/MOddqZhuAQ4ZWZuK8+FYDu9q6OW/B1KBLERFJqKQJH+dcAx88lfYBZrYW6AEWA/dF500D5gAvDfbzzCwPmA0si6feRHh4XTUTxmRzih6bICKjXNKcdhss51wT8GvgBjM7w8wWAL8FXgee7V3PzDaZ2ZdiXv/czE42sxlmdgzwB2AscI+/LehfS2cPT2+o5ZzDy8nJSrk/i4jIkCTNkc8QfRUIAb8H8oHngEucc+GYdWbhnZrrNQ24n3+crnsZONY5t82PgvfnifW1dIUinKtTbiKSBlIyfJxzXcCXo9NA61if1xckuq7heGRdNdMnjeHIivFBlyIiknA6v5MEapo6WLllF+cumKoRDUQkLSh8ksAj63bgHOrlJiJpQ+GTBJ7cUMuHDhjPgZPGBl2KiIgvFD4B29nSyd/fbWTxHHWvFpH0ofAJ2PObvPtkT5tdGnAlIiL+UfgE7LlNdZSPy2NOWWHQpYiI+EbhE6DOnjDL32rgtDmT1ctNRNKKwidAq6p2094d5nSdchORNKPwCdDfKuvIy87guIMGfKqDiMiopPAJiHOOZyt3cuLBxeRl66FxIpJeFD4BebOulerGDk6fo1NuIpJ+FD4BeW5THQCn6vEJIpKGFD4BeWFzPfPKi5gyLi/oUkREfKfwCUBXKMy6dxs5dqY6GohIelL4BOCN95roDkU4esbEoEsREQmEwicAq6p2A7BousJHRNKTwicAr2zdzSGTC5g4NifoUkREAqHw8Vk44li7dQ+LdMpNRNKYwsdnlTXNtHSFOEbhIyJpTOHjs9W63iMiovDx2ytbdzN1fD7l4/ODLkVEJDAKHx8553hl626dchORtKfw8dGWhjYaWrvV2UBE0p7Cx0evRK/36OZSEUl3Ch8fra7aTXFBDjOLxwZdiohIoBQ+Pnrt3UYWVEzQI7NFJO0pfHzS3h2ialcb88qLgi5FRCRwCh+fbKptwTmYU6bwERFR+PiksqYZgLkKHxERhY9fKmuaKczNYtoE3VwqIqLw8UllTQtzyorU2UBEBIWPLyIRx6aaZuaUFQZdiohIUlD4+ODdPe20dYfV2UBEJErh44ONO7zOBgofERGPwscHlTXNZBjMmqLTbiIioPDxxcaaFmYUjyUvOzPoUkREkoLCxweVNc3MLR8XdBkiIklD4ZNgTR09VDd2qKebiEiMlAwfM7vczJaZWaOZOTObPsjtzjezjWbWFf15XoJLZVONOhuIiPSVkuEDjAGeBq4b7AZmdhzwe+B3wBHRnw+Z2TEJqG8vDasjIvJBWUEXEA/n3M0AZrZwCJt9FVjmnPuP6Ov/MLNTo/MvHMn6Ym2saWbi2BwmF+Ym6iNERFJOqh75xOM4vKOlWE8BxyfyQ71hdQo1rI6ISIyUPPKJ0xSgrs+8uuj8fpnZ5cDlABUVFXF96JEV45mhJ5eKiLxP0hz5mNn10c4D+5pO8bMm59wdzrmFzrmFJSUlcb3HDz95GEtOmDHClYmIpLZkOvK5Gbh3P+tsH8b71wKlfeaVRueLiIiPkiZ8nHMNQEMCP2IlsBi4MWbeYuClBH6miIj0I2nCZyjMbAretZpDo7Pmmtl4YLtzbnd0neeA1c65b0fXuQX4XzP7FvAIcB5wKnCij6WLiAhJdM1niK4A1uHdqwPwWPT1J2LWOQgo633hnHsJuABYArwOXAJ82jm3yod6RUQkhjnngq4hJSxcuNCtWbMm6DJERFKGma11zvV7P2aqHvmIiEgKU/iIiIjvFD4iIuI7XfMZJDOrB7bFuXkxie1GnozU5vSQbm1Ot/bC8Np8oHOu3zv0FT4+MLM1A110G63U5vSQbm1Ot/ZC4tqs024iIuI7hY+IiPhO4eOPO4IuIABqc3pItzanW3shQW3WNR8REfGdjnxERMR3Ch8REfGdwkdERHyn8BkBZnaVmVWZWaeZrTWzk/az/snR9TrNbIuZXeFXrSNlKG02s0+Z2dNmVm9mLWa2ysw+MdD6yWiof+OY7U40s5CZrU90jSMtjv+vc8zsR9Ftusxsu5ld7Ve9IyGONl9kZq+ZWbuZ1ZrZvdFHvqQEM/uwmT1qZtXRp0UvGcQ2883sBTPriG73fTOzoX62wmeYzOzTeM8K+gmwAO/hdE+YWcUA688AHo+utwD4KXCrmZ3vT8XDN9Q2AycDfwPOjq7/OPCnwe7AgxZHe3u3mwAsBZ5LeJEjLM42PwCcCVwOzAL+Ge/xJSkhjn/LJwC/Be4B5gHnAnP5x6NeUkEBsB74CtCxv5XNrAh4BqgDFkW3+wZwzZA/2TmnaRgTsAr4nz7z3gJ+OsD6PwPe6jPvTmBl0G1JVJsHeI/VwC+Cbksi2ws8DPwAuA5YH3Q7Etlm4CNAE1AcdO0+tvnrwLY+8y4DWoNuS5ztbwWW7GedK4FmID9m3veAaqK9pwc76chnGMwsBzgKeLrPoqeB4wfY7Lh+1n8KWGhm2SNb4ciLs839KQT2jFRdiRJve83sKqAUuD5x1SVGnG0+F3gFuMbM3jOzt8zs/5lZQeIqHTlxtnkFUGZmHzdPMd4DKx9PXKWBOw5Y7pyLPUp6CigHpg/ljRQ+w1MMZOIdgsaqw3vMd3+mDLB+VvT9kl08bX4fM/tXYBreKYtkN+T2mtl8vCOezzjnwoktLyHi+RvPxHsk/YeA84Ev4Z2CuzsxJY64IbfZObcSL2x+B3QD9YABlyauzMANtP/qXTZoCh/xVfTa1o3ARc65eEcJT1pmlgv8Hvi6c64q6Hp8lAE4vL/rKufcU3gBdL6ZlQZbWmKY2VzgVuDHeEdNZ+LtgP87yLpSRVbQBaS4BiCMd3olVilQO8A2tQOsHyI1hmqPp80AmNk/4V2Av8Q595fElDfihtreMmAOcJeZ3RWdlwGYmYWAs5xzfU/tJJt4/sY1QLVzrilmXmX0ZwUf/LacbOJp87eB1c65G6OvXzezNmC5mX3HOfdeYkoN1ED7r95lg6Yjn2FwznUDa4HFfRYtxusp05+VA6y/xjnXM7IVjrw424yZ/QveabYlzrk/JK7CkRVHe6uB+cARMdPtwNvR3wf8b5Qs4vwbrwDK+1zjOTT6M+mPcONs8xi8wIrV+3q07ltXAieZWV7MvMXADmDrkN4p6B4WqT4Bn8Y73/sFvG+8t+D1GjkwunwpsDRm/RlAG3BzdP0vRLc/P+i2JLDNFwA9eN0yp8RME4NuSyLa28/215F6vd2G+jcuAN4FHsLrdnwCXhfeh4JuSwLbvCT6//WVeNe8TsDrdLE26LYMoc0F/ONLUjvw/ejvFdHlPwWei1l/HN4RzgPAYcCn8Hq/fW3Inx1040fDBFyFl/pdeN+ePhyz7Hng+T7rnwy8Gl2/Crgi6DYkss3R166f6Xm/6/brb9xn25QLn3jajHdvz9PRnVg18CugMOh2JLjNXwY2RNtcg9f5YFrQ7RhCe08Z4N/m3dHldwNb+2wzH/hfoDPa5h8wxG7WzjmNai0iIv4breclRUQkiSl8RETEdwofERHxncJHRER8p/ARERHfKXxERMR3Ch+RFBN9GOGbZpY5zPdZnUrPkZLRReEjknpuBP7DDX/E7B8D/2lm2g+I7/Q/nUgKMbPjgdnAgyPwdo/jPVfpYyPwXiJDovARCYCZlZhZjZn9IGbe4WbWaWb/vI9NL8Iba6sjZrvrzGy9mV1qZlvNrM3M7jKzHDO7yszeNbNdZnZT7FFO9MjpceDCRLRRZF/0SAWRADjn6s1sCfAXM3saeA24H7jfOffQPjY9if6PeqYDnwTOAaYCf8R7vEMN3iOue4+WVkSX9VoNfHcYTRGJi8JHJCDOuafM7Da8wShfAHLxBqrclwPxhq/vKxO4zHnP01lvZk/iDWA71XmPC6g0sxXAqbw/fHYAU80syzkXGl6LRAZPp91EgnUt3jD+lwAXO+da97N+Pt5own1td+9/kFsd8GY0eGLnTe6zXQfeo5/zEPGRwkckWNOBA/CGsZ85iPUbgAn9zO/7IEI3wLy+/+YnAp2DCD2REaXwEQmImWUD9wGPAl8HbjOziv1stg6YO4JlHIb3bCkRX+maj0hwfgyUAKcDTcCZwFIzO805Fxlgm6eAz49gDScBT47g+4kMio58RAJgZicDXwMucc41Ou+pjkvwjmqu3cem9wKHmtm8EahhKnA8cNdw30tkqPQkU5EUY2b/CZQ454Z1BGRmNwLjnHOXj0xlIoOnIx+R1PMTYMtwx3YDdgL/PgL1iAyZjnxERMR3OvIRERHfKXxERMR3Ch8REfGdwkdERHyn8BEREd8pfERExHf/H+EcVrEd4nXGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rc('font', size=14)\n",
    "plt.plot(x,q/(np.pi*Ib))\n",
    "plt.xlabel('x (m)')\n",
    "plt.ylabel(r'$q/\\sigma T^4$');\n",
    "plt.savefig('pp_qabc.svg')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,Q/(np.pi*k*Ib))\n",
    "plt.xlabel('x (m)')\n",
    "plt.ylabel(r'$Q/kσT^4$');\n",
    "plt.savefig('pp_Qdef.svg')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rc('font', size=14)\n",
    "plt.plot(x,q/(np.pi*Ib))\n",
    "plt.xlabel('x (m)')\n",
    "plt.plot(x,Q/(np.pi*k*Ib))\n",
    "plt.xlabel('x (m)')\n",
    "plt.ylabel(r'$q/\\sigma T^4,\\,\\,Q/kσT^4$')\n",
    "plt.tight_layout()\n",
    "plt.legend(['q', 'Q'], frameon=False)\n",
    "plt.savefig('pp_Qq.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
