code/chap15.ipynb

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   "source": [
    "# Modeling and Simulation in Python\n",
    "\n",
    "Chapter 15\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The coffee cooling problem\n",
    "\n",
    "I'll use a `State` object to store the initial temperature.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "init = State(T=90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And a `System` object to contain the system parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "coffee = System(init=init,\n",
    "                volume=300,\n",
    "                r=0.01,\n",
    "                T_env=22,\n",
    "                t_end=30,\n",
    "                dt=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The update function implements Newton's law of cooling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_func(state, t, system):\n",
    "    \"\"\"Update the thermal transfer model.\n",
    "    \n",
    "    state: State (temp)\n",
    "    t: time\n",
    "    system: System object\n",
    "    \n",
    "    returns: State (temp)\n",
    "    \"\"\"\n",
    "    unpack(system)\n",
    "    \n",
    "    T = state.T\n",
    "    T += -r * (T - T_env) * dt\n",
    "    \n",
    "    return State(T=T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's how it works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "update_func(init, 0, coffee)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a version of `run_simulation` that uses `linrange` to make an array of time steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_simulation(system, update_func):\n",
    "    \"\"\"Runs a simulation of the system.\n",
    "    \n",
    "    Add a TimeFrame to the System: results\n",
    "    \n",
    "    system: System object\n",
    "    update_func: function that updates state\n",
    "    \"\"\"\n",
    "    unpack(system)\n",
    "    \n",
    "    frame = TimeFrame(columns=init.index)\n",
    "    frame.row[0] = init\n",
    "    ts = linrange(0, t_end, dt)\n",
    "    \n",
    "    for t in ts:\n",
    "        frame.row[t+dt] = update_func(frame.row[t], t, system)\n",
    "        \n",
    "    # store the final temperature in T_final\n",
    "    system.T_final = get_last_value(frame.T)\n",
    "    \n",
    "    return frame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's how it works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = run_simulation(coffee, update_func)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the results look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot(results.T, label='coffee')\n",
    "decorate(xlabel='Time (minutes)',\n",
    "         ylabel='Temperature (C)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's the final temperature:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "coffee.T_final"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Encapsulation\n",
    "\n",
    "Before we go on, let's define a function to initialize `System` objects with relevant parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_system(T_init, r, volume, t_end):\n",
    "    \"\"\"Makes a System object with the given parameters.\n",
    "\n",
    "    T_init: initial temperature in degC\n",
    "    r: heat transfer rate, in 1/min\n",
    "    volume: volume of liquid in mL\n",
    "    t_end: end time of simulation\n",
    "    \n",
    "    returns: System object\n",
    "    \"\"\"\n",
    "    init = State(T=T_init)\n",
    "    \n",
    "    # T_final is used to store the final temperature.\n",
    "    # Before the simulation runs, T_final = T_init\n",
    "    T_final = T_init\n",
    "\n",
    "    T_env = 22 \n",
    "    dt = 1\n",
    "                \n",
    "    return System(locals())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's how we use it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "coffee = make_system(T_init=90, r=0.01, volume=300, t_end=30)\n",
    "results = run_simulation(coffee, update_func)\n",
    "coffee.T_final"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "\n",
    "**Exercise:**  Simulate the temperature of 50 mL of milk with a starting temperature of 5 degC, in a vessel with the same insulation, for 15 minutes, and plot the results.\n",
    "\n",
    "By trial and error, find a values for `r` that makes the final temperature close to 20 C."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot(results.T, label='milk')\n",
    "decorate(xlabel='Time (minutes)',\n",
    "         ylabel='Temperature (C)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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