{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we've seen in my [previous post on rice cooker temperature measurements](http://flothesof.github.io/rice-cooker-temperature.html), sometimes it's easier to perform an experiment than to explain it, as the post ended on many open questions. In this post, I'll propose a simple model of what's going on during the cooking process that I measured previously."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recap about what's happening in the rice cooker "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Essentially, the rice cooker does what other cooking instruments in your kitchen do: it uses electric energy and converts it to heat to break molecular links in food, making it easier to digest for humans. This is what's called cooking. \n",
    "\n",
    "When we look into the details of this heat transfer to food, this is what seems to happen: an electric heater transfers heat to the metal pot. The pot transfers the heat to the water. The water transfers the heat to the rice, which gets cooked. While transfering heat to the rice, water boils and evaporates. Once it has evaporated entirely, the cooking is finished and the rice cooker turns itself off.\n",
    "\n",
    "As you've surely noticed, the previous paragraph is full of references to heat. The model we will propose below will thus center around the heat balance of our system."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Heat balance for the rice cooker "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's denote by $Q_h$ the heat produced by the thermal heater of the rice cooker. Assuming it has the fixed power of 500 W as described on the seller's website, the quantity of heat generated after a time $t$ is written as:\n",
    "\n",
    "$$\n",
    "Q_h = P \\Delta t\n",
    "$$\n",
    "\n",
    "Here, $P$ are the 500 W from the thermal resistance.\n",
    "\n",
    "We'll assume that the metal pot instantly transfers the heat to the water. Thus the heat absorbed by the water will elevate its temperature. We will assume that the temperature is uniform in the water. Thus the temperature, while the water is not boiling, is written as:\n",
    "\n",
    "$$\n",
    "T_w = T_0 + Q_h / c_p / m\n",
    "$$\n",
    "\n",
    "Above, we've made use of the [specific heat capacity](https://en.wikipedia.org/wiki/Heat_capacity) of water, which we will assume to be $c_p = 4.2 \\, kJ/(kg⋅K)$. This means that if we want to raise the temperature of a kilogram of water by 1 degree, we need to transfer it 4200 joules.\n",
    "\n",
    "When the water reaches 100°C at atmospheric pressure, it begins to boil. The boiling process is an indication of the transformation that is taking place: water turns from a liquid to a gas. This process costs a lot more energy than the heating process. We'll assume [vaporization](https://en.wikipedia.org/wiki/Enthalpy_of_vaporization) to take $\\Delta H _{vap} = 2257 \\, kJ / kg$. \n",
    "\n",
    "Once it becomes gas, the water mixes with the air in the rice cooker atmosphere. At the same time, a flux of outgoing hot air and water gas appears. This is where our measurement is carried out. In a first step, we'll simplify our problem and just assume we measure the temperature of the water.\n",
    "\n",
    "Let's now turn to some numerical computation based on these numbers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numerical solution "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll try to compute the solution of the previous problem description using simple time stepping. At each time step, we can compute the heat produced by the heater, the remaining mass of water and the temperature of the water (and thus the temperature of the air, which is our measured value)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def solve(t, P, m_0, T_0):\n",
    "    \"Returns the heat produced, remaining water mass and water temperature at time t (in seconds).\"\n",
    "    CP = 4.2e3\n",
    "    DeltaHV = 2257e3\n",
    "    Q_h = P * t\n",
    "    T = T_0 + Q_h / CP / m_0\n",
    "    if T >= 100:\n",
    "        delta_Q = Q_h - (100 - T_0) * CP * m_0\n",
    "        T = 100\n",
    "    else:\n",
    "        delta_Q = 0\n",
    "    m = m_0 - delta_Q / DeltaHV\n",
    "    if m < 0:\n",
    "        m = 0\n",
    "    return Q_h, m, T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I've introduced all of the starting parameters to our solving function. Let's now evaluate it at different times:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time 0 s: Q_h=0.00 J, m=1.0 kg, T=20.00 °C\n",
      "time 120 s: Q_h=60000.00 J, m=1.0 kg, T=34.29 °C\n",
      "time 600 s: Q_h=300000.00 J, m=1.0 kg, T=91.43 °C\n",
      "time 1800 s: Q_h=900000.00 J, m=0.75 kg, T=100.00 °C\n",
      "time 3600 s: Q_h=1800000.00 J, m=0.35 kg, T=100.00 °C\n"
     ]
    }
   ],
   "source": [
    "for t in [0, 2*60, 10*60, 30*60, 60*60]:\n",
    "    print(\"time {} s: Q_h={:.2f} J, m={:.2} kg, T={:.2f} °C\".format(t, *solve(t, 500, 1, 20)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = np.array([(t,) + solve(t, 500, 0.5, 20) for t in np.arange(35 * 60)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.05, 0.55)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/f5necqubQa2Gh4cHPDzk/8dBiJyYoAJr4/v/3bH/9j1g55RfPOo2kDseIRWi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\n9n9643qPW+l8eQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef71080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(data[:, 0]/60, data[:, 2])\n",
    "plt.xlabel('time (minutes)')\n",
    "plt.ylabel('remaining water (kg)')\n",
    "plt.title('remaining water in the rice cooker')\n",
    "plt.ylim(-0.05, 0.55)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also plot the temperature above the rice cooker as a function of time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(15, 115)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/Px8TJ07UmRYVFYX/+7//M0koa8FrnxORPTNoF5ZKpUJVVRXatWsHtVqNvLw8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\nEREZhQWEiIiMwgJCRERG+X8cRthf1VSW2gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fb134e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(data[:, 0]/60, data[:, 3])\n",
    "plt.xlabel('time (minutes)')\n",
    "plt.ylabel('temperature (°C)')\n",
    "plt.title('temperature above the rice cooker')\n",
    "plt.ylim(15, 115)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now compare this simple model to our previous measurement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparison with experiment "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "df = pd.read_csv('log_20160327_v2.txt', parse_dates=['time'])\n",
    "ind = df.pop('time')\n",
    "df = df.set_index((ind - ind.values[0]).astype('timedelta64[s]') / 60.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10e7cb550>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gIiJSbRo2jUDWWj7OCDBSQ6YRyRw9wO8IIiJSDSreItDqXQUUlLgc3TrO7yhS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\ngvw/uyPIGjpsQz4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e3f0438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(df.index.values, df.temperature.values, label='experiment')\n",
    "plt.plot(data[:, 0]/60, data[:, 3], label='simulation')\n",
    "plt.xlim(0, 35)\n",
    "plt.ylim(0, 115)\n",
    "plt.legend(loc='lower right')\n",
    "plt.ylabel('temperature (°C)')\n",
    "plt.xlabel('time (s)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "This graph allows us to pinpoint a lot of things.\n",
    "\n",
    "First, we see that our model has the same shape but does not yield good predictions. For instance:\n",
    "\n",
    "- the initial temperature increase is not well matched: experiment goes up smoothly while our model assumes we heat the bulk of the water instantly\n",
    "- our model underestimates the time to reach the maximum temperature\n",
    "- our model undersestimates the maximum temperature: we assume the air water-gas mixture reaches 100°C, while it seems it reaches slightly higher temperatures\n",
    "- our model doesn't allow for cooling of the rice cooker once the cooking is finished\n",
    "- our model also doesn't predict the right cooking stopping time (checking the previous plot above, we see that the rice cooker stops earlier than our model, which hasn't yet reached an empty water state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusions "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model described in this blog post is really simple. Although it allows to qualitatively understand the heating process, which is basically just making water boil, it's pretty bad at enabling finer understanding of the cooking process. Improvements that would be needed to make it more accurate (in my opinion, but I'm no expert) would be:\n",
    "\n",
    "- take into account layers of water: could allow the replication of the inital slope in the temperature\n",
    "- investigate water air mixture: explain the final temperature constantly higher than 100°C (due to a balance between hot air and hot water gas?)\n",
    "- take into account thermal losses, which explain the decrease of the temperature after t=30 minutes\n",
    "- take into account the rice itself, which is heated and cooked in the process\n"
   ]
  }
 ],
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