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diff --git a/Material_Science/material_science_ch_12.ipynb b/Material_Science/material_science_ch_12.ipynb new file mode 100755 index 00000000..7deff30f --- /dev/null +++ b/Material_Science/material_science_ch_12.ipynb @@ -0,0 +1,461 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 12: Thermal Properties"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.1, page no-350"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Change in length due to heating\n",
+ "\n",
+ "import math\n",
+ "#Variable Declaration\n",
+ "alfe=8.8*10**-6 # linear coefficient of thermal expansion for alumina\n",
+ "lo=0.1 # length of the alumina rod\n",
+ "delT=973.0 # difference in temperature\n",
+ "\n",
+ "#Calculation\n",
+ "delL=alfe*lo*delT\n",
+ "\n",
+ "#Result\n",
+ "print('The change in length produced by heating is %.3f mm'%(delL*10**3))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The change in length produced by heating is 0.856 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.2, page no-350"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Change in length due to heating\n",
+ "\n",
+ "import math\n",
+ "#Variable Declaration\n",
+ "alfe=5.3*10**-6 # linear coefficient of thermal expansion or alumina\n",
+ "lo=0.1 # length of the alumina rod\n",
+ "delT=973.0 # difference in temperature\n",
+ "\n",
+ "#Calculation\n",
+ "delL=alfe*lo*delT\n",
+ "\n",
+ "#Result\n",
+ "print('The change in length produced by heating is %.3f mm'%(delL*10**3))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The change in length produced by heating is 0.516 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 12.3, page no-351"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Steady state heat Transfer\n",
+ "\n",
+ "import math\n",
+ "#Variable Declaration\n",
+ "k=371.0 # Thermal conductivity of copper in J/msk\n",
+ "delT=50.0 # change in temperature\n",
+ "delx=10*10**-3 # change in thickness of the copper's sheet \n",
+ "\n",
+ "#Calculation\n",
+ "ht=k*delT/delx\n",
+ "\n",
+ "#Result\n",
+ "print('The steady state heat transfer of 10 mm copper sheet is %.3f *10^6 J.m^-2.s^-1'%(ht*10**-6))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The steady state heat transfer of 10 mm copper sheet is 1.855 *10^6 J.m^-2.s^-1\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.4, page no-351"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Compression Stress due to Heating\n",
+ "\n",
+ "import math\n",
+ "#Variable Declaration\n",
+ "alfe=8.8*10**-6 # linear coefficient of thermal expansion for alumina\n",
+ "t1=1300.0 # Temperature 1\n",
+ "t2=327.0 # Temperature 2\n",
+ "E=370.0 # modulus of elasticity\n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "delT=t1-t2\n",
+ "ep=alfe*delT\n",
+ "sig=ep*E\n",
+ "\n",
+ "#Result\n",
+ "print('\\nThe unconstrained thermal expansion produced by the heating is %.4f *10^-3'%(ep*10**3))\n",
+ "print('\\nthe compression stress produced by heating is %.3f GPa'%(math.ceil(sig*1000)/1000))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "The unconstrained thermal expansion produced by the heating is 8.5624 *10^-3\n",
+ "\n",
+ "the compression stress produced by heating is 3.169 GPa\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 12.5, page no-352"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Heat flux transmitted\n",
+ "\n",
+ "import math\n",
+ "#Variable Declaration\n",
+ "K=120.0 # thermal conductivity of brass\n",
+ "t2=423.0 # Temperature 2\n",
+ "t1=323.0 # Temperature 1\n",
+ "delT=t2-t1 # temperature difference\n",
+ "delx=7.5*10**-3 # change in thickness of the brass's sheet\n",
+ "A=0.5 # Area of the sheet\n",
+ "\n",
+ "#Calculation\n",
+ "Q=K*A*(delT/delx)\n",
+ "hph=Q*3600\n",
+ "\n",
+ "#Result\n",
+ "print('The heat flux transmitted through a sheet per hour is %.2f *10^9 J.h^-1'%(hph*10**-9))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat flux transmitted through a sheet per hour is 2.88 *10^9 J.h^-1\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.6, page no-353"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Young's Modulus\n",
+ "\n",
+ "import math\n",
+ "#Variable Declaration\n",
+ "alfe=17*10**-6 # linear coefficient of thermal expansion for copper\n",
+ "t2=293.0 # Temperature 2\n",
+ "t1=233.0 # Temperature 1\n",
+ "delT=t2-t1 # temperature difference\n",
+ "st=119.0 # Maximum thermally induced stress\n",
+ "\n",
+ "#Calculation\n",
+ "k=alfe*delT\n",
+ "E=(st*10**6)/k\n",
+ "\n",
+ "#Result\n",
+ "print('\\nThe strain produced in te rod is %.2f * 10^-3'%(k*10**3))\n",
+ "print('\\nThe Youngs Modulus of the rod is %.1f GPa'%(E*10**-9))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "The strain produced in te rod is 1.02 * 10^-3\n",
+ "\n",
+ "The Youngs Modulus of the rod is 116.7 GPa\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.7, page no-353"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Temperature Change\n",
+ "\n",
+ "import math\n",
+ "#Variable Declaration\n",
+ "lo=11.6 # length of the steel rod\n",
+ "delx=5.4*10**-3 # difference in length\n",
+ "alfL=12*10**-6 # Linear coefficient of thermal expansion for steel\n",
+ "\n",
+ "#Calculation\n",
+ "delT=delx/(lo*alfL)\n",
+ "\n",
+ "#Result\n",
+ "print('The maximum temperature cange can withstand without any thermal stress is %.2f K'%delT)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The maximum temperature cange can withstand without any thermal stress is 38.79 K\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.8, page no-354"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#compressive Sress\n",
+ "\n",
+ "import math\n",
+ "#Variable Declaration\n",
+ "lo=0.35 # length of the Al rod\n",
+ "alfe=23.6*10**-6 # Linear coefficient of thermal expansion for Al\n",
+ "t2=358.0 # temperature 2\n",
+ "t1=288.0 # temperature 1\n",
+ "delT=t2-t1 # temperature difference\n",
+ "ym=69.0 # Young's modulus\n",
+ "\n",
+ "#Calculation\n",
+ "k=alfe*delT\n",
+ "E=ym*k*10**9\n",
+ "\n",
+ "#Result\n",
+ "print('\\nThe strain produced in te rod is %.3f * 10^-3'%(k*10**3))\n",
+ "print('\\nThe compressive stress produced in Al rod is %.3f GPa'%(E*10**-9))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "The strain produced in te rod is 1.652 * 10^-3\n",
+ "\n",
+ "The compressive stress produced in Al rod is 0.114 GPa\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.9, page no-355"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# limit to compression stress\n",
+ "\n",
+ "import math\n",
+ "#Variable Declaration\n",
+ "alfe=20*10**-6 # Linear coefficient of thermal expansion for alumina\n",
+ "t1=293.0 # temperature \n",
+ "sig=172.0 # compressive stress\n",
+ "E=100.0 # modulus of elasticity\n",
+ "\n",
+ "#Calculation\n",
+ "delT=(sig*10**6)/(E*alfe*10**9)\n",
+ "\n",
+ "#Result\n",
+ "print('\\nTf-Ti=%.0f'%delT)\n",
+ "print('\\n\\nThe maximum temperature at which the rod may be heated without\\nexceeding a compresssive stress of %.0f MPa is %.0f K'%(sig,delT+t1))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "Tf-Ti=86\n",
+ "\n",
+ "\n",
+ "The maximum temperature at which the rod may be heated without\n",
+ "exceeding a compresssive stress of 172 MPa is 379 K\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 12.10, page no-356"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Heat energy Requirement\n",
+ "\n",
+ "import math\n",
+ "#Variable Declaration\n",
+ "h_ir=444.0 # specific heat capacity of iron in J.kg^-1.K^-1\n",
+ "h_gr=711.0 # specific heat capacity of graphite in J.kg^-1.K^-1\n",
+ "h_pl=1880.0 # specific heat capacity of polypropylene in J.kg^-1.K^-1\n",
+ "t2=373.0 # Temperature 2\n",
+ "t1=300.0 # Temperature 1\n",
+ "delT=t2-t1 # difference in temperature\n",
+ "W=2.0 # weight\n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#(a) For Iron\n",
+ "q=W*h_ir*delT\n",
+ "\n",
+ "#(b)for Graphite\n",
+ "q1=W*h_gr*delT\n",
+ "\n",
+ "#(b)for polypropylene\n",
+ "q2=W*h_pl*delT\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print('The heat energy required to raise temperature %.0f K from its temperature of \\niron, graphite and polypropylene is %.0f,%.0f,%.0f J respectively'%(delT,q,q1,q2))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat energy required to raise temperature 73 K from its temperature of \n",
+ "iron, graphite and polypropylene is 64824,103806,274480 J respectively\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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