lmtd.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, m1, m2, cp1, cp2, U, A, l, T10, T2l = sympy.symbols(\n",
    "    r\"x \\dot{m}_1 \\dot{m}_2 c_p\\,1 c_p\\,2 U A l T_{1\\,0} T_{2\\,l}\"\n",
    ")\n",
    "\n",
    "T1, T2, DT = sympy.symbols(r\"T_1 T_2 \\Delta\\ T\", cls=sympy.Function)\n",
    "\n",
    "dT1 = T1(x).diff(x)\n",
    "dT2 = T2(x).diff(x)\n",
    "dDT = DT(x).diff(x)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're dealing with an open system and are looking for a stationary solution. Assuming $T_2$ has its inlet at $x=l$, $T_1$ its inlet at $x=0$ and $T_2(x) > T_1(x)$ everywhere we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\dot{m}_1 c_{p,1} \\left. \\frac{d}{d \\xi_{1}} T_{1}{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }} - \\dot{m}_2 c_{p,2} \\left. \\frac{d}{d \\xi_{1}} T_{2}{\\left(\\xi_{1} \\right)} \\right|_{\\substack{ \\xi_{1}=x }}$"
      ],
      "text/plain": [
       "\\dot{m}_1*c_p,1*Subs(Derivative(T_1(_xi_1), _xi_1), _xi_1, x) - \\dot{m}_2*c_p,2*Subs(Derivative(T_2(_xi_1), _xi_1), _xi_1, x)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dx = sympy.symbols(r\"\\mathrm{d}x\")\n",
    "\n",
    "sympy.limit(\n",
    "    m1 * cp1 * (T1(x + dx) - T1(x)) / dx + m2 * cp2 * (T2(x - dx) - T2(x)) / dx, dx, 0\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\dot{m}_1 c_{p,1} \\frac{d}{d x} T_{1}{\\left(x \\right)} = \\frac{A U \\left(- T_{1}{\\left(x \\right)} + T_{2}{\\left(x \\right)}\\right)}{l}$"
      ],
      "text/plain": [
       "Eq(\\dot{m}_1*c_p,1*Derivative(T_1(x), x), A*U*(-T_1(x) + T_2(x))/l)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{A U \\left(- T_{1}{\\left(x \\right)} + T_{2}{\\left(x \\right)}\\right)}{l} = \\dot{m}_2 c_{p,2} \\frac{d}{d x} T_{2}{\\left(x \\right)}$"
      ],
      "text/plain": [
       "Eq(-A*U*(-T_1(x) + T_2(x))/l, \\dot{m}_2*c_p,2*Derivative(T_2(x), x))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "du1 = m1 * cp1 * dT1\n",
    "du2 = m2 * cp2 * dT2\n",
    "dq = U * (A / l) * (T2(x) - T1(x))\n",
    "\n",
    "en_eq1 = sympy.Eq(du1, dq)\n",
    "en_eq2 = sympy.Eq(-dq, du2)\n",
    "\n",
    "display(en_eq1, en_eq2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With boundary conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T_{1}{\\left(0 \\right)} = T_{1,0}$"
      ],
      "text/plain": [
       "Eq(T_1(0), T_{1,0})"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T_{2}{\\left(l \\right)} = T_{2,l}$"
      ],
      "text/plain": [
       "Eq(T_2(l), T_{2,l})"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bc1_eq = sympy.Eq(T1(0), T10)\n",
    "bc2_eq = sympy.Eq(T2(l), T2l)\n",
    "display(bc1_eq, bc2_eq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T_{1}{\\left(x \\right)} = \\frac{\\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}\\right) \\left(\\dot{m}_2 c_{p,2} \\left(T_{1,0} - T_{2,l}\\right) e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}} + \\left(T_{1,0} \\dot{m}_1 c_{p,1} + T_{2,l} \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}\\right) e^{\\frac{A U x \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2} l}}\\right) e^{- \\frac{A U x \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2} l}}}{\\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U}{\\dot{m}_2 c_{p,2}} + \\frac{A U}{\\dot{m}_1 c_{p,1}}}\\right)^{2}}$"
      ],
      "text/plain": [
       "Eq(T_1(x), (\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)))*(\\dot{m}_2*c_p,2*(T_{1,0} - T_{2,l})*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)) + (T_{1,0}*\\dot{m}_1*c_p,1 + T_{2,l}*\\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)))*exp(A*U*x*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2*l)))*exp(-A*U*x*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2*l))/(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U/(\\dot{m}_2*c_p,2) + A*U/(\\dot{m}_1*c_p,1)))**2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T_{2}{\\left(x \\right)} = \\frac{\\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}\\right) \\left(\\dot{m}_1 c_{p,1} \\left(- T_{1,0} + T_{2,l}\\right) e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}} + \\left(T_{1,0} \\dot{m}_1 c_{p,1} + T_{2,l} \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}\\right) e^{\\frac{A U x \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2} l}}\\right) e^{- \\frac{A U x \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2} l}}}{\\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U}{\\dot{m}_2 c_{p,2}} + \\frac{A U}{\\dot{m}_1 c_{p,1}}}\\right)^{2}}$"
      ],
      "text/plain": [
       "Eq(T_2(x), (\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)))*(\\dot{m}_1*c_p,1*(-T_{1,0} + T_{2,l})*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)) + (T_{1,0}*\\dot{m}_1*c_p,1 + T_{2,l}*\\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)))*exp(A*U*x*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2*l)))*exp(-A*U*x*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2*l))/(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U/(\\dot{m}_2*c_p,2) + A*U/(\\dot{m}_1*c_p,1)))**2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T1_eq, T2_eq = sympy.dsolve(\n",
    "    [en_eq1, en_eq2],\n",
    "    [T1(x), T2(x)],\n",
    "    ics={bc1_eq.lhs: bc1_eq.rhs, bc2_eq.lhs: bc2_eq.rhs},\n",
    ")\n",
    "\n",
    "T1_eq = T1_eq.simplify()\n",
    "T2_eq = T2_eq.simplify()\n",
    "\n",
    "display(T1_eq, T2_eq)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1ab7b3c4e50>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subs = {\n",
    "    m1: 1.5 * 0.16,\n",
    "    m2: -0.16,\n",
    "    cp1: 4184,\n",
    "    cp2: 4184,\n",
    "    l: 20,\n",
    "    A: 5,\n",
    "    U: 500,\n",
    "    T10: 60,\n",
    "    T2l: 90,\n",
    "}\n",
    "\n",
    "sympy.plot(T1_eq.rhs.subs(subs), T2_eq.rhs.subs(subs), (x, 0, subs[l]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming $T_{1,0}$, $T_{2,l}$ and $\\dot{m}_2$ are fixed what is the mass flow $\\dot{m}_1$ which maximizes the transfered energy?\n",
    "\n",
    "First, solve for the mass flows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\dot{m}_2 c_{p,2} \\left(- T_{1,0} e^{\\frac{A U}{\\dot{m}_2 c_{p,2}} + \\frac{A U}{\\dot{m}_1 c_{p,1}}} + T_{1,0} + T_{2,l} e^{\\frac{A U}{\\dot{m}_2 c_{p,2}} + \\frac{A U}{\\dot{m}_1 c_{p,1}}} - T_{2,l}\\right)}{\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U}{\\dot{m}_2 c_{p,2}} + \\frac{A U}{\\dot{m}_1 c_{p,1}}}}$"
      ],
      "text/plain": [
       "\\dot{m}_2*c_p,2*(-T_{1,0}*exp(A*U/(\\dot{m}_2*c_p,2) + A*U/(\\dot{m}_1*c_p,1)) + T_{1,0} + T_{2,l}*exp(A*U/(\\dot{m}_2*c_p,2) + A*U/(\\dot{m}_1*c_p,1)) - T_{2,l})/(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U/(\\dot{m}_2*c_p,2) + A*U/(\\dot{m}_1*c_p,1)))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dT1 = (T1_eq.rhs.subs({x: l})-T10).simplify()\n",
    "dT1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2} \\left(- T_{1,0} e^{\\frac{A U}{\\dot{m}_2 c_{p,2}} + \\frac{A U}{\\dot{m}_1 c_{p,1}}} + T_{1,0} + T_{2,l} e^{\\frac{A U}{\\dot{m}_2 c_{p,2}} + \\frac{A U}{\\dot{m}_1 c_{p,1}}} - T_{2,l}\\right)}{\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U}{\\dot{m}_2 c_{p,2}} + \\frac{A U}{\\dot{m}_1 c_{p,1}}}}$"
      ],
      "text/plain": [
       "\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2*(-T_{1,0}*exp(A*U/(\\dot{m}_2*c_p,2) + A*U/(\\dot{m}_1*c_p,1)) + T_{1,0} + T_{2,l}*exp(A*U/(\\dot{m}_2*c_p,2) + A*U/(\\dot{m}_1*c_p,1)) - T_{2,l})/(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U/(\\dot{m}_2*c_p,2) + A*U/(\\dot{m}_1*c_p,1)))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E = (m1*cp1*dT1).simplify()\n",
    "E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\dot{m}_2 c_{p,2} \\cdot \\left(1 - e^{\\frac{A U}{\\dot{m}_2 c_{p,2}}}\\right) \\left(T_{1,0} - T_{2,l}\\right)$"
      ],
      "text/plain": [
       "\\dot{m}_2*c_p,2*(1 - exp(A*U/(\\dot{m}_2*c_p,2)))*(T_{1,0} - T_{2,l})"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Emax = sympy.limit(E, m1, sympy.oo).simplify()\n",
    "Emax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.0"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subs2 = subs.copy()\n",
    "del subs2[m1]\n",
    "-100*subs2[m2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1ab1855dbb0>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.plot(\n",
    "    E.subs(subs2),\n",
    "    (m1, 0, 100 * -subs2[m2]),\n",
    "    xlabel=r\"$\\dot{m}_1$\",\n",
    "    ylabel=r\"P\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{\\dot{m}_2 \\tilde{m} c_{p,1} c_{p,2} \\left(T_{1,0} e^{\\frac{A U \\left(\\tilde{m} c_{p,1} - c_{p,2}\\right)}{\\dot{m}_2 \\tilde{m} c_{p,1} c_{p,2}}} - T_{1,0} - T_{2,l} e^{\\frac{A U \\left(\\tilde{m} c_{p,1} - c_{p,2}\\right)}{\\dot{m}_2 \\tilde{m} c_{p,1} c_{p,2}}} + T_{2,l}\\right)}{\\tilde{m} c_{p,1} - c_{p,2} e^{\\frac{A U \\left(\\tilde{m} c_{p,1} - c_{p,2}\\right)}{\\dot{m}_2 \\tilde{m} c_{p,1} c_{p,2}}}}$"
      ],
      "text/plain": [
       "-\\dot{m}_2*\\tilde{m}*c_p,1*c_p,2*(T_{1,0}*exp(A*U*(\\tilde{m}*c_p,1 - c_p,2)/(\\dot{m}_2*\\tilde{m}*c_p,1*c_p,2)) - T_{1,0} - T_{2,l}*exp(A*U*(\\tilde{m}*c_p,1 - c_p,2)/(\\dot{m}_2*\\tilde{m}*c_p,1*c_p,2)) + T_{2,l})/(\\tilde{m}*c_p,1 - c_p,2*exp(A*U*(\\tilde{m}*c_p,1 - c_p,2)/(\\dot{m}_2*\\tilde{m}*c_p,1*c_p,2)))"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mrel = sympy.Symbol(r\"\\tilde{m}\")\n",
    "Emrel = E.subs({m1: mrel*-m2}).simplify()\n",
    "Emrel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{\\dot{m}_2: -0.16,\n",
       " c_p,1: 4184,\n",
       " c_p,2: 4184,\n",
       " l: 20,\n",
       " A: 5,\n",
       " U: 500,\n",
       " T_{1,0}: 60,\n",
       " T_{2,l}: 90}"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subs2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1aca64baa90>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.plot(\n",
    "    Emrel.subs(subs2)/Emax.subs(subs2),\n",
    "    (mrel, 0, 100),\n",
    "    xlabel=r\"$\\tilde{m}$\",\n",
    "    ylabel=r\"P\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<string>:1: RuntimeWarning: divide by zero encountered in scalar divide\n",
      "<string>:1: RuntimeWarning: invalid value encountered in multiply\n",
      "<string>:1: RuntimeWarning: invalid value encountered in scalar divide\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1aca655d730>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.plot(\n",
    "    Emrel.subs(subs2)/Emax.subs(subs2),\n",
    "    (mrel, 0, 10),\n",
    "    xlabel=r\"$\\tilde{m}$\",\n",
    "    ylabel=r\"P\",\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 19603.4935777336$"
      ],
      "text/plain": [
       "19603.4935777336"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Emax.subs(subs2).simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.93867413625092$"
      ],
      "text/plain": [
       "0.938674136250920"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Emrel.subs(subs2).evalf(subs={mrel: 2})/Emax.subs(subs2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\dot{m}_1 \\cdot \\left(84028108.8 - 2007091.67076248 e^{\\frac{625}{1046 \\dot{m}_1}}\\right)}{4184.0 \\dot{m}_1 - 15.9902140755456 e^{\\frac{625}{1046 \\dot{m}_1}}}$"
      ],
      "text/plain": [
       "\\dot{m}_1*(84028108.8 - 2007091.67076248*exp(625/(1046*\\dot{m}_1)))/(4184.0*\\dot{m}_1 - 15.9902140755456*exp(625/(1046*\\dot{m}_1)))"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E.subs(subs2).simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.47486085199031$"
      ],
      "text/plain": [
       "1.47486085199031"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m1_99 = sympy.nsolve(0.90*Emax.subs(subs2)-E.subs(subs2), -subs2[m2])\n",
    "mrel99 = m1_99/-subs2[m2]\n",
    "mrel99"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We want to look at the influcence of $T_{2,l}$ and $\\dot{m}_2$ on $T_{1,l}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle T_{1}{\\left(l \\right)} = \\frac{T_{1,0} \\dot{m}_1 c_{p,1} + T_{2,l} \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}} + \\dot{m}_2 c_{p,2} \\left(T_{1,0} - T_{2,l}\\right)}{\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}}$"
      ],
      "text/plain": [
       "Eq(T_1(l), (T_{1,0}*\\dot{m}_1*c_p,1 + T_{2,l}*\\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)) + \\dot{m}_2*c_p,2*(T_{1,0} - T_{2,l}))/(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2))))"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T1l = T1_eq.rhs.subs({x: l}).simplify()\n",
    "T1l_eq = sympy.Eq(T1(l), T1l)\n",
    "T1l_eq\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d T_{2,l}} T_{1}{\\left(T_{2,l} \\right)} = \\frac{\\dot{m}_2 c_{p,2} \\left(e^{\\frac{A U}{\\dot{m}_2 c_{p,2}} + \\frac{A U}{\\dot{m}_1 c_{p,1}}} - 1\\right)}{\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U}{\\dot{m}_2 c_{p,2}} + \\frac{A U}{\\dot{m}_1 c_{p,1}}}}$"
      ],
      "text/plain": [
       "Eq(Derivative(T_1(T_{2,l}), T_{2,l}), \\dot{m}_2*c_p,2*(exp(A*U/(\\dot{m}_2*c_p,2) + A*U/(\\dot{m}_1*c_p,1)) - 1)/(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U/(\\dot{m}_2*c_p,2) + A*U/(\\dot{m}_1*c_p,1))))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d T_{2,l}^{2}} T_{1}{\\left(T_{2,l} \\right)} = 0$"
      ],
      "text/plain": [
       "Eq(Derivative(T_1(T_{2,l}), (T_{2,l}, 2)), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(1, 3):\n",
    "    display(sympy.Eq(T1(T2l).diff(T2l, i), sympy.diff(T1l, T2l, i).simplify()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1ab15be3ca0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subs2 = subs.copy()\n",
    "del subs2[T2l]\n",
    "\n",
    "sympy.plot(\n",
    "    T1_eq.rhs.subs(subs2 | {x: subs2[l]}),\n",
    "    (T2l, subs2[T10], 2 * subs2[T10]),\n",
    "    xlabel=\"$T_{2,l}$\",\n",
    "    ylabel=\"$T_{1,l}$\",\n",
    "    axis_center=(subs2[T10], 60),\n",
    "    xlim=[subs2[T10], 2 * subs2[T10]],\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d \\dot{m}_2} T_{1}{\\left(\\dot{m}_2 \\right)} = \\frac{- \\left(- A U + \\dot{m}_2 c_{p,2}\\right) \\left(T_{1,0} \\dot{m}_1 c_{p,1} + T_{2,l} \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}} + \\dot{m}_2 c_{p,2} \\left(T_{1,0} - T_{2,l}\\right)\\right) e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}} + \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}\\right) \\left(- A T_{2,l} U e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}} + \\dot{m}_2 c_{p,2} \\left(T_{1,0} + T_{2,l} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}} - T_{2,l}\\right)\\right)}{\\dot{m}_2 \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}\\right)^{2}}$"
      ],
      "text/plain": [
       "Eq(Derivative(T_1(\\dot{m}_2), \\dot{m}_2), (-(-A*U + \\dot{m}_2*c_p,2)*(T_{1,0}*\\dot{m}_1*c_p,1 + T_{2,l}*\\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)) + \\dot{m}_2*c_p,2*(T_{1,0} - T_{2,l}))*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)) + (\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)))*(-A*T_{2,l}*U*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)) + \\dot{m}_2*c_p,2*(T_{1,0} + T_{2,l}*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)) - T_{2,l})))/(\\dot{m}_2*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)))**2))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d \\dot{m}_2^{2}} T_{1}{\\left(\\dot{m}_2 \\right)} = \\frac{\\left(A^{2} T_{2,l} U^{2} \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}\\right)^{2} - 2 \\dot{m}_2 c_{p,2} \\left(- A U + \\dot{m}_2 c_{p,2}\\right) \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}\\right) \\left(- A T_{2,l} U e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}} + \\dot{m}_2 c_{p,2} \\left(T_{1,0} + T_{2,l} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}} - T_{2,l}\\right)\\right) - \\left(A^{2} U^{2} \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}\\right) - 2 \\dot{m}_2 c_{p,2} \\left(- A U + \\dot{m}_2 c_{p,2}\\right)^{2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}\\right) \\left(T_{1,0} \\dot{m}_1 c_{p,1} + T_{2,l} \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}} + \\dot{m}_2 c_{p,2} \\left(T_{1,0} - T_{2,l}\\right)\\right)\\right) e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}}{\\dot{m}_2^{3} c_{p,2} \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}\\right)^{3}}$"
      ],
      "text/plain": [
       "Eq(Derivative(T_1(\\dot{m}_2), (\\dot{m}_2, 2)), (A**2*T_{2,l}*U**2*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)))**2 - 2*\\dot{m}_2*c_p,2*(-A*U + \\dot{m}_2*c_p,2)*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)))*(-A*T_{2,l}*U*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)) + \\dot{m}_2*c_p,2*(T_{1,0} + T_{2,l}*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)) - T_{2,l})) - (A**2*U**2*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2))) - 2*\\dot{m}_2*c_p,2*(-A*U + \\dot{m}_2*c_p,2)**2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)))*(T_{1,0}*\\dot{m}_1*c_p,1 + T_{2,l}*\\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)) + \\dot{m}_2*c_p,2*(T_{1,0} - T_{2,l})))*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2))/(\\dot{m}_2**3*c_p,2*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)))**3))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(1, 3):\n",
    "    display(sympy.Eq(T1(m2).diff(m2, i), sympy.diff(T1l, m2, i).simplify()))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1ab137467f0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subs2 = subs.copy()\n",
    "del subs2[m2]\n",
    "\n",
    "sympy.plot(\n",
    "    T1_eq.rhs.subs(subs2 | {x: subs2[l]}),\n",
    "    (m2, -0.5 * subs2[m1], -2 * subs2[m1]),\n",
    "    xlabel=\"$\\dot{m}_1$\",\n",
    "    ylabel=\"$T_{1,l}$\",\n",
    "    axis_center=(-0.5 * subs2[m1], 74),\n",
    "    xlim=[-0.5 * subs2[m1], -2 * subs2[m1]],\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How much do we need to increase the mass flow $\\dot{m}_2$ to $\\dot{m}'_2 = f_m \\dot{m}_2$ to get the same increase in $T_{1,l}$ as for increasing $T_{2,l}$ to $T'_{2,l} = f_T T_{2,l}$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{T_{1,0} \\dot{m}_1 c_{p,1} + T_{1,0} \\dot{m}_2 c_{p,2} f_{m} + T_{2,l} \\dot{m}_2 c_{p,2} f_{m} e^{\\frac{A U}{\\dot{m}_2 c_{p,2} f_{m}} + \\frac{A U}{\\dot{m}_1 c_{p,1}}} - T_{2,l} \\dot{m}_2 c_{p,2} f_{m}}{\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} f_{m} e^{\\frac{A U}{\\dot{m}_2 c_{p,2} f_{m}} + \\frac{A U}{\\dot{m}_1 c_{p,1}}}} = \\frac{T_{1,0} \\dot{m}_1 c_{p,1} + T_{2,l} \\dot{m}_2 c_{p,2} f_{T} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}} + \\dot{m}_2 c_{p,2} \\left(T_{1,0} - T_{2,l} f_{T}\\right)}{\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2} e^{\\frac{A U \\left(\\dot{m}_1 c_{p,1} + \\dot{m}_2 c_{p,2}\\right)}{\\dot{m}_1 \\dot{m}_2 c_{p,1} c_{p,2}}}}$"
      ],
      "text/plain": [
       "Eq((T_{1,0}*\\dot{m}_1*c_p,1 + T_{1,0}*\\dot{m}_2*c_p,2*f_m + T_{2,l}*\\dot{m}_2*c_p,2*f_m*exp(A*U/(\\dot{m}_2*c_p,2*f_m) + A*U/(\\dot{m}_1*c_p,1)) - T_{2,l}*\\dot{m}_2*c_p,2*f_m)/(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*f_m*exp(A*U/(\\dot{m}_2*c_p,2*f_m) + A*U/(\\dot{m}_1*c_p,1))), (T_{1,0}*\\dot{m}_1*c_p,1 + T_{2,l}*\\dot{m}_2*c_p,2*f_T*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2)) + \\dot{m}_2*c_p,2*(T_{1,0} - T_{2,l}*f_T))/(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2*exp(A*U*(\\dot{m}_1*c_p,1 + \\dot{m}_2*c_p,2)/(\\dot{m}_1*\\dot{m}_2*c_p,1*c_p,2))))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm, fT = sympy.symbols(\"f_m f_T\")\n",
    "eq = sympy.Eq(T1l.subs({m2: fm*m2}).simplify(), T1l.subs({T2l: fT*T2l}).simplify())\n",
    "eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{- T_{1,0} \\dot{m}_1 c_{p,1} f_{m} e^{A U \\left(\\frac{1}{\\dot{m}_2 c_{p,2} f_{m}} + \\frac{1}{\\dot{m}_1 c_{p,1}}\\right)} + T_{1,0} \\dot{m}_1 c_{p,1} f_{m} + T_{1,0} \\dot{m}_1 c_{p,1} e^{A U \\left(\\frac{1}{\\dot{m}_2 c_{p,2}} + \\frac{1}{\\dot{m}_1 c_{p,1}}\\right)} - T_{1,0} \\dot{m}_1 c_{p,1} + T_{1,0} \\dot{m}_2 c_{p,2} f_{m} e^{A U \\left(\\frac{1}{\\dot{m}_2 c_{p,2}} + \\frac{1}{\\dot{m}_1 c_{p,1}}\\right)} - T_{1,0} \\dot{m}_2 c_{p,2} f_{m} e^{A U \\left(\\frac{1}{\\dot{m}_2 c_{p,2} f_{m}} + \\frac{1}{\\dot{m}_1 c_{p,1}}\\right)} + T_{2,l} \\dot{m}_1 c_{p,1} f_{m} e^{A U \\left(\\frac{1}{\\dot{m}_2 c_{p,2} f_{m}} + \\frac{1}{\\dot{m}_1 c_{p,1}}\\right)} - T_{2,l} \\dot{m}_1 c_{p,1} f_{m} - T_{2,l} \\dot{m}_2 c_{p,2} f_{m} e^{A U \\left(\\frac{1}{\\dot{m}_2 c_{p,2}} + \\frac{1}{\\dot{m}_1 c_{p,1}}\\right)} + T_{2,l} \\dot{m}_2 c_{p,2} f_{m} e^{A U \\left(\\frac{1}{\\dot{m}_2 c_{p,2}} + \\frac{1}{\\dot{m}_2 c_{p,2} f_{m}} + \\frac{2}{\\dot{m}_1 c_{p,1}}\\right)}}{T_{2,l} \\left(\\dot{m}_1 c_{p,1} e^{A U \\left(\\frac{1}{\\dot{m}_2 c_{p,2}} + \\frac{1}{\\dot{m}_1 c_{p,1}}\\right)} - \\dot{m}_1 c_{p,1} - \\dot{m}_2 c_{p,2} f_{m} e^{A U \\left(\\frac{1}{\\dot{m}_2 c_{p,2} f_{m}} + \\frac{1}{\\dot{m}_1 c_{p,1}}\\right)} + \\dot{m}_2 c_{p,2} f_{m} e^{A U \\left(\\frac{1}{\\dot{m}_2 c_{p,2}} + \\frac{1}{\\dot{m}_2 c_{p,2} f_{m}} + \\frac{2}{\\dot{m}_1 c_{p,1}}\\right)}\\right)}$"
      ],
      "text/plain": [
       "(-T_{1,0}*\\dot{m}_1*c_p,1*f_m*exp(A*U*(1/(\\dot{m}_2*c_p,2*f_m) + 1/(\\dot{m}_1*c_p,1))) + T_{1,0}*\\dot{m}_1*c_p,1*f_m + T_{1,0}*\\dot{m}_1*c_p,1*exp(A*U*(1/(\\dot{m}_2*c_p,2) + 1/(\\dot{m}_1*c_p,1))) - T_{1,0}*\\dot{m}_1*c_p,1 + T_{1,0}*\\dot{m}_2*c_p,2*f_m*exp(A*U*(1/(\\dot{m}_2*c_p,2) + 1/(\\dot{m}_1*c_p,1))) - T_{1,0}*\\dot{m}_2*c_p,2*f_m*exp(A*U*(1/(\\dot{m}_2*c_p,2*f_m) + 1/(\\dot{m}_1*c_p,1))) + T_{2,l}*\\dot{m}_1*c_p,1*f_m*exp(A*U*(1/(\\dot{m}_2*c_p,2*f_m) + 1/(\\dot{m}_1*c_p,1))) - T_{2,l}*\\dot{m}_1*c_p,1*f_m - T_{2,l}*\\dot{m}_2*c_p,2*f_m*exp(A*U*(1/(\\dot{m}_2*c_p,2) + 1/(\\dot{m}_1*c_p,1))) + T_{2,l}*\\dot{m}_2*c_p,2*f_m*exp(A*U*(1/(\\dot{m}_2*c_p,2) + 1/(\\dot{m}_2*c_p,2*f_m) + 2/(\\dot{m}_1*c_p,1))))/(T_{2,l}*(\\dot{m}_1*c_p,1*exp(A*U*(1/(\\dot{m}_2*c_p,2) + 1/(\\dot{m}_1*c_p,1))) - \\dot{m}_1*c_p,1 - \\dot{m}_2*c_p,2*f_m*exp(A*U*(1/(\\dot{m}_2*c_p,2*f_m) + 1/(\\dot{m}_1*c_p,1))) + \\dot{m}_2*c_p,2*f_m*exp(A*U*(1/(\\dot{m}_2*c_p,2) + 1/(\\dot{m}_2*c_p,2*f_m) + 2/(\\dot{m}_1*c_p,1)))))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = sympy.solve(eq, fT)[0].simplify()\n",
    "sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/b0+T0wGOhSIHAHAI8cfS9fLKfVq3/6QkydvTTcNuaKwxXcNUo5qXyekAx0SRAwCY6tDJLL3+3X4t33lCkuThZtGAjvX16K3NFOjvbXI6wLFR5AAApjh+Lldvfn9An289qmK7IYtFuisyWBP+1FwNa/maHQ9wChQ5AEClOpdToBmxhzRrfZIKiuySpO4tA/V4j+YKD/I3OR3gXChyAIBKkVdYrJk/J2lG7EFl5hVJkjo1rqlJd4SrXcPrTE4HOCeKHACgQhUV27V46zG9vmq/UjJKdmMID/LTkz3DdUvzOrJY2A8VuFYUOQBAhTAMQ9/vSdPL3+7VgbQsSVJIDR/97fbmuiuKDe2B8kCRAwCUuy2Hz+if3+zVpqSSteBqVPPUI92aanDnhuzGAJQjihwAoNwcTMvSy9/u1Xe7UyWVrAU3oktjPdS1iQJ8WMwXKG8UOQDAH3YqK1///n6/5m9MVrHdkJtF6te+vsZ3b66gANaCAyoKRQ4AcM1yC4r18c+Jeif2kLLyS2aidm8ZqKd6tlDTun4mpwNcH0UOAHDV7HZDi7cd06sr95XORG0TGqC/92qpTmG1TE4HVB0UOQDAVfnpwCm9tGKPdp/IkFQyE3XSHS3Up02w3JiJClQqihwA4IrsT83USyv2KHZfyab2ft4eeqRbUw29oREzUQGTUOQAAJd0Oitfb3y/X/N+OSK7UbKp/eDODTXutmaq6etldjygSqPIAQAuKL+oWLPXJ+k/a/63pVaPiEA91bOlGtdmU3vAEVDkAABlGIahlbtSNe2bPTp8OkeSFBHsryl/vl6dmcgAOBSKHACgVPyxdD2/bLd+STwjSarjZ9UTPVronuhQttQCHBBFDgCgtIw8vbJynz7felSGIVk93PTgzWEa07WJfK38qgAcFT+dAFCF5RcV66OfEjV9zUFlFxRLku6MDNaTPcMVUsPH5HQALsfN7AC/tW7dOvXp00fBwcGyWCxaunTpZV8TGxur6OhoWa1WNW3aVLNmzSrz9eLiYk2ZMkWNGzeWj4+PmjRpoueff16GYVTMmwAAJ2AYhlbtTtXtb6zTy9/uU3ZBsaLq19Div96gtwa2pcQBTsKhrshlZ2crMjJSI0aM0N13333Z4xMTE9W7d2+NGTNGc+fO1erVqzVq1CjVq1dPPXr0kCT961//0jvvvKPZs2crIiJCmzdv1vDhwxUQEKBx48ZV9FsCAIdzMC1TU7/erR8PnJIk1fWz6qme4eobFcKCvoCTsRgOemnKYrFoyZIl6tu370WPefLJJ7V8+XLFx8eXjg0YMEDnzp3Tt99+K0n685//rMDAQH300Uelx9xzzz3y8fHRp59+ekVZMjIyFBAQoPT0dPn7+1/bGwIAk6XnFuqt1Qc0e32SiuyGvNzdNPKmxhrbramq8xwc4JQc6tbq1YqLi1P37t3LjPXo0UNxcXGln99www1avXq19u/fL0navn27fvrpJ/Xs2fOi3zc/P18ZGRllPgDAWRXbDS3YeES3vhqrj35KVJHdUPeWgfpuws168o5wShzgxJz6pzclJUWBgYFlxgIDA5WRkaHc3Fz5+PjoqaeeUkZGhsLDw+Xu7q7i4mK9+OKLGjRo0EW/77Rp0zR16tSKjg8AFW5z0hn939e7FH+s5B+kTer46tk+EeravI7JyQCUB6cucldi4cKFmjt3rubNm6eIiAjZbDaNHz9ewcHBGjp06AVfM3nyZE2cOLH084yMDNWvX7+yIgPAH5aakadpK/Zoqe24JMnP6qHxf2quITEN5enu1DdjAPyGUxe5oKAgpaamlhlLTU2Vv7+/fHxKZlw98cQTeuqppzRgwABJUuvWrXX48GFNmzbtokXOarXKarVWbHgAqACFxXbNXp+kN1btV3ZBsSwWqX/7+nq8RwvVrs7fa4CrceoiFxMToxUrVpQZW7VqlWJiYko/z8nJkZtb2X99uru7y263V0pGAKgscYdO67mv4rU/NUuSFFW/hp6/q5VahwaYnAxARXGoIpeVlaWDBw+Wfp6YmCibzaaaNWuqQYMGmjx5so4dO6Y5c+ZIksaMGaO3335bkyZN0ogRI7RmzRotXLhQy5cvL/0effr00YsvvqgGDRooIiJC27Zt0+uvv64RI0ZU+vsDgIqQmpGnF5fv0VfbS26j1vT10lN3hOvedqEsJwK4OIdafiQ2NlbdunU7b3zo0KGaNWuWhg0bpqSkJMXGxpZ5zYQJE7R7926FhoZqypQpGjZsWOnXMzMzNWXKFC1ZskRpaWkKDg7WwIED9eyzz8rLy+uKcrH8CABHVFhs16yfk/Tv7/93G3VQpwZ6/PYWqlHtyv5+A+DcHKrIOSqKHABHE3fotJ79Ml4H0riNClRlDnVrFQBwadxGBfBbFDkAcAJFxXZ9suGwXvtuv7Lyi2SxSIM7NdTfbm/ObVSgCqPIAYCDsyWf09+X7NSu4yWL+kbWr6EXuI0KQBQ5AHBY6bmFenXlPn36y2EZhuTv7aEne4ZrYIcG3EYFIIkiBwAOxzAMfbX9uJ5ftkensvIlSXe3DdHkXi1Vx49FfQH8D0UOABxIwsksTfkyXj8fPC1JCqvjqxf6ttINTWqbnAyAI6LIAYADyCss1ozYQ3o39pAKiu2yerjp0VubavTNYbJ6uJsdD4CDosgBgMnWHzqlvy+JV+KpbElS1+Z19I+7ItSwlq/JyQA4OoocAJjkbHaBXlqxR4u2HJUk1fWz6rk+EerVOkgWC5MZAFweRQ4AKplhGPrSdlz/WLZbZ7ILSrfWmnRHuPy9Pc2OB8CJUOQAoBIdOZ2jvy/dqR8PnJIkNQ+srml3t1a7hjVNTgbAGVHkAKASFBbb9dFPifr39/uVV2iXl4ebxt3aVA/e3EReHm5mxwPgpChyAFDBdhw9pye/2Kk9J0p2ZogJq6WX7m6txrWZzADgj6HIAUAFyS0o1uur9umjnxJlN6Qa1Tz1914tdW+7UCYzACgXFDkAqADrD57SU4t36siZHEnSnZHBerbP9apdnZ0ZAJQfihwAlKP03EK9tHyPPtucLEmqF+CtF//SSreGB5qcDIArosgBQDn5Nv6Epny5SyczS/ZHHdy5gZ68I1x+LCkCoIJQ5ADgDzqZma9nv4zXN/EpkqSw2r765z1t1LExS4oAqFgUOQC4RoZh6Kvtx/XcV7t0LqdQ7m4WPXRzmMbd1kzenuyPCqDiUeQA4BqkZeTp6SXx+n5PqiTp+nr+evneNmoVEmByMgBVCUUOAK6CYRj6Yusx/ePrXcrIK5Knu0WP3tpMD9/SRJ7uLOwLoHJR5ADgCp1Iz9XTi3fqh30nJUmtQwL0yn1tFB7kb3IyAFUVRQ4ALsMwDC3cnKwXlu1RZn6RvNzdNP5PzfTgTWHy4CocABNR5ADgEo6fy9WTX+wo3eQ+qn4NvXJvGzUL9DM5GQBQ5ADgggzD0KItR/X817uVmV8kq4ebHr+9hUbc2FjubmyvBcAxUOQA4HfSMvI0efFOrd6bJkmKblBDr94XqbA61U1OBgBlUeQA4FeGYejrHSc0ZWm80nML5eXupom3N9fom8K4CgfAIVHkAEDS6ax8TfkyXit2luzO0CrEX6/3i1JznoUD4MAocgCqvJW7UvT3JTt1KqtAHm4l68L9tRvrwgFwfBQ5AFVWem6hpn61S4u3HZMkNQ+srtf7RbE7AwCnQZEDUCX9dOCUHl+0XSkZeXKzSA91baLx3ZvJ6sEeqQCcB0UOQJWSV1isf36zV7PWJ0mSGtf21av3Rapdw+vMDQYA14AiB6DK2HH0nCZ8ZtOhk9mSpMGdG+jpXi1VzYu/CgE4J/72AuDyiortmhF7SG+tPqAiu6G6fla9fG8b3dKirtnRAOAPocgBcGlJp7I1/jObbMnnJEm9W9fTC31b6TpfL3ODAUA5oMgBcEmGYeizTcn6x7Ldyikolp+3h56/q5XuigqWxcLivgBcA0UOgMs5k12gp77Yoe92p0qSOofV1Gv9ohRSw8fkZABQvihyAFzK2v0n9fii7TqZmS9Pd4sev72FRt8UJje22ALggihyAFzC75cVaVq3uv7dn8V9Abg2ihwAp7c3JUPj5m/T/tQsSdLQmIZ6qmdL+XixuC8A10aRA+C0DMPQnLjDenHFHhUU2VW7ulWv3NdG3VhWBEAVQZED4JROZ+Vr0uc7tHpvmiTp1vC6evneNqpd3WpyMgCoPBQ5AE7nxwMnNXFhyYQGLw83Pd0zXENvaMSyIgCqHIocAKdRUGTXq9/t0/vrEiRJzepW11sD26plPX+TkwGAOShyAJxCwsksjVuwTfHHMiSV7JP6917XM6EBQJVGkQPg8L7YclRTvoxXTkGxalTz1Mv3tNHtEUFmxwIA01HkADis7PwiTVkar8Xbjkkq2aHh3/3bKijA2+RkAOAYKHIAHFL8sXQ9On+bEk9ly80iTejeXH/t1lTu7NAAAKUocgAcimEYmr0+SS+t2KuCYrvqBXjrzQFt1bFxTbOjAYDDocgBcBjncgr0xOc7tOrXze67twzUK/e20XW+XiYnAwDHRJED4BC2HD6rR+dt1fH0PHm5u+npXqwNBwCXQ5EDYCrDMPThj4n617d7VWQ31KhWNb19fzSb3QPAFaDIATDNuZwCPb5ou77fU7LN1p/b1NO0u1vLz9vT5GQA4BwocgBMsfXIWT06b5uOncuVl4ebnutzve7v2IBbqQBwFShyACrVhW6lTh8UrYhgbqUCwNWiyAGoNNxKBYDyRZEDUClsyec0du7W0lupz/75eg3qxK1UAPgjKHIAKpRhGPp0w2H9Y9luFRYzKxUAyhNFDkCFyc4v0tNLdupL23FJ0h0RQXr5vjby51YqAJQLihyACnEwLVMPf7pVB9Ky5O5m0eSe4Rp5Y2NupQJAOaLIASh3X28/rie/2KGcgmLV9bNq+qBodWjEXqkAUN7czA7wW+vWrVOfPn0UHBwsi8WipUuXXvY1sbGxio6OltVqVdOmTTVr1qzzjjl27JgGDx6sWrVqycfHR61bt9bmzZvL/w0AVVxBkV3/99UuPTp/m3IKihUTVkvLx91EiQOACuJQRS47O1uRkZGaPn36FR2fmJio3r17q1u3brLZbBo/frxGjRqllStXlh5z9uxZdenSRZ6envrmm2+0e/duvfbaa7ruuusq6m0AVdLxc7nq/36cZq1PkiT99ZYm+mRkR9Xxs5obDABcmMUwDMPsEBdisVi0ZMkS9e3b96LHPPnkk1q+fLni4+NLxwYMGKBz587p22+/lSQ99dRT+vnnn/Xjjz9ec5aMjAwFBAQoPT1d/v7+1/x9AFe1/uApPTJ/m85kF8jf20Nv9I/SbS0DzY4FAC7Poa7IXa24uDh17969zFiPHj0UFxdX+vlXX32l9u3b67777lPdunXVtm1bffDBB5f8vvn5+crIyCjzAeB8hmHo/XWHNPijX3Qmu0ARwf5aPu4mShwAVBKnLnIpKSkKDCz7CyMwMFAZGRnKzc2VJCUkJOidd95Rs2bNtHLlSj388MMaN26cZs+efdHvO23aNAUEBJR+1K9fv0LfB+CMsvKL9Mi8bXppxV7ZDeme6FB98fANql+zmtnRAKDKcPlZq3a7Xe3bt9dLL70kSWrbtq3i4+P17rvvaujQoRd8zeTJkzVx4sTSzzMyMihzwG8cOpmlMZ9s0YG0LHm6W/RsnwgNZpcGAKh0Tl3kgoKClJqaWmYsNTVV/v7+8vHxkSTVq1dP119/fZljWrZsqS+++OKi39dqtcpq5QFt4EJW7krR3xZuV1Z+ker6WfXO4Gi1a8isVAAwg1MXuZiYGK1YsaLM2KpVqxQTE1P6eZcuXbRv374yx+zfv18NGzaslIyAqyi2G3pj1X69/cNBSVLHRjX19qC2quvnbXIyAKi6HOoZuaysLNlsNtlsNkkly4vYbDYdOXJEUsktzyFDhpQeP2bMGCUkJGjSpEnau3evZsyYoYULF2rChAmlx0yYMEEbNmzQSy+9pIMHD2revHl6//33NXbs2Ep9b4AzS88p1IhZm0pL3LAbGmnu6E6UOAAwmUMtPxIbG6tu3bqdNz506FDNmjVLw4YNU1JSkmJjY8u8ZsKECdq9e7dCQ0M1ZcoUDRs2rMzrly1bpsmTJ+vAgQNq3LixJk6cqNGjR19xLpYfQVW2PzVTo+ds1uHTOfL2dNM/726jvm1DzI4FAJCDFTlHRZFDVfVtfIr+ttCm7IJihdTw0ftD2ikiOMDsWACAXzn1M3IAKobdbujfqw/ordUHJEkxYbU0fVC0avp6mZwMAPBbFDkAZWTmFWrCZ9v1/Z6SGeHDuzTS071aytPdoR6pBQCIIgfgNxJOZmn0nM06dDJbXh5ueukvrXVvu1CzYwEALoIiB0CS9MPeNI1bsE2ZeUUK8vfWuw+0U1T9GmbHAgBcAkUOqOIMw9B76xL0r2/3yjCk9g2v04zB0SwtAgBOgCIHVGF5hcV6evFOLd52TJI0sGMDTb0zQl4ePA8HAM6AIgdUUWkZeXrwky2yJZ+Tu5tFz/W5Xg90bsh+qQDgRChyQBW082i6Rs/ZrJSMPAX4eGrGoGh1aVrb7FgAgKtEkQOqmK+3H9cTn29XXqFdTer46qOhHdSotq/ZsQAA14AiB1QRdruhf3+/X2+tKdkv9ZYWdfTWwLby9/Y0ORkA4FpR5IAqIKegSBM/265vd6VIkh68OUxP3hEudzeehwMAZ0aRA1xcSnqeRs7epF3HM+Tl7qaX7maRXwBwFRQ5wIXtOHpOo2ZvVlpmvmr5eum9B9qpfaOaZscCAJSTP7RY1DvvvFNeOQCUs292nlC/9+KUlpmv5oHVtXRsF0ocALiYP1TkPvjgg/LKAaCcGIah6T8c1MNztyqv0K5bWtTRFw/foPo1q5kdDQBQzri1CriQ/KJiTV68U4u3luzUMLxLI/29V0t5uLNTAwC4oj9U5Hbt2qWYmBhFREQoIiJCrVq1UkREhIKDg8srH4ArdDa7QA99skUbk87I3c2iqXdGaHDnhmbHAgBUoCv+Z/qkSZOUl5dXZqxFixZ6//331b17d50+fVozZsxQ165dVadOHd10003lHhbAhSWeytbd76zXxqQz8rN6aNbwDpQ4AKgCLIZhGFdyoJeXl5KTkxUYGKhhw4Zp+vTpuvHGG7Vt27bzjs3Ly9OePXvUtm3bcg9shoyMDAUEBCg9PV3+/v5mxwHK2Jh4Rg9+slnncgoVUsNHM4d3UPNAP7NjAQAqwRVfkQsODpbNZpMkffLJJ8rOztaYMWMueKy3t7fLlDjAkS3ZdlSDP/xF53IKFVm/hpaO7UKJA4Aq5Iqfkfvb3/6mPn36qFOnTpKkuXPnqkuXLsrNzZWPj0+FBQRwPsMw9O/vD+jN1QckST1bBen1flHy8XI3ORkAoDJd8a1VSdqxY4e+/vprTZkyRWFhYUpKSpLFYlHTpk0VGRmpqKgoRUZGqmfPnhWZudJxaxWOpKDIrqe+2KHF20pmpj7UNUxP9giXG9ttAUCVc1VF7r+aNWumuLg4+fr6aseOHbLZbKUf8fHxyszMrIispqHIwVGk5xZqzCdbFJdwWu5uFr3Qt5UGdmxgdiwAgEmuqchdimEYslhc68oARQ6O4Pi5XA2buVH7U7Pk6+WuGYPbqWvzOmbHAgCYqNwXBHa1Egc4gl3H0zVi1ialZuSrrp9VM4d3UERwgNmxAAAmY2cHwMGt3X9Sf/10i7ILitU8sLpmDu+okBpMMAIAUOQAh/bZpiN6ekm8iu2GYsJq6d0H2inAx9PsWAAAB0GRAxyQYRh6Y9V+vbXmoCTp7rYh+uc9beTlwZ6pAID/ocgBDqaw2K7Ji3fq8y1HJUnjbm2qCX9qzvOnAIDzUOQAB5KdX6S/zt2qtftPyt3Nohf7ttIAlhcBAFwERQ5wEKey8jVi1ibtOJoub083zRgUrVvDA82OBQBwYBQ5wAEcPp2tIR9v1OHTObqumqc+HtZBbRtcZ3YsAICDo8gBJttx9JyGz9yk09kFCr3OR3NGdFRYnepmxwIAOAGKHGCi2H1p+uvcrcopKFZEsL9mDu+gun7eZscCADgJihxgksVbj2rS5ztUZDd0Y9PaemdwtPy8WSMOAHDlKHKACT5Yl6AXV+yRJN0VFaxX7o1kjTgAwFWjyAGVyDAM/fObvXpvXYIkadSNjfV0r5Zyc2ONOADA1aPIAZWkqNiup36z0O9TPcP10M1hLPQLALhmFDmgEuQWFOuReVu1em+a3N0smnZ3a/VrX9/sWAAAJ0eRAypYek6hRs7epM2Hz8rq4abp90er+/Us9AsA+OMockAFSsvI05CPN2pvSqb8vD308bAO6tCoptmxAAAugiIHVJAjp3M0+KNfdORMjur4WTVnREe1rOdvdiwAgAuhyAEVYG9KhoZ8tFFpmflqULOaPh3ZSQ1qVTM7FgDAxVDkgHK29chZDZ+5Sem5hWoR6KdPRnZUXX92awAAlD+KHFCOfjxwUg/O2aLcwmJFN6ihmcM6KqAauzUAACoGRQ4oJ9/sPKFxC7apsNjQTc1q670H2qmaFz9iAICKw28ZoBws2pysJ7/YIbsh9W5dT2/0j2LLLQBAhaPIAX/QzJ8TNfXr3ZKkAR3q68W/tJY7W24BACoBRQ64RoZh6O01B/Xaqv2SpJE3NtYzvVuy5RYAoNJQ5IBrYBiGpn2zV++vS5Akje/eTI/d1owSBwCoVBQ54CrZ7YamfBmvub8ckSQ907ulRt0UZnIqAEBVRJEDrkJRsV2TvtihxVuPyWKRpv2ltQZ0bGB2LABAFUWRA65QYbFd4z+zafmOE3J3s+j1fpG6KyrE7FgAgCqMIgdcgfyiYj0yb5tW7U6Vp7tF/xkYrTtaBZkdCwBQxVHkgMvIKyzWQ59s0dr9J+Xl4ab3BrdTt/C6ZscCAIAiB1xKdn6RRs3erLiE0/LxdNeHQ9urS9PaZscCAEASRQ64qIy8Qg2fuUlbDp9VdauHZg7voA6NapodCwCAUhQ54ALO5RRoyMcbteNouvy9PTRnZCdF1a9hdiwAAMqgyAG/cyorX4M//EV7UzJV09dLn4zsqIjgALNjAQBwHooc8BtpGXm6/8NfdDAtS3X8rJo7qpOaB/qZHQsAgAtyMzvAb61bt059+vRRcHCwLBaLli5detnXxMbGKjo6WlarVU2bNtWsWbMueuw///lPWSwWjR8/vtwyw3WkZuRpwPsbdDAtS/UCvLXwoRhKHADAoTlUkcvOzlZkZKSmT59+RccnJiaqd+/e6tatm2w2m8aPH69Ro0Zp5cqV5x27adMmvffee2rTpk15x4YLSEkvKXEJp7IVUsNHnz0Yo8a1fc2OBQDAJTnUrdWePXuqZ8+eV3z8u+++q8aNG+u1116TJLVs2VI//fST3njjDfXo0aP0uKysLA0aNEgffPCBXnjhhXLPDed2/FyuBn6wQYdP5yikho8WPNhZ9WtWMzsWAACX5VBX5K5WXFycunfvXmasR48eiouLKzM2duxY9e7d+7xjLyY/P18ZGRllPuCajp3L1YD3S0pc/Zo++uwhShwAwHk41BW5q5WSkqLAwMAyY4GBgcrIyFBubq58fHy0YMECbd26VZs2bbri7ztt2jRNnTq1vOPCwSSfydHADzbo6NlcNahZTfMf7KyQGj5mxwIA4Io59RW5y0lOTtZjjz2muXPnytvb+4pfN3nyZKWnp5d+JCcnV2BKmCH5TI4GvF9S4hrVqqbPHqLEAQCcj1NfkQsKClJqamqZsdTUVPn7+8vHx0dbtmxRWlqaoqOjS79eXFysdevW6e2331Z+fr7c3d3P+75Wq1VWq7XC88McR06XXIk7di5XjWv7av7ozgoKuPKiDwCAo3DqIhcTE6MVK1aUGVu1apViYmIkSbfddpt27txZ5uvDhw9XeHi4nnzyyQuWOLi2w6ezNeD9DTqRnqewOiUlLtCfEgcAcE4OVeSysrJ08ODB0s8TExNls9lUs2ZNNWjQQJMnT9axY8c0Z84cSdKYMWP09ttva9KkSRoxYoTWrFmjhQsXavny5ZIkPz8/tWrVqsz/h6+vr2rVqnXeOFxf8pkcDfy1xDX5tcTVpcQBAJyYQz0jt3nzZrVt21Zt27aVJE2cOFFt27bVs88+K0k6ceKEjhw5Unp848aNtXz5cq1atUqRkZF67bXX9OGHH5ZZegSQ/vdM3PH/Xol7kBIHAHB+FsMwDLNDOLqMjAwFBAQoPT1d/v7+ZsfBVTp2Llf934vT0bMlz8QteJDbqQAA1+BQV+SA8nYiPVcDf52d2rBWNZ6JAwC4FIocXFZKep4Gvr9BR87klKwTx+xUAICLocjBJaVl5On+DzYo6XSOQq/z0fwHOyuYdeIAAC6GIgeXk5aZpwEfbFDCqWyF1PDR/NEs9gsAcE0UObiUU1n5uv+DX5RwMlvBAd6aP5q9UwEArosiB5dxLqdAgz/8RQfTshTk7635D3ZWg1qUOACA66LIwSVk5BXqgY82am9KpmpXt2re6E5qWMvX7FgAAFQoihycXnZ+kYbP3KSdx9JV09dL80Z3Ulid6mbHAgCgwlHk4NTyCos1avZmbTl8Vv7eHvpkZEc1D/QzOxYAAJWCIgenlV9UrAc/2aK4hNOqbvXQnJGdFBEcYHYsAAAqDUUOTqmw2K5H5m3Tuv0n5ePprpnDOyiqfg2zYwEAUKkocnA6RcV2jf/MplW7U+Xl4aYPh7ZXh0Y1zY4FAEClo8jBqdjthp78YqeW7zghT3eL3hvcTl2a1jY7FgAApqDIwWkYhqH/+3qXvth6VO5uFv1nYLS6hdc1OxYAAKahyMFpvPrdPs2JOyyLRXrtvkjd0SrI7EgAAJiKIgen8O7aQ5r+wyFJ0gt9W6lv2xCTEwEAYD6KHBzepxsO65/f7JUkPdUzXIM6NTQ5EQAAjoEiB4e2dNsxTfkyXpI0tlsTjenaxOREAAA4DoocHNZ3u1L0t0XbZRjS0JiGevz2FmZHAgDAoVDk4JB+PnhKj8zbpmK7obujQ/RcnwhZLBazYwEA4FAocnA4W4+c1eg5m1VQbNcdEUF6+Z42cnOjxAEA8HsUOTiUfSmZGj5zk3IKinVTs9p6c2CUPNz5YwoAwIXwGxIOI/lMjoZ8/IvScwsV3aCG3nugnawe7mbHAgDAYVHk4BBOZeXrgY9+UWpGvloE+unjYR1UzcvD7FgAADg0ihxMl5lXqKEfb1TS6RyFXuejOSM7qkY1L7NjAQDg8ChyMFVeYbFGzd6sXcczVLu6lz4Z2UmB/t5mxwIAwClQ5GCaomK7xs3fpl8Sz8jP6qFZwzuqcW1fs2MBAOA0KHIwhWEYenrJTn23O1VeHm76YGh7tQoJMDsWAABOhSIHU/zz271auPmo3CzS2wPbqnNYLbMjAQDgdChyqHTvrzuk99YmSJL+eU8b3R4RZHIiAACcE0UOlerzLUf10oq9kqSne4WrX/v6JicCAMB5UeRQaX7Yl6Ynv9ghSXqoa5gevLmJyYkAAHBuFDlUClvyOf31060qthu6OzpET90RbnYkAACcHkUOFS7hZJZGzNqk3MJi3dy8jv51TxtZLBazYwEA4PQocqhQaZl5GvLxRp3JLlCb0AC9Myhanu78sQMAoDzwGxUVJjOvUMM+3qSjZ3PVqFY1fTysg3yt7J8KAEB5ocihQuQXFWvMp1u0+0TJ1ltzRnRS7epWs2MBAOBSKHIod3a7occX7dDPB0/L18tdM4d1VINa1cyOBQCAy6HIody9tGKPvt5+XB5uFr37QDu1DmXrLQAAKgJFDuXq458S9eFPiZKkV++L1E3N6picCAAA10WRQ7n5ZucJPb98tyRp0h0t1LdtiMmJAABwbRQ5lIsth89o/Gc2GYY0uHMDPdyVXRsAAKhoFDn8YQknszRq9mblF9nVvWVd/V+fCBb8BQCgElDk8IeczMzX0JkbdTanUJGhAXprYFt5sOAvAACVgt+4uGY5BUUaOXuTks/kqkHNavpoWAdV82LBXwAAKgtFDtek2G5o3Pxt2nE0XddV89Ss4R1Y8BcAgEpGkcM1eX7Zbn2/J01WDzd9OLS9wupUNzsSAABVDkUOV+3jnxI1a32SJOmN/lFq17CmuYEAAKiiKHK4Kt/tSildK25yz3D1al3P5EQAAFRdFDlcsZ1H0/XYgpK14gZ2bKAHbw4zOxIAAFUaRQ5X5Ni5XI2YvUm5hcW6qVlt/eMu1ooDAMBsFDlcVmZeoUbO2qSTmflqEein6YOi5clacQAAmI7fxrikwmK7xs7bpr0pmarjZ9XHwzvI39vT7FgAAEAUOVyCYRh67qtdWrf/pHw83fXx0A4KqeFjdiwAAPArihwu6oMfEzTvlyOyWKQ3B0SpdWiA2ZEAAMBvUORwQd/Gp2jaN3slSc/0vl63RwSZnAgAAPweRQ7niT+WrgmflSwz8kDnhhrRpZHZkQAAwAVQ5FBGakaeRs3eXLrMyHN9rmeZEQAAHBRFDqVyC4o1es5mpWTkqUkdX719f7Q8WGYEAACHxW9pSJLsdkOPL9quHUfTdV01T308rIMCfFhmBAAAR0aRgyTp39/v1/KdJ+TpbtG7g9upYS1fsyMBAIDLcKgit27dOvXp00fBwcGyWCxaunTpZV8TGxur6OhoWa1WNW3aVLNmzSrz9WnTpqlDhw7y8/NT3bp11bdvX+3bt69i3oCT+tJ2TG+tOShJevEvrdUprJbJiQAAwJVwqCKXnZ2tyMhITZ8+/YqOT0xMVO/evdWtWzfZbDaNHz9eo0aN0sqVK0uPWbt2rcaOHasNGzZo1apVKiws1O23367s7OyKehtOZcvhs3ri8x2SpIduDlO/9vVNTgQAAK6UxTAMw+wQF2KxWLRkyRL17dv3osc8+eSTWr58ueLj40vHBgwYoHPnzunbb7+94GtOnjypunXrau3atbr55puvKEtGRoYCAgKUnp4uf3//q3ofjuzo2Rz1nf6zTmUVqHvLQL33QDu5uzFDFQAAZ+FQV+SuVlxcnLp3715mrEePHoqLi7voa9LT0yVJNWvWvOgx+fn5ysjIKPPharLzizRq9madyipQy3r+enNAFCUOAAAn49RFLiUlRYGBgWXGAgMDlZGRodzc3POOt9vtGj9+vLp06aJWrVpd9PtOmzZNAQEBpR/167vW7Ua73dCEz2zam5Kp2tWt+nBoe/laPcyOBQAArpJTF7mrNXbsWMXHx2vBggWXPG7y5MlKT08v/UhOTq6khJXj39/v13e7U+Xl7qb3h7RTSA0fsyMBAIBr4NSXYYKCgpSamlpmLDU1Vf7+/vLxKVtOHnnkES1btkzr1q1TaGjoJb+v1WqV1Wot97yOYNmO46UzVF+6u7WiG1xnciIAAHCtnPqKXExMjFavXl1mbNWqVYqJiSn93DAMPfLII1qyZInWrFmjxo0bV3ZMhxF/LF2PL9ouSRp9U2Pd2+7ShRYAADg2hypyWVlZstlsstlskkqWF7HZbDpy5IikklueQ4YMKT1+zJgxSkhI0KRJk7R3717NmDFDCxcu1IQJE0qPGTt2rD799FPNmzdPfn5+SklJUUpKygWfoXNlJzPz9eCczcortKtr8zp6qmdLsyMBAIA/yKGWH4mNjVW3bt3OGx86dKhmzZqlYcOGKSkpSbGxsWVeM2HCBO3evVuhoaGaMmWKhg0bVvr1i234PnPmzDLHXYqzLz9SUGTX/R9s0ObDZxVW21dLxnZh+y0AAFyAQxU5R+XMRc4wDD31xU59tjlZft4eWjq2i5rUqW52LAAAUA4c6tYqyt/s9Un6bHOy3CzSfwa2pcQBAOBCKHIu7KcDp/T88j2SpMk9W+qWFnVNTgQAAMoTRc5FHT6drbHztqrYbuju6BCNuqnqztYFAMBVUeRcUHZ+kR6cs0XpuYWKql9DL/2l9UUnfQAAAOdFkXMxhmHoic+3a19qpur4WfXeA+3k7eludiwAAFABKHIu5t21CVqxM0We7ha9Ozhagf7eZkcCAAAVhCLnQtbuP6mXV+6VJP3fnRFq17CmyYkAAEBFosi5iMOns/XovK0yDGlAh/q6v2MDsyMBAIAKRpFzAf+d3JCRV6So+jU09a4IJjcAAFAFUOScnGEYmvTFjtLJDe8ObierB5MbAACoCihyTu69dQlavuOEPN0temdQtIICmNwAAEBVQZFzYuv2n9TL35ZMbniuT4TaN2JyAwAAVQlFzkkdPp2tR+dvk92Q+revr0GdmNwAAEBVQ5FzQjkFRXrok//t3PCPvkxuAACgKqLIORnDMPT04p3am5Kp2tWZ3AAAQFVGkXMyn2w4rKW243J3s2j6/W2Z3AAAQBVGkXMiWw6f1fPLdkuSJvcMV6ewWiYnAgAAZqLIOYlTWfkaO3erCosN9WodpJE3NjY7EgAAMBlFzgkUFdv16LxtSsnIU5M6vnr53kgmNwAAAIqcM3j1u/2KSzital7ueu+Bdqpu9TA7EgAAcAAUOQe3cleK3l17SJL08r1t1LSun8mJAACAo6DIObCEk1l6fOF2SdKILo315zbBJicCAACOhCLnoHIKivTwp1uVmV+kDo2u0+Re4WZHAgAADoYi54AMw9DkxTu1L7Vk0d/p90fL051TBQAAyqIdOKA5cYf15W8W/a3rz6K/AADgfBQ5B7P1yFm9sJxFfwEAwOVR5BzI2ewCPcKivwAA4ApR5ByE3W5o4kKbjqfnqVGtavrXPW1Y9BcAAFwSRc5BvLcuQT/sOykvDzdNHxQtP29PsyMBAAAHR5FzABsTz+jV7/ZJkqbeGaGI4ACTEwEAAGdAkTPZqax8PTp/q4rthvpGBWtAh/pmRwIAAE6CImeiYruhCZ/ZlJqRryZ1fPXiX1rzXBwAALhiFDkTTf/hoH48cErenm56Z3A7+Vo9zI4EAACcCEXOJOsPntIb3++XJL3Qt7WaB/qZnAgAADgbipwJ0jLyNG6BTYYh9WsfqnvbhZodCQAAOCGKXCUrKrZr3IJtOpWVr/AgP029s5XZkQAAgJOiyFWyN1cf0IaEM/L1ctf0QdHy8XI3OxIAAHBSFLlKFLsvTf9Zc1CS9NLdrdWkTnWTEwEAAGdGkaskqRl5mrhwuyRpcOcGuisqxOREAADA2VHkKkGx3dD4BTadyS7Q9fX89Uzv682OBAAAXABFrhLM+OGg4hJOq5qXu96+v628PXkuDgAA/HEUuQq2MfFM6Xpxz9/VSmE8FwcAAMoJRa4Cncsp0GMLtsluSHe3DdE9rBcHAADKEUWughiGoSc+36ET6XlqXNtX/+jLenEAAKB8UeQqyJy4w1q1O1Ve7m76z8C2qs4+qgAAoJxR5CrAruPpenH5HknS5F7hahUSYHIiAADgiihy5Sw7v0iPztumgmK7uresq2E3NDI7EgAAcFEUuXL23Fe7lHAqW0H+3nrl3khZLBazIwEAABdFkStHS7Yd1edbjsrNIr05IErX+XqZHQkAALgwilw5STyVrWeWxEuSHrutuTqF1TI5EQAAcHUUuXKQX1SsR+dvVXZBsTo1rqlHbm1qdiQAAFAFUOTKwb++2af4Yxm6rpqn3hzQVu5uPBcHAAAqHkXuD/phb5o+/jlRkvRav0gFBXibnAgAAFQVFLk/4GRmvp74fLskaXiXRro1PNDkRAAAoCqhyF2jki24tutUVoHCg/z05B3hZkcCAABVDEXuGs1en6TYfSdl9XDTWwPbytvT3exIAACgiqHIXYO9KRl66Zu9kqS/926p5oF+JicCAABVEUXuKuUVFuux+TYVFNl1a3hdPdC5odmRAABAFUWRu0r//Gav9qVmqnZ1q16+tw1bcAEAANNQ5K7Cuv0nNWt9kiTp1fvaqHZ1q7mBAABAlUaRuwpTlu6UVLLUyC0t6pqcBgAAVHUOVeTWrVunPn36KDg4WBaLRUuXLr3sa2JjYxUdHS2r1aqmTZtq1qxZ5x0zffp0NWrUSN7e3urUqZM2btx4VbkMw5Aknc4uZKkRAADgMByqyGVnZysyMlLTp0+/ouMTExPVu3dvdevWTTabTePHj9eoUaO0cuXK0mM+++wzTZw4Uc8995y2bt2qyMhI9ejRQ2lpaVeca94vhyVJXiw1AgAAHIjF+O/lJgdjsVi0ZMkS9e3b96LHTJo0SV9//bV++eWX0rHhw4crPT1dixcvliTdeuutio6O1quvvipJstvtatmypR566CFNnDjxgt83Pz9f+fn5kqSDJ3M0/OMNSnp7qF5fsl4jb40op3cIAABwaX5+fpecWOnURe6GG25QXFxc5YUCAACoROnp6fL397/o1z0qMUu5O3nypJ599ln97W9/Kx377rvvdN999yklJUXnzp1TeHi4Vq1apY4dO5YeM2XKFP38889as2bNBb/vb6/IFRTZ9ea3O/TWw320e/duhYSEVOybwlXJyMhQ/fr1lZycfMk/6Kh8nBvHxvlxXJwbx1bZ58fP79KbDjh1kbNYLPL29i7zH7JatWqSJH9/fxUXF0uSfH19yxxjtVrl7u5+xSfgiT+76a2HS/5j8kPlmPz9/Tk3Dopz49g4P46Lc+PYHOX8OHWRCwoKUmpqapmx1NRU+fv7y8fHR+7u7nJ3d7/gMUFBQZUZFQAAoNw51KzVqxUTE6PVq1eXGVu1apViYmIkSV5eXmrXrl2ZY+x2u1avXl16DAAAgLNyqCKXlZUlm80mm80mqWR5EZvNpiNHjkiSJk+erCFDhpQeP2bMGCUkJGjSpEnau3evZsyYoYULF2rChAmlx0ycOFEffPCBZs+erT179ujhhx9Wdna2hg8ffsW5rFZrmf+F47BarXruuec4Nw6Ic+PYOD+Oi3Pj2Bzt/DjUrNXY2Fh169btvPGhQ4dq1qxZGjZsmJKSkhQbG1vmNRMmTNDu3bsVGhqqKVOmaNiwYWVe//bbb+uVV15RSkqKoqKi9NZbb6lTp05XnCsjI0MBAQGXnTkCAABQmRyqyDkqihwAAHBEDnVrFQAAAFeOIgcAAOCkKHIAAABOiiIHAADgpKp8kVu3bp369Omj4OBgWSwWLV269LKviY2NVXR0tKxWq5o2bapZs2ZVeM6q6mrPz+LFi/WnP/1JderUkb+/v2JiYrRy5crKCVvFXMvPzn/9/PPP8vDwUFRUVIXlq8qu5dzk5+fr73//uxo2bCir1apGjRrp448/rviwVdC1nJ+5c+cqMjJS1apVU7169TRixAidPn264sNWMdOmTVOHDh3k5+enunXrqm/fvtq3b99lX7do0SKFh4fL29tbrVu31ooVKyohbYkqX+Sys7MVGRmp6dOnX9HxiYmJ6t27t7p16yabzabx48dr1KhRlIUKcrXnZ926dfrTn/6kFStWaMuWLerWrZv69Omjbdu2VXDSqudqz81/nTt3TkOGDNFtt91WQclwLeemX79+Wr16tT766CPt27dP8+fPV4sWLSowZdV1tefn559/1pAhQzRy5Ejt2rVLixYt0saNGzV69OgKTlr1rF27VmPHjtWGDRu0atUqFRYW6vbbb1d2dvZFX7N+/XoNHDhQI0eO1LZt29S3b1/17dtX8fHxlRPaQClJxpIlS84bT09PNyQZ6enpxqRJk4yIiIgyX+/fv7/Ro0ePSkpZdV3s/FzO9ddfb0ydOrX8A6HU1Zyb/v37G88884zx3HPPGZGRkRWaC1d2br755hsjICDAOH36dOWEQqkrOT+vvPKKERYWVmbsrbfeMkJCQiowGQzDMNLS0gxJxtq1ay96TL9+/YzevXuXGevUqZPx0EMPVXQ8wzAMo8pfkbtacXFx6t69e5mxHj16KC4uzqREuBS73a7MzEzVrFnT7CiQNHPmTCUkJOi5554zOwp+46uvvlL79u318ssvKyQkRM2bN9fjjz+u3Nxcs6NBJdtRJicna8WKFTIMQ6mpqfr888/Vq1cvs6O5vPT0dEm65O8Qs3uBR6X8v7iQlJQUBQYGlhkLDAxURkaGcnNz5ePjY1IyXMirr76qrKws9evXz+woVd6BAwf01FNP6ccff5SHB3/1OJKEhAT99NNP8vb21pIlS3Tq1Cn99a9/1enTpzVz5kyz41V5Xbp00dy5c9W/f3/l5eWpqKhIffr0uerHGnB17Ha7xo8fry5duqhVq1YXPe5ivSAlJaWiI0riGTm4sHnz5mnq1KlauHCh6tata3acKq24uFj333+/pk6dqubNm5sdB79jt9tlsVg0d+5cdezYUb169dLrr7+u2bNnc1XOAezevVuPPfaYnn32WW3ZskXffvutkpKSNGbMGLOjubSxY8cqPj5eCxYsMDvKJfHP4qsUFBSk1NTUMmOpqany9/fnapwDWbBggUaNGqVFixadd8kblS8zM1ObN2/Wtm3b9Mgjj0gqKQ+GYcjDw0Pfffedbr31VpNTVl316tVTSEiIAgICSsdatmwpwzB09OhRNWvWzMR0mDZtmrp06aInnnhCktSmTRv5+vrqpptu0gsvvKB69eqZnND1PPLII1q2bJnWrVun0NDQSx57sV4QFBRUkRFLcUXuKsXExGj16tVlxlatWqWYmBiTEuH35s+fr+HDh2v+/Pnq3bu32XEgyd/fXzt37pTNZiv9GDNmjFq0aCGbzaZOnTqZHbFK69Kli44fP66srKzSsf3798vNze2yv8RQ8XJycuTmVvbXtbu7uyTJYLv0cmUYhh555BEtWbJEa9asUePGjS/7GrN7QZW/IpeVlaWDBw+Wfp6YmCibzaaaNWuqQYMGmjx5so4ePar09HT5+flpzJgxevvttzVp0iSNGDFCa9as0cKFC7V8+XIT34XrupLzc+zYMc2ZM0dSye3UoUOH6s0331SnTp1Kn1Hw8fEpc7UBf9zVnBs3N7fznjGpW7euvL29L/nsCa7N1f7c3H///Xr++ec1fPhwTZ06VadOndITTzyhESNGcKehAlzt+enTp49Gjx6td955Rz169NCJEyc0fvx4dezYUcHBwWa9DZc0duxYzZs3T19++aX8/PxKf4cEBASU/iwMGTJEISEhmjZtmiTpscceU9euXfXaa6+pd+/eWrBggTZv3qz333+/ckJXytxYB/bDDz8Yks77GDp0qGEYhjF06FCja9eu570mKirK8PLyMsLCwoyZM2dWeu6q4mrPT9euXS95PMrPtfzs/BbLj1Scazk3e/bsMbp37274+PgYoaGhxsSJE42cnJzKD18FXMv5eeutt4zrr7/e8PHxMerVq2cMGjTIOHr0aOWHd3EXOi+Syvye79q163m/UxYuXGg0b97c8PLyMiIiIozly5dXWmbLr8EBAADgZHhGDgAAwElR5AAAAJwURQ4AAMBJUeQAAACcFEUOAADASVHkAAAAnBRFDgAAwElR5AAAAJwURQ4AAMBJUeQA4CL+85//qGHDhvLw8NDjjz9udhwAOA9bdAHABWzfvl3t27fXl19+qbZt2yogIEDVqlUzOxYAlOFhdgAAcETLli1Tx44d1atXL7OjAMBFUeQA4HeaNm2qQ4cOSZIsFoseeOABzZkzx+RUAHA+bq0CwO+kpaUpJiZGDz/8sAYPHqzq1aurevXqZscCgPNwRQ4Afqd69epKSkrSjTfeqKCgILPjAMBFMWsVAH5nx44dkqTWrVubnAQALo0iBwC/Y7PZ1LRpU/n6+kqS7rzzTj322GPq3LmzWrRooY0bN+quu+5Sw4YNNWPGDJPTAqjKKHIA8Ds2m02RkZGln+/cuVNt2rTRhg0bdNttt+mJJ57Qp59+qh9++EEzZ840MSmAqo4iBwC/Y7PZFBUVJUnKzMyUYRgaOXJk6dfHjRsnPz8/GYYhf39/k1ICAEUOAMqw2+3auXNn6RW5Xbt2qUOHDqVf37lzpzp16iRJio+P5zk6AKZi1ioA/Iabm5uys7NLP//vbdX/Onr0qEJDQ0u/RpEDYCauyAHAJfy2yCUnJ6t+/fplvkaRA2AmFgQGAABwUlyRAwAAcFIUOQAAACdFkQMAAHBSFDkAAAAnRZEDAABwUhQ5AAAAJ0WRAwAAcFIUOQAAACdFkQMAAHBSFDkAAAAnRZEDAABwUv8PgUO7x/MHPsQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x1ab7b1144f0>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.plot(\n",
    "    sol.subs(subs),\n",
    "    (fm, 1, 2),\n",
    "    xlabel=\"$f_m$\",\n",
    "    ylabel=\"$f_T$\",\n",
    "    axis_center=(1.0, 1.0),\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read: increasing the hot side inflow temperature by just 8 per cent will increase the cold side outflow temperature by as much as increasing the hot side mass flow by 60 per cent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "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": "3.9.13"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}