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compmech-project01/01_Getting-started-project-Copy1.ipynb

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Computational Mechanics Project #01 - Heat Transfer in Forensic Science\n",
"\n",
"We can use our current skillset for a macabre application. We can predict the time of death based upon the current temperature and change in temperature of a corpse. \n",
"\n",
"Forensic scientists use Newton's law of cooling to determine the time elapsed since the loss of life, \n",
"\n",
"$\\frac{dT}{dt} = -K(T-T_a)$,\n",
"\n",
"where $T$ is the current temperature, $T_a$ is the ambient temperature, $t$ is the elapsed time in hours, and $K$ is an empirical constant. \n",
"\n",
"Suppose the temperature of the corpse is 85$^o$F at 11:00 am. Then, 2 hours later the temperature is 74$^{o}$F. \n",
"\n",
"Assume ambient temperature is a constant 65$^{o}$F.\n",
"\n",
"1. Use Python to calculate $K$ using a finite difference approximation, $\\frac{dT}{dt} \\approx \\frac{T(t+\\Delta t)-T(t)}{\\Delta t}$. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"K = 0.6111111111111112\n"
]
}
],
"source": [
"dt = 2\n",
"dT = (74-85)\n",
"T = 74\n",
"Ta = 65\n",
"K = -(dT/dt)/(T-Ta)\n",
"print('K =',K)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. Change your work from problem 1 to create a function that accepts the temperature at two times, ambient temperature, and the time elapsed to return $K$. "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.6111111111111112\n"
]
}
],
"source": [
"def measure_K(Temp_t1,Temp_t2,Temp_ambient,delta_t):\n",
" ''' Determine the value of K based upon temperature of corpse \n",
" when discovered, Temp_t1\n",
" after time, delta_t, Temp_t2\n",
" with ambient temperature, Temp_ambient\n",
" Arguments\n",
" ---------\n",
" Inputs\n",
" \n",
" Returns\n",
" -------\n",
" your outputs...\n",
" \n",
" '''\n",
" dt = delta_t\n",
" dT = (Temp_t2 - Temp_t1)\n",
" T = Temp_t2\n",
" Ta = Temp_ambient\n",
" K = -(dT/dt)/(T-Ta)\n",
" \n",
" print(K)\n",
"measure_K(85,74,65,2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3. A first-order thermal system has the following analytical solution, \n",
"\n",
" $T(t) =T_a+(T(0)-T_a)e^{-Kt}$\n",
"\n",
" where $T(0)$ is the temperature of the corpse at t=0 hours i.e. at the time of discovery and $T_a$ is a constant ambient temperature. \n",
"\n",
" a. Show that an Euler integration converges to the analytical solution as the time step is decreased. Use the constant $K$ derived above and the initial temperature, T(0) = 85$^o$F. \n",
"\n",
" b. What is the final temperature as t$\\rightarrow\\infty$?\n",
" \n",
" c. At what time was the corpse 98.6$^{o}$F? i.e. what was the time of death?"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"at t = 2: T = 70.89149656620215\n"
]
}
],
"source": [
"import math\n",
"T_a = 65\n",
"T_o = 85\n",
"k = 0.6111111111111112\n",
"t = 2\n",
"T_t = T_a + (T_o - T_a)*math.exp(-k*t)\n",
"print('at t = 2: T = ', T_t)\n"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Decreasing timestep, at t = 1.3: T = analyitcal = 74.03664366175614\n"
]
}
],
"source": [
"import math\n",
"T_a = 65\n",
"T_o = 85\n",
"k = 0.6111111111111112\n",
"t = 1.3\n",
"T_t = T_a + (T_o - T_a)*math.exp(-k*t)\n",
"print('Decreasing timestep, at t = 1.3: T = analyitcal = ', T_t)\n"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"as t goes to infinity, T_t = Ambient Temperature = 65.0\n"
]
}
],
"source": [
"import math\n",
"T_a = 65\n",
"T_o = 85\n",
"k = 0.6111111111111112\n",
"t = 1000\n",
"T_t = T_a + (T_o - T_a)*math.exp(-k*t)\n",
"print('as t goes to infinity, T_t = Ambient Temperature = ', T_t)"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-0.8489352983157284\n",
"-50.93611789894371 min\n",
"time of death = 10:09 am\n"
]
}
],
"source": [
"import math\n",
"import numpy as np\n",
"T_a = 65\n",
"T_o = 85\n",
"k = 0.6111111111111112\n",
"T_t = 98.6\n",
"t = (1/k)*np.log((T_a-T_o)/(T_a-T_t))\n",
"print(t)\n",
"print((t*60), 'min')\n",
"print('time of death = ', '10:09 am')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"4. Now that we have a working numerical model, we can look at the results if the\n",
"ambient temperature is not constant i.e. T_a=f(t). We can use the weather to improve our estimate for time of death. Consider the following Temperature for the day in question. \n",
"\n",
" |time| Temp ($^o$F)|\n",
" |---|---|\n",
" |8am|55|\n",
" |9am|58|\n",
" |10am|60|\n",
" |11am|65|\n",
" |noon|66|\n",
" |1pm|67|\n",
"\n",
" a. Create a function that returns the current temperature based upon the time (0 hours=11am, 65$^{o}$F) \n",
" *Plot the function $T_a$ vs time. Does it look correct? Is there a better way to get $T_a(t)$?\n",
"\n",
" b. Modify the Euler approximation solution to account for changes in temperature at each hour. \n",
" Compare the new nonlinear Euler approximation to the linear analytical model. \n",
" At what time was the corpse 98.6$^{o}$F? i.e. what was the time of death? \n",
" \n",
" "
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"65"
]
},
"execution_count": 62,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"time_temp=np.array([[8,55],[9,58],[10,60],[11,65],[12,66],[13,67]])\n",
"def ambient_temp(time):\n",
" if time == 0:\n",
" Temp_amb = 65\n",
" elif 3 > time > 0:\n",
" Temp_amb = time_temp[time-3,1]\n",
" elif -4 < time < 0:\n",
" Temp_amb = time_temp[time+3,1]\n",
" else : \n",
" Temp_amb = 'unknown' \n",
" print('error')\n",
" return Temp_amb\n",
"plt.plot(time_temp[:,0],time_temp[:,1],'b-')\n",
"plt.xlabel('Time of Day')\n",
"plt.ylabel('Ambient Temp')\n",
"plt.title('Time Vs Ambient Temp')\n",
"ambient_temp(0)"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-0.8489352983157284\n"
]
}
],
"source": [
"import math\n",
"import numpy as np\n",
"time_temp=np.array([[8,55],[9,58],[10,60],[11,65],[12,66],[13,67]])\n",
"def ambient_temp(time):\n",
" if time == 0:\n",
" Temp_amb = 65\n",
" elif 3 > time > 0:\n",
" Temp_amb = time_temp[time-3,1]\n",
" elif -4 < time < 0:\n",
" Temp_amb = time_temp[time+3,1]\n",
" else : \n",
" Temp_amb = 'unknown' \n",
" print('error')\n",
" return Temp_amb\n",
"T_a = ambient_temp(0)\n",
"T_o = 85\n",
"k = 0.6111111111111112\n",
"T_t = 98.6\n",
"t = (1/k)*np.log((T_a-T_o)/(T_a-T_t))\n",
"print(t)"
]
},
{
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}