Melting Ice.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling and Simulation in Python\n",
    "\n",
    "Project 2\n",
    "\n",
    "Maalvika Bhat & Richard Gao"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "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": [
    "### Setup model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16500.0"
      ]
     },
     "execution_count": 291,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the heat necessary to melt .05 kg of ice\n",
    "m_solid = .05\n",
    "latent_heat_fusion = 3.3 * 10 ** 5\n",
    "q = m_solid * latent_heat_fusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>material</th>\n",
       "      <th>thermal_conductivity_factor</th>\n",
       "      <th>specific_heat_capacity</th>\n",
       "      <th>density</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>aluminum</td>\n",
       "      <td>205.00</td>\n",
       "      <td>897</td>\n",
       "      <td>2700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>nickel</td>\n",
       "      <td>91.00</td>\n",
       "      <td>461</td>\n",
       "      <td>8908</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>marble</td>\n",
       "      <td>2.50</td>\n",
       "      <td>880</td>\n",
       "      <td>2570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>wood</td>\n",
       "      <td>0.16</td>\n",
       "      <td>2000</td>\n",
       "      <td>240</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   material  thermal_conductivity_factor  specific_heat_capacity  density\n",
       "0  aluminum                       205.00                     897     2700\n",
       "1    nickel                        91.00                     461     8908\n",
       "2    marble                         2.50                     880     2570\n",
       "3      wood                         0.16                    2000      240"
      ]
     },
     "execution_count": 293,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Specify material information\n",
    "material_info = {'material': ['aluminum', 'nickel', 'marble', 'wood'],\n",
    "                 'thermal_conductivity_factor': [205, 91, 2.5, 0.16],\n",
    "                 'specific_heat_capacity': [897, 461, 880, 2000],\n",
    "                 'density': [2700, 8908, 2570, 240]}\n",
    "\n",
    "plate_materials = pd.DataFrame(material_info,\n",
    "                              columns=['material','thermal_conductivity_factor', 'specific_heat_capacity', 'density'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulating Melting Ice on Aluminum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_system(params):\n",
    "    \"\"\"Makes a System object with the given parameters held within the params object.\n",
    "    \n",
    "    params:\n",
    "        material: type of material as a string\n",
    "        plate_materials: dataframe of recorded material information \n",
    "                         (name, thermal conductivity factor, \n",
    "                          specific heat capacity, density)\n",
    "        surface_area: area of plate in contact with ice, in meters^2\n",
    "        plate_temp: temperature of the plate, in celsius \n",
    "        thickness: thickness of the plate, in meters\n",
    "        dt: time interval, in seconds\n",
    "    \n",
    "    returns: System object\n",
    "    \"\"\"\n",
    "    material, plate_materials, surface_area, plate_temp, thickness, dt = params\n",
    "    \n",
    "    # Assumption that the thermal energy in hand is unlimited as long as the human keeps eating, therefore\n",
    "    # thermal_energy_hand is set to a random large number\n",
    "    init = State(thermal_energy_hand = 100000, \n",
    "                 thermal_energy_ice = 0,\n",
    "                 plate_temp=plate_temp)\n",
    "    \n",
    "    t0 = 0\n",
    "    dt = dt\n",
    "    \n",
    "    return System(locals())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_func(state, system):\n",
    "    \"\"\"Update the ice-plate-hand melting model.\n",
    "    \n",
    "    state: State\n",
    "    system: System object\n",
    "    \n",
    "    returns: State\n",
    "    \"\"\"\n",
    "    unpack(system)\n",
    "    thermal_energy_hand, thermal_energy_ice, plate_temp = state\n",
    "    \n",
    "    index = pd.Index(plate_materials['material']).get_loc(material)\n",
    "    \n",
    "    thermal_conductivity_factor = plate_materials['thermal_conductivity_factor'][index]\n",
    "    specific_heat_capacity = plate_materials['specific_heat_capacity'][index]\n",
    "    \n",
    "    #-------Calulating mass---------\n",
    "    # mass is dependent on the parameters surface_area and thickness and material type, m=V*p\n",
    "    density = plate_materials['density'][index]\n",
    "    mass = (surface_area * thickness) * density\n",
    "    \n",
    "    #-------Hand temperature---------\n",
    "    # We make the assumption that the hand temperature is constant\n",
    "    hand_temperature = 37\n",
    "    \n",
    "    #------Calculating heat (flows)-------\n",
    "    hand_to_plate = mass * specific_heat_capacity * (hand_temperature - plate_temp) * dt\n",
    "    plate_to_ice = (thermal_conductivity_factor * surface_area * plate_temp / thickness) * dt\n",
    "\n",
    "    #------Euler's method--------\n",
    "    thermal_energy_hand -= hand_to_plate\n",
    "    thermal_energy_ice += plate_to_ice\n",
    "    \n",
    "    #------Changing plate temperature-------\n",
    "    # We've abstracted the scenario to not take convection or radiation into account\n",
    "    deltaQ = hand_to_plate - plate_to_ice\n",
    "    plate_temp += deltaQ / (specific_heat_capacity * mass)\n",
    "    \n",
    "    return State(thermal_energy_hand=thermal_energy_hand,\n",
    "                 thermal_energy_ice=thermal_energy_ice,\n",
    "                 plate_temp=plate_temp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "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[t0] = init\n",
    "    \n",
    "    # Runs simulation until ice has completely melted -> thermal_energy_ice surpasses heat necessary to melt ice q\n",
    "    melted = False\n",
    "    t = 0\n",
    "    while not melted:\n",
    "        new_state = update_func(frame.row[t], system)\n",
    "        if new_state.thermal_energy_ice >= q:\n",
    "            melted = True\n",
    "        else:\n",
    "            t = round(t + dt, 3)\n",
    "            frame.row[t] = new_state\n",
    "#             print(frame.row[t])\n",
    "        \n",
    "    return frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 318,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>thermal_energy_hand</th>\n",
       "      <th>thermal_energy_ice</th>\n",
       "      <th>plate_temp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>100000</td>\n",
       "      <td>0</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.1</th>\n",
       "      <td>96609.3</td>\n",
       "      <td>1178.75</td>\n",
       "      <td>23.9133</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.2</th>\n",
       "      <td>93439.9</td>\n",
       "      <td>2404.31</td>\n",
       "      <td>24.7159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.3</th>\n",
       "      <td>90464.8</td>\n",
       "      <td>3671</td>\n",
       "      <td>25.4213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.4</th>\n",
       "      <td>87660.6</td>\n",
       "      <td>4973.84</td>\n",
       "      <td>26.0413</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.5</th>\n",
       "      <td>85006.5</td>\n",
       "      <td>6308.46</td>\n",
       "      <td>26.5861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.6</th>\n",
       "      <td>82484.3</td>\n",
       "      <td>7670.99</td>\n",
       "      <td>27.0649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.7</th>\n",
       "      <td>80078.1</td>\n",
       "      <td>9058.07</td>\n",
       "      <td>27.4857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.8</th>\n",
       "      <td>77773.8</td>\n",
       "      <td>10466.7</td>\n",
       "      <td>27.8555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.9</th>\n",
       "      <td>75559.1</td>\n",
       "      <td>11894.3</td>\n",
       "      <td>28.1805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>73423.1</td>\n",
       "      <td>13338.5</td>\n",
       "      <td>28.4661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.1</th>\n",
       "      <td>71356.3</td>\n",
       "      <td>14797.4</td>\n",
       "      <td>28.7171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.2</th>\n",
       "      <td>69350.3</td>\n",
       "      <td>16269.2</td>\n",
       "      <td>28.9377</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    thermal_energy_hand thermal_energy_ice plate_temp\n",
       "0.0              100000                  0         23\n",
       "0.1             96609.3            1178.75    23.9133\n",
       "0.2             93439.9            2404.31    24.7159\n",
       "0.3             90464.8               3671    25.4213\n",
       "0.4             87660.6            4973.84    26.0413\n",
       "0.5             85006.5            6308.46    26.5861\n",
       "0.6             82484.3            7670.99    27.0649\n",
       "0.7             80078.1            9058.07    27.4857\n",
       "0.8             77773.8            10466.7    27.8555\n",
       "0.9             75559.1            11894.3    28.1805\n",
       "1.0             73423.1            13338.5    28.4661\n",
       "1.1             71356.3            14797.4    28.7171\n",
       "1.2             69350.3            16269.2    28.9377"
      ]
     },
     "execution_count": 318,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params = Params(material='aluminum',\n",
    "                plate_materials=plate_materials,\n",
    "                surface_area=.05,\n",
    "                plate_temp=23,\n",
    "                thickness=.02,\n",
    "                dt=.1)\n",
    "system = make_system(params)\n",
    "results = run_simulation(system, update_func)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 298,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(results.thermal_energy_hand, 'g', label='Thermal energy of hand')\n",
    "plot(results.thermal_energy_ice, 'b', label='Thermal energy of ice')\n",
    "decorate(xlabel='Time (sec)', \n",
    "         ylabel='Thermal Energy (Joules)', \n",
    "         title='Ice Melting on Aluminum')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sweeping Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_melt_time(results):\n",
    "    \"\"\"Returns the total runtime of simulation in seconds\n",
    "    \n",
    "    results: results of run_simulation\n",
    "\n",
    "    returns: last index of TimeFrame \n",
    "    \"\"\"\n",
    "    return results.index[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sweep Material Type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sweep_material(params):\n",
    "    \"\"\"Sweeps through different materials to test how long ice would melt for each\n",
    "    \n",
    "    params:\n",
    "        plate_materials: dataframe of recorded material information \n",
    "                         (name, thermal conductivity factor, \n",
    "                          specific heat capacity, density)\n",
    "        surface_area: area of plate in contact with ice, in meters^2\n",
    "        plate_temp: temperature of the plate, in celsius \n",
    "        thickness: thickness of the plate, in meters\n",
    "\n",
    "    returns: DataFrame with results of sweep\n",
    "    \"\"\"\n",
    "    \n",
    "    plate_materials, surface_area, plate_temp, thickness = params\n",
    "    \n",
    "    thermal_conductivity_factors = plate_materials['thermal_conductivity_factor']\n",
    "    specific_heat_capacities = plate_materials['specific_heat_capacity']\n",
    "    \n",
    "    sweep = SweepSeries()\n",
    "    for i in range(0, plate_materials['material'].size):\n",
    "        system_params = Params(plate_materials['material'][i],\n",
    "                plate_materials=plate_materials,\n",
    "                surface_area=surface_area,\n",
    "                plate_temp=plate_temp,\n",
    "                thickness=thickness,\n",
    "                dt=.1)\n",
    "        system = make_system(system_params)\n",
    "        results = run_simulation(system, update_func)\n",
    "        sweep[plate_materials['material'][i]] = calc_melt_time(results)\n",
    "    return sweep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "aluminum       1.2\n",
      "nickel         2.3\n",
      "marble        71.9\n",
      "wood        1116.1\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "params = Params(plate_materials=plate_materials,\n",
    "                surface_area=.05,\n",
    "                plate_temp=23,\n",
    "                thickness=.02)\n",
    "sweep = sweep_material(params)\n",
    "\n",
    "print(sweep)\n",
    "\n",
    "plot(sweep, 'or')\n",
    "decorate(xlabel='Material', \n",
    "         ylabel='Time (sec)', \n",
    "         title='Sweep Material Type')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sweep Surface Area of Plate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sweep_surface_area(params):\n",
    "    \"\"\"Sweeps through range of surface areas to test how long ice would melt for each\n",
    "    \n",
    "    params:\n",
    "        material: type of material as a string\n",
    "        plate_materials: dataframe of recorded material information \n",
    "                         (name, thermal conductivity factor, \n",
    "                          specific heat capacity, density)\n",
    "        plate_temp: temperature of the plate, in celsius \n",
    "        thickness: thickness of the plate, in meters\n",
    "        surface_area_array: list holding surface areas to test\n",
    "\n",
    "    returns: DataFrame with results of sweep\n",
    "    \"\"\"\n",
    "    \n",
    "    material, plate_materials, plate_temp, thickness, surface_area_array = params\n",
    "    sweep = SweepSeries()\n",
    "    for surface_area in surface_area_array:\n",
    "        system_params = Params(material=material,\n",
    "                plate_materials=plate_materials,\n",
    "                surface_area=surface_area,\n",
    "                plate_temp=plate_temp,\n",
    "                thickness=thickness,\n",
    "                dt=.1)\n",
    "        system = make_system(system_params)\n",
    "        results = run_simulation(system, update_func)\n",
    "        sweep[system.surface_area]= calc_melt_time(results)\n",
    "    return sweep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.01    5.4\n",
      "0.02    2.8\n",
      "0.03    1.9\n",
      "0.04    1.4\n",
      "0.05    1.2\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "surface_area_array = linspace(0.01, 1, 100)\n",
    "\n",
    "params = Params(material='aluminum',\n",
    "                plate_materials=plate_materials,\n",
    "                plate_temp=23,\n",
    "                thickness=.02,\n",
    "                surface_area_array=surface_area_array)\n",
    "sweep = sweep_surface_area(params)\n",
    "\n",
    "print(sweep.head())\n",
    "\n",
    "plot(sweep, 'oc', label='Sweep surface area')\n",
    "decorate(xlabel='Surface Area (m^2)', \n",
    "         ylabel='Time (sec)', \n",
    "         title='Sweeping Surface Area')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sweep Temperature of Plate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sweep_plate_temp(params):\n",
    "    \"\"\"Sweeps through different plate temperatures to test how long ice would melt for each\n",
    "    \n",
    "    params:\n",
    "        material: type of material as a string\n",
    "        plate_materials: dataframe of recorded material information \n",
    "                         (name, thermal conductivity factor, \n",
    "                          specific heat capacity, density)\n",
    "        surface_area: area of plate in contact with ice, in meters^2\n",
    "        thickness: thickness of the plate, in meters\n",
    "        plate_temp_array: list holding plate temperatures to test\n",
    "\n",
    "    returns: DataFrame with results of sweep\n",
    "    \"\"\"\n",
    "    \n",
    "    material, plate_materials, surface_area, thickness, plate_temp_array = params\n",
    "    sweep = SweepSeries()\n",
    "    for plate_temp in plate_temp_array:\n",
    "        system_params = Params(material=material,\n",
    "                plate_materials=plate_materials,\n",
    "                surface_area=surface_area,\n",
    "                plate_temp=plate_temp,\n",
    "                thickness=thickness,\n",
    "                dt=.1)\n",
    "        system = make_system(system_params)\n",
    "        results = run_simulation(system, update_func)\n",
    "        sweep[system.plate_temp]= calc_melt_time(results)\n",
    "    return sweep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0     1.7\n",
      "5     1.6\n",
      "10    1.5\n",
      "15    1.4\n",
      "20    1.2\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plate_temp_array = linrange(0, 100, 5)\n",
    "\n",
    "params = Params(material='aluminum',\n",
    "                plate_materials=plate_materials,\n",
    "                surface_area=.05,\n",
    "                thickness=.02,\n",
    "                plate_temp_array=plate_temp_array)\n",
    "sweep = sweep_plate_temp(params)\n",
    "\n",
    "print(sweep.head())\n",
    "\n",
    "plot(sweep, 'yo', label='Sweep plate temperature')\n",
    "decorate(xlabel='Plate Temperature (celsius)', \n",
    "         ylabel='Time (sec)', \n",
    "         title='Sweeping Plate Temperature')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sweep Thickness of Plate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sweep_thickness(params):\n",
    "    \"\"\"Sweeps through different thicknesses to test how long ice would melt for each\n",
    "    \n",
    "    params:\n",
    "        material: type of material as a string\n",
    "        plate_materials: dataframe of recorded material information \n",
    "                         (name, thermal conductivity factor, \n",
    "                          specific heat capacity, density)\n",
    "        surface_area: area of plate in contact with ice, in meters^2\n",
    "        plate_temp: temperature of the plate, in celsius \n",
    "        thickness_array: list holding thicknesses to test\n",
    "\n",
    "    returns: DataFrame with results of sweep\n",
    "    \"\"\"\n",
    "    \n",
    "    material, plate_materials, surface_area, plate_temp, thickness_array = params\n",
    "    sweep = SweepSeries()\n",
    "    for thickness in thickness_array:\n",
    "        system_params = Params(material=material,\n",
    "                plate_materials=plate_materials,\n",
    "                surface_area=surface_area,\n",
    "                plate_temp=plate_temp,\n",
    "                thickness=thickness,\n",
    "                dt=.1)\n",
    "        system = make_system(system_params)\n",
    "        results = run_simulation(system, update_func)\n",
    "        sweep[system.thickness]= calc_melt_time(results)\n",
    "    return sweep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.010000    0.7\n",
      "0.062105    3.1\n",
      "0.114211    5.3\n",
      "0.166316    7.6\n",
      "0.218421    9.8\n",
      "dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thickness_array = linspace(0.01, 1, 20)\n",
    "\n",
    "params = Params(material='aluminum',\n",
    "                plate_materials=plate_materials,\n",
    "                surface_area=.05,\n",
    "                plate_temp=23,\n",
    "                thickness_array=thickness_array)\n",
    "sweep = sweep_thickness(params)\n",
    "\n",
    "print(sweep.head())\n",
    "\n",
    "plot(sweep, 'ko', label='Sweeping thickness')\n",
    "decorate(xlabel='Thickness (meters)', \n",
    "         ylabel='Time (sec)', \n",
    "         title='Sweeping Thickness')\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Sweep Dimensions of Plate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sweep_plate_dimensions(surface_area_array, thickness_array):\n",
    "    \"\"\"Sweep a range of values for surface area and thickness.\n",
    "    \n",
    "    surface_area_array: array of surface areas\n",
    "    thickness_array: array of thicknesses\n",
    "    \n",
    "    returns: SweepFrame with one row for each surface area\n",
    "             and one column for each thickness\n",
    "    \"\"\"\n",
    "    frame = SweepFrame(columns=thickness_array)\n",
    "    for thickness in thickness_array:\n",
    "        params = Params(material='aluminum',\n",
    "                        plate_materials=plate_materials,\n",
    "                        plate_temp=23,\n",
    "                        thickness=thickness,\n",
    "                        surface_area_array=surface_area_array)\n",
    "    \n",
    "        frame[thickness] = sweep_surface_area(params)\n",
    "    return frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0.01</th>\n",
       "      <th>0.12</th>\n",
       "      <th>0.23</th>\n",
       "      <th>0.34</th>\n",
       "      <th>0.45</th>\n",
       "      <th>0.56</th>\n",
       "      <th>0.67</th>\n",
       "      <th>0.78</th>\n",
       "      <th>0.89</th>\n",
       "      <th>1.0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.01</th>\n",
       "      <td>3.9</td>\n",
       "      <td>26.6</td>\n",
       "      <td>50.4</td>\n",
       "      <td>74.3</td>\n",
       "      <td>98.3</td>\n",
       "      <td>122.2</td>\n",
       "      <td>146.1</td>\n",
       "      <td>170.0</td>\n",
       "      <td>194.0</td>\n",
       "      <td>217.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.12</th>\n",
       "      <td>0.2</td>\n",
       "      <td>2.5</td>\n",
       "      <td>4.5</td>\n",
       "      <td>6.5</td>\n",
       "      <td>8.5</td>\n",
       "      <td>10.5</td>\n",
       "      <td>12.5</td>\n",
       "      <td>14.5</td>\n",
       "      <td>16.5</td>\n",
       "      <td>18.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.23</th>\n",
       "      <td>0.1</td>\n",
       "      <td>1.4</td>\n",
       "      <td>2.5</td>\n",
       "      <td>3.5</td>\n",
       "      <td>4.6</td>\n",
       "      <td>5.6</td>\n",
       "      <td>6.7</td>\n",
       "      <td>7.7</td>\n",
       "      <td>8.7</td>\n",
       "      <td>9.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.34</th>\n",
       "      <td>0.1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.7</td>\n",
       "      <td>2.5</td>\n",
       "      <td>3.2</td>\n",
       "      <td>3.9</td>\n",
       "      <td>4.6</td>\n",
       "      <td>5.3</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.45</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.7</td>\n",
       "      <td>1.4</td>\n",
       "      <td>1.9</td>\n",
       "      <td>2.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>4.1</td>\n",
       "      <td>4.6</td>\n",
       "      <td>5.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.56</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.6</td>\n",
       "      <td>1.1</td>\n",
       "      <td>1.6</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>2.9</td>\n",
       "      <td>3.3</td>\n",
       "      <td>3.8</td>\n",
       "      <td>4.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.67</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.9</td>\n",
       "      <td>1.3</td>\n",
       "      <td>1.7</td>\n",
       "      <td>2.1</td>\n",
       "      <td>2.5</td>\n",
       "      <td>2.8</td>\n",
       "      <td>3.2</td>\n",
       "      <td>3.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.78</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.8</td>\n",
       "      <td>1.2</td>\n",
       "      <td>1.5</td>\n",
       "      <td>1.8</td>\n",
       "      <td>2.2</td>\n",
       "      <td>2.5</td>\n",
       "      <td>2.8</td>\n",
       "      <td>3.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.89</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.7</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.3</td>\n",
       "      <td>1.6</td>\n",
       "      <td>1.9</td>\n",
       "      <td>2.2</td>\n",
       "      <td>2.5</td>\n",
       "      <td>2.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.00</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.9</td>\n",
       "      <td>1.2</td>\n",
       "      <td>1.5</td>\n",
       "      <td>1.7</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.2</td>\n",
       "      <td>2.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0.01  0.12  0.23  0.34  0.45   0.56   0.67   0.78   0.89   1.00\n",
       "0.01   3.9  26.6  50.4  74.3  98.3  122.2  146.1  170.0  194.0  217.9\n",
       "0.12   0.2   2.5   4.5   6.5   8.5   10.5   12.5   14.5   16.5   18.5\n",
       "0.23   0.1   1.4   2.5   3.5   4.6    5.6    6.7    7.7    8.7    9.8\n",
       "0.34   0.1   1.0   1.7   2.5   3.2    3.9    4.6    5.3    6.0    6.7\n",
       "0.45   0.0   0.7   1.4   1.9   2.5    3.0    3.6    4.1    4.6    5.2\n",
       "0.56   0.0   0.6   1.1   1.6   2.0    2.5    2.9    3.3    3.8    4.2\n",
       "0.67   0.0   0.5   0.9   1.3   1.7    2.1    2.5    2.8    3.2    3.6\n",
       "0.78   0.0   0.4   0.8   1.2   1.5    1.8    2.2    2.5    2.8    3.1\n",
       "0.89   0.0   0.4   0.7   1.0   1.3    1.6    1.9    2.2    2.5    2.8\n",
       "1.00   0.0   0.3   0.6   0.9   1.2    1.5    1.7    2.0    2.2    2.5"
      ]
     },
     "execution_count": 338,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "surface_area_array = linspace(0.01, 1, 10)\n",
    "thickness_array = linspace(0.01, 1, 10)\n",
    "frame = sweep_plate_dimensions(surface_area_array, thickness_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for thickness in thickness_array:\n",
    "    label = 'thickness = ' + str(thickness) + 'm'\n",
    "    plot(frame[thickness], label=label)\n",
    "    \n",
    "decorate(xlabel='Surface Area',\n",
    "         ylabel='Time (sec)',\n",
    "         title='Sweeping Surface Area and Thickness vs Time')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for thickness in frame.columns:\n",
    "    series = frame[thickness]\n",
    "    for surface_area in series.index:\n",
    "        time = series[surface_area]\n",
    "        plot(surface_area/thickness, time, 'ro')\n",
    "        \n",
    "decorate(xlabel='Dimension Ratio (surface area/thickness)',\n",
    "         ylabel='Time (sec)',\n",
    "         title='Plate Dimension Analysis')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the Plate Dimension Analysis, we can determine that a wide yet thin plate would melt the ice fastest."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulating Extreme Condition for Ice Melting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we run a simulation of the extreme cases of each paramter to see how quickly ice could potentially melt (unrealistic scenario):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>thermal_energy_hand</th>\n",
       "      <th>thermal_energy_ice</th>\n",
       "      <th>plate_temp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.000</th>\n",
       "      <td>100000</td>\n",
       "      <td>0</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.001</th>\n",
       "      <td>101526</td>\n",
       "      <td>2050</td>\n",
       "      <td>99.8524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.002</th>\n",
       "      <td>103048</td>\n",
       "      <td>4096.97</td>\n",
       "      <td>99.705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.003</th>\n",
       "      <td>104567</td>\n",
       "      <td>6140.93</td>\n",
       "      <td>99.5579</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.004</th>\n",
       "      <td>106082</td>\n",
       "      <td>8181.86</td>\n",
       "      <td>99.4111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.005</th>\n",
       "      <td>107593</td>\n",
       "      <td>10219.8</td>\n",
       "      <td>99.2645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.006</th>\n",
       "      <td>109101</td>\n",
       "      <td>12254.7</td>\n",
       "      <td>99.1182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.007</th>\n",
       "      <td>110606</td>\n",
       "      <td>14286.6</td>\n",
       "      <td>98.9722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.008</th>\n",
       "      <td>112107</td>\n",
       "      <td>16315.6</td>\n",
       "      <td>98.8265</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      thermal_energy_hand thermal_energy_ice plate_temp\n",
       "0.000              100000                  0        100\n",
       "0.001              101526               2050    99.8524\n",
       "0.002              103048            4096.97     99.705\n",
       "0.003              104567            6140.93    99.5579\n",
       "0.004              106082            8181.86    99.4111\n",
       "0.005              107593            10219.8    99.2645\n",
       "0.006              109101            12254.7    99.1182\n",
       "0.007              110606            14286.6    98.9722\n",
       "0.008              112107            16315.6    98.8265"
      ]
     },
     "execution_count": 308,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params = Params(material='aluminum',\n",
    "                plate_materials=plate_materials,\n",
    "                surface_area=1,\n",
    "                plate_temp=100,\n",
    "                thickness=.01,\n",
    "                dt=.001)\n",
    "system = make_system(params)\n",
    "results = run_simulation(system, update_func)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(results.thermal_energy_hand, 'g', label='Thermal energy of hand')\n",
    "plot(results.thermal_energy_ice, 'b', label='Thermal energy of ice')\n",
    "decorate(xlabel='Time (sec)', \n",
    "         ylabel='Thermal Energy (Joules)', \n",
    "         title='Ice Melting on Aluminum (Extreme)')"
   ]
  },
  {
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}