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put current notebook status on github
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‎code/chap02mine.ipynb‎

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‎code/chap15mine.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Modeling and Simulation in Python\n",
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"\n",
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"Chapter 15\n",
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"\n",
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"Copyright 2017 Allen Downey\n",
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"\n",
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"License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Configure Jupyter so figures appear in the notebook\n",
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"%matplotlib inline\n",
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"\n",
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"# Configure Jupyter to display the assigned value after an assignment\n",
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"%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
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"\n",
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"# import functions from the modsim.py module\n",
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"from modsim import *"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### The coffee cooling problem\n",
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"\n",
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"I'll use a `State` object to store the initial temperature.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"init = State(T=90)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"And a `System` object to contain the system parameters."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"coffee = System(init=init,\n",
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" volume=300,\n",
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" r=0.01,\n",
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" T_env=22,\n",
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" t_end=30,\n",
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" dt=1)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The update function implements Newton's law of cooling."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"def update_func(state, t, system):\n",
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" \"\"\"Update the thermal transfer model.\n",
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" \n",
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" state: State (temp)\n",
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" t: time\n",
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" system: System object\n",
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" \n",
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" returns: State (temp)\n",
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" \"\"\"\n",
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" unpack(system)\n",
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" \n",
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" T = state.T\n",
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" T += -r * (T - T_env) * dt\n",
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" \n",
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" return State(T=T)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Here's how it works."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"update_func(init, 0, coffee)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Here's a version of `run_simulation` that uses `linrange` to make an array of time steps."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [],
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"source": [
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"def run_simulation(system, update_func):\n",
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" \"\"\"Runs a simulation of the system.\n",
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" \n",
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" Add a TimeFrame to the System: results\n",
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" \n",
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" system: System object\n",
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" update_func: function that updates state\n",
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" \"\"\"\n",
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" unpack(system)\n",
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" \n",
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" frame = TimeFrame(columns=init.index)\n",
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" frame.row[0] = init\n",
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" ts = linrange(0, t_end, dt)\n",
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" \n",
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" for t in ts:\n",
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" frame.row[t+dt] = update_func(frame.row[t], t, system)\n",
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" \n",
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" # store the final temperature in T_final\n",
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" system.T_final = get_last_value(frame.T)\n",
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" \n",
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" return frame"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"And here's how it works."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"results = run_simulation(coffee, update_func)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Here's what the results look like."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {},
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"outputs": [],
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"source": [
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"plot(results.T, label='coffee')\n",
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"decorate(xlabel='Time (minutes)',\n",
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" ylabel='Temperature (C)')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"And here's the final temperature:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [],
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"source": [
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"coffee.T_final"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Encapsulation\n",
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"\n",
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"Before we go on, let's define a function to initialize `System` objects with relevant parameters:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"def make_system(T_init, r, volume, t_end):\n",
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" \"\"\"Makes a System object with the given parameters.\n",
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"\n",
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" T_init: initial temperature in degC\n",
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" r: heat transfer rate, in 1/min\n",
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" volume: volume of liquid in mL\n",
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" t_end: end time of simulation\n",
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" \n",
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" returns: System object\n",
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" \"\"\"\n",
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" init = State(T=T_init)\n",
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" \n",
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" # T_final is used to store the final temperature.\n",
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" # Before the simulation runs, T_final = T_init\n",
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" T_final = T_init\n",
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"\n",
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" T_env = 22 \n",
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" dt = 1\n",
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" \n",
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" return System(locals())"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Here's how we use it:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [],
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"source": [
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"coffee = make_system(T_init=90, r=0.01, volume=300, t_end=30)\n",
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"results = run_simulation(coffee, update_func)\n",
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"coffee.T_final"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Exercises\n",
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"\n",
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"**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",
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"\n",
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"By trial and error, find a values for `r` that makes the final temperature close to 20 C."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Solution goes here"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [],
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"source": [
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"plot(results.T, label='milk')\n",
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"decorate(xlabel='Time (minutes)',\n",
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" ylabel='Temperature (C)')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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