<?xml version="1.0" encoding="UTF-8"?>
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</Annotation-table>
<Task>
</Task>
<Group labelreference="L2" drawlabel="true">
<Input>
<Text-field style="Heading 3" layout="Heading 3"><Font italic="false">Example 2.3 Heating of Fluid in a Series of Tanks</Font></Text-field>
</Input>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Equations (equation (2.17)) can be used solving Maple and the procedure described above for nonhomogeneous simultaneous lineaer ODEs follows.</Text-field>
</Input>
</Group>
<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the number of differential equations.</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=3;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIiJA==">IiIk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Since all the equations are in the same form, a 'for' loop can be used to generate the equations.</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do eq[i]:=diff(T[i](t),t)=eval(alpha*(T[i-1](t)-T[i](t))+beta*(T[steam]-T[i](t)));od;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJUR0YlRiY2I0kidEdGJUYxLCYqJkkmYWxwaGFHRiVGJywmLSZGLzYjIiIhRjBGJ0YtISIiRidGJyomSSViZXRhR0YlRicsJiZGLzYjSSZzdGVhbUdGJUYnRi1GOkYnRic=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkiVEc2IjYjIiIiNiNJInRHRipGLiwmKiZJJmFscGhhR0YqRiwsJi0mRik2IyIiIUYtRixGJyEiIkYsRiwqJkklYmV0YUdGKkYsLCYmRik2I0kmc3RlYW1HRipGLEYnRjdGLEYs</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJUR0YlRiY2I0kidEdGJUYxLCYqJkkmYWxwaGFHRiUiIiIsJi0mRi82I0Y1RjBGNUYtISIiRjVGNSomSSViZXRhR0YlRjUsJiZGLzYjSSZzdGVhbUdGJUY1Ri1GOkY1RjU=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkiVEc2IjYjIiIjNiNJInRHRipGLiwmKiZJJmFscGhhR0YqIiIiLCYtJkYpNiNGMkYtRjJGJyEiIkYyRjIqJkklYmV0YUdGKkYyLCYmRik2I0kmc3RlYW1HRipGMkYnRjdGMkYy</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJUR0YlRiY2I0kidEdGJUYxLCYqJkkmYWxwaGFHRiUiIiIsJi0mRi82IyIiI0YwRjVGLSEiIkY1RjUqJkklYmV0YUdGJUY1LCYmRi82I0kmc3RlYW1HRiVGNUYtRjtGNUY1">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkiVEc2IjYjIiIkNiNJInRHRipGLiwmKiZJJmFscGhhR0YqIiIiLCYtJkYpNiMiIiNGLUYyRichIiJGMkYyKiZJJWJldGFHRipGMiwmJkYpNiNJJnN0ZWFtR0YqRjJGJ0Y4RjJGMg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Next, enter the temperature of the inlet steam to the first tank T<Font subscript="true" style="Text">0</Font> and the temperature of the steam 'Tsteam' as parameters (pars).</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={T[0](t)=20,T[steam]=250};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkLy0mSSJUR0YkNiMiIiE2I0kidEdGJCIjPy8mRik2I0kmc3RlYW1HRiQiJF0j">PCQvLSZJIlRHNiI2IyIiITYjSSJ0R0YnIiM/LyZGJjYjSSZzdGVhbUdGJyIkXSM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Specify the dependent variables.</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=[seq(T[i](t),i=1..N)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkldmFyc0c2IjclLSZJIlRHRiQ2IyIiIjYjSSJ0R0YkLSZGKDYjIiIjRistJkYoNiMiIiRGKw==">NyUtJkkiVEc2IjYjIiIiNiNJInRHRiYtJkYlNiMiIiNGKS0mRiU2IyIiJEYp</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Specify the right hand sides of the governing equations.</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=[seq(rhs(eq[i]),i=1..N)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNyUsJiomSSZhbHBoYUdGJCIiIiwmLSZJIlRHRiQ2IyIiITYjSSJ0R0YkRiktJkYtNiNGKUYwISIiRilGKSomSSViZXRhR0YkRiksJiZGLTYjSSZzdGVhbUdGJEYpRjJGNUYpRiksJiomRihGKSwmRjJGKS0mRi02IyIiI0YwRjVGKUYpKiZGN0YpLCZGOUYpRj9GNUYpRiksJiomRihGKSwmRj9GKS0mRi02IyIiJEYwRjVGKUYpKiZGN0YpLCZGOUYpRkhGNUYpRik=">NyUsJiomSSZhbHBoYUc2IiIiIiwmLSZJIlRHRiY2IyIiITYjSSJ0R0YmRictJkYrNiNGJ0YuISIiRidGJyomSSViZXRhR0YmRicsJiZGKzYjSSZzdGVhbUdGJkYnRjBGM0YnRicsJiomRiVGJywmRjBGJy0mRis2IyIiI0YuRjNGJ0YnKiZGNUYnLCZGN0YnRj1GM0YnRicsJiomRiVGJywmRj1GJy0mRis2IyIiJEYuRjNGJ0YnKiZGNUYnLCZGN0YnRkZGM0YnRic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Update these right hand sides by substituting the parameters:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=subs(pars,eqs);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNyUsJiomSSZhbHBoYUdGJCIiIiwmIiM/RiktJkkiVEdGJDYjRik2I0kidEdGJCEiIkYpRikqJkklYmV0YUdGJEYpLCYiJF0jRilGLEYyRilGKSwmKiZGKEYpLCZGLEYpLSZGLjYjIiIjRjBGMkYpRikqJkY0RiksJkY2RilGOkYyRilGKSwmKiZGKEYpLCZGOkYpLSZGLjYjIiIkRjBGMkYpRikqJkY0RiksJkY2RilGQ0YyRilGKQ==">NyUsJiomSSZhbHBoYUc2IiIiIiwmIiM/RictJkkiVEdGJjYjRic2I0kidEdGJiEiIkYnRicqJkklYmV0YUdGJkYnLCYiJF0jRidGKkYwRidGJywmKiZGJUYnLCZGKkYnLSZGLDYjIiIjRi5GMEYnRicqJkYyRicsJkY0RidGOEYwRidGJywmKiZGJUYnLCZGOEYnLSZGLDYjIiIkRi5GMEYnRicqJkYyRicsJkY0RidGQUYwRidGJw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Generate the coefficient matrix A and the vector B (recall that b = -B):</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=genmatrix(eqs,vars,'B');</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyU3JSwmSSZhbHBoYUdGJCEiIkklYmV0YUdGJEYsIiIhRi43JUYrRipGLjclRi5GK0Yq">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalm(B);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkndmVjdG9yRzYiNiM3JSwmKiYiIz8iIiJJJmFscGhhR0YkRiohIiIqJiIkXSNGKkklYmV0YUdGJEYqRiwsJEYtRixGMA==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The forcing function vector b is the negative of the B vector.</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b:=matrix(N,1);for i to N do b[i,1]:=-B[i];od:evalm(b);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiYkc2Ii1JJmFycmF5RyUqcHJvdGVjdGVkRzYlOyIiIiIiJDtGKkYqNyI=">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</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUknbWF0cml4RzYiNiM3JTcjLCYqJiIjPyIiIkkmYWxwaGFHRiRGK0YrKiYiJF0jRitJJWJldGFHRiRGK0YrNyMsJEYtRitGMA==">PTYiNiQ7IiIiIiIkO0YmRiZFXFtsJDYkRidGJiwkKiYiJF0jRiZJJWJldGFHRiNGJkYmNiQiIiNGJkYrNiRGJkYmLCYqJiIjP0YmSSZhbHBoYUdGI0YmRiZGLEYm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Next, find the exponential matrix for the coefficient matrix A:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=exponential(A,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkbWF0RzYiLUknbWF0cml4R0YkNiM3JTclLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComLCZJJmFscGhhR0YkIiIiSSViZXRhR0YkRjRGNEkidEdGJEY0ISIiIiIhRjg3JSooRjNGNEY2RjRGKkY0RipGODclLCQqKiNGNCIiI0Y0KUYzRj9GNClGNkY/RjRGKkY0RjRGOkYq">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Specify the initial tank temperatures.</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=matrix(3,1,[20,20,20]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWTBHNiItSSdtYXRyaXhHRiQ2IzclNyMiIz9GKUYp">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Since the <Font bold="true" style="Text">b</Font> vector is the constant vector, find the intermediate vector s1.</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">s1:=evalm(Y0+inverse(A)&amp;*b);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjczFHNiItSSdtYXRyaXhHRiQ2IzclNyMsJiIjPyIiIiomLCZJJmFscGhhR0YkRixJJWJldGFHRiRGLCEiIiwmKiZGK0YsRi9GLEYsKiYiJF0jRixGMEYsRixGLEYxNyMsKEYrRiwqKEYvRiwpRi4iIiNGMUYyRixGMSooRjVGLEYuRjFGMEYsRjE3IywqRitGLCooKUYvRjpGLClGLiIiJEYxRjJGLEYxKipGNUYsRi9GLEY5RjFGMEYsRjFGO0Yx">[encoded data, 4164 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Next, find the solution vector:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=evalm(mat&amp;*s1-inverse(A)&amp;*b);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">[encoded data, 15576 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The elements of the solution vector 'sol' are the desired temperatures of the three tanks.  Store these in T1, T2, and T3:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T1:=sol[1,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVDFHNiIsJiomLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComLCZJJmFscGhhR0YkIiIiSSViZXRhR0YkRjFGMUkidEdGJEYxISIiRjEsJiIjP0YxKiZGL0Y0LCYqJkY2RjFGMEYxRjEqJiIkXSNGMUYyRjFGMUYxRjRGMUYxRjdGMQ==">LCYqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiwmSSZhbHBoYUdGKSIiIkklYmV0YUdGKUYvRi9JInRHRilGLyEiIkYvLCYiIz9GLyomRi1GMiwmKiZGNEYvRi5GL0YvKiYiJF0jRi9GMEYvRi9GL0YyRi9GL0Y1Ri8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T2:=sol[2,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVDJHNiIsKioqSSZhbHBoYUdGJCIiIkkidEdGJEYoLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComLCZGJ0YoSSViZXRhR0YkRihGKEYpRighIiJGKCwmIiM/RigqJkYyRjQsJiomRjZGKEYnRihGKComIiRdI0YoRjNGKEYoRihGNEYoRigqJkYqRigsKEY2RigqKEYnRigpRjIiIiNGNEY4RihGNCooRjtGKEYyRjRGM0YoRjRGKEYoRj5GKEZBRig=">LCoqKkkmYWxwaGFHNiIiIiJJInRHRiVGJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCQqJiwmRiRGJkklYmV0YUdGJUYmRiZGJ0YmISIiRiYsJiIjP0YmKiZGMEYyLCYqJkY0RiZGJEYmRiYqJiIkXSNGJkYxRiZGJkYmRjJGJkYmKiZGKEYmLChGNEYmKihGJEYmKUYwIiIjRjJGNkYmRjIqKEY5RiZGMEYyRjFGJkYyRiZGJkY8RiZGP0Ym</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T3:=sol[3,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVDNHNiIsLiosIyIiIiIiI0YoKUkmYWxwaGFHRiRGKUYoKUkidEdGJEYpRigtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiYsJkYrRihJJWJldGFHRiRGKEYoRi1GKCEiIkYoLCYiIz9GKComRjZGOCwmKiZGOkYoRitGKEYoKiYiJF0jRihGN0YoRihGKEY4RihGKCoqRitGKEYtRihGLkYoLChGOkYoKihGK0YoKUY2RilGOEY8RihGOCooRj9GKEY2RjhGN0YoRjhGKEYoKiZGLkYoLCpGOkYoKihGKkYoKUY2IiIkRjhGPEYoRjgqKkY/RihGK0YoRkNGOEY3RihGOEZERjhGKEYoRkdGKEZKRihGREYo">LC4qLCMiIiIiIiNGJSlJJmFscGhhRzYiRiZGJSlJInRHRilGJkYlLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YpNiMsJComLCZGKEYlSSViZXRhR0YpRiVGJUYrRiUhIiJGJSwmIiM/RiUqJkY0RjYsJiomRjhGJUYoRiVGJSomIiRdI0YlRjVGJUYlRiVGNkYlRiUqKkYoRiVGK0YlRixGJSwoRjhGJSooRihGJSlGNEYmRjZGOkYlRjYqKEY9RiVGNEY2RjVGJUY2RiVGJSomRixGJSwqRjhGJSooRidGJSlGNCIiJEY2RjpGJUY2KipGPUYlRihGJUZBRjZGNUYlRjZGQkY2RiVGJUZFRiVGSEYlRkJGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Next, determine values for <Equation executable="false" style="Normal" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==</Equation><Font encoding="UTF-8"> and \316\262 and then substitute them into the expression for T1, T2, and T3.</Font></Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={alpha=(100./1000.),beta=10./(1000*2)};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kmYWxwaGFHRiQkIisrKysrNSEjNS9JJWJldGFHRiQkIisrKysrXSEjNw==">PCQvSSZhbHBoYUc2IiQiKysrKys1ISM1L0klYmV0YUdGJSQiKysrKytdISM3</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TT1:=subs(pars,T1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkVFQxRzYiLCYqJiQiKyY0UV80IiEiKSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJiQiKysrK101ISM1RipJInRHRiRGKiEiIkYqRjckIismNFFfNCRGKUYq">LCYqJiQiKyY0UV80IiEiKSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiQiKysrK101ISM1RidJInRHRi1GJyEiIkYnRjUkIismNFFfNCRGJkYn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TT2:=subs(pars,T2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkVFQyRzYiLCgqKCQiKyY0UV80IiEiKiIiIkkidEdGJEYqLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComJCIrKysrXTUhIzVGKkYrRiohIiJGKkY3KiYkIismKj5LUUAhIilGKkYsRipGNyQiKyYqPktRVEY7Rio=">LCgqKCQiKyY0UV80IiEiKiIiIkkidEc2IkYnLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YpNiMsJComJCIrKysrXTUhIzVGJ0YoRichIiJGJ0Y1KiYkIismKj5LUUAhIilGJ0YqRidGNSQiKyYqPktRVEY5Ric=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TT3:=subs(pars,T3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkVFQzRzYiLCoqKCQiK3YvPndhISM2IiIiKUkidEdGJCIiI0YqLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComJCIrKysrXTUhIzVGKkYsRiohIiJGKkY5KigkIismKj5LUUAhIipGKkYsRipGLkYqRjkqJiQiK0xfdEpKISIpRipGLkYqRjkkIitMX3RKXkZBRio=">LCoqKCQiK3YvPndhISM2IiIiKUkidEc2IiIiI0YnLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YqNiMsJComJCIrKysrXTUhIzVGJ0YpRichIiJGJ0Y3KigkIismKj5LUUAhIipGJ0YpRidGLEYnRjcqJiQiK0xfdEpKISIpRidGLEYnRjckIitMX3RKXkY/Ric=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Finally, plot the temperature profiles:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[1]:=plot(TT1,t=0..60,thickness=4,linestyle=1,color=red,legend=&quot;T1&quot;):</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[2]:=plot(TT2,t=0..60,thickness=4,linestyle=1,color=green,legend=&quot;T2&quot;):</Text-field>
</Input>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[3]:=plot(TT3,t=0..60,thickness=4,linestyle=1,color=gold,legend=&quot;T3&quot;):</Text-field>
</Input>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(p[i],i=1..3)},title=&quot;Figure Exp 2.3 Temperatures for three tanks.&quot;,axes=boxed,labels=[&quot;t(min)&quot;,&quot;Temperature (degrees C)&quot;],labeldirections=[HORIZONTAL,VERTICAL]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="true">[encoded data, 9812 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The time taken for the third tank to reach 99% of the steady state value can be obtained from the TT3 equation by first finding its value for infinity by using Maple's 'limit' command:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T3steadystate:=limit(TT3,t=infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkuVDNzdGVhZHlzdGF0ZUc2IiQiK0xfdEpeISIp">JCIrTF90Sl4hIik=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Next, the time taken to reach 99% of this steady state value is determined by using 'fsolve' to find the time T when TT3 is 99% of it steady state value.  First, define eq3:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq3:=0.99*T3steadystate=TT3;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXEzRzYiLyQiKyIpeVQhMyYhIiksKiooJCIrdi8+d2EhIzYiIiIpSSJ0R0YkIiIjRi4tSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiYkIisrKytdNSEjNUYuRjBGLiEiIkYuRj0qKCQiKyYqPktRQCEiKkYuRjBGLkYyRi5GPSomJCIrTF90SkpGKEYuRjJGLkY9JCIrTF90Sl5GKEYu">LyQiKyIpeVQhMyYhIiksKiooJCIrdi8+d2EhIzYiIiIpSSJ0RzYiIiIjRistSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRi42IywkKiYkIisrKytdNSEjNUYrRi1GKyEiIkYrRjsqKCQiKyYqPktRQCEiKkYrRi1GK0YwRitGOyomJCIrTF90SkpGJUYrRjBGK0Y7JCIrTF90Sl5GJUYr</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Next, solve eq3 for t and call that Timereqd.</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Timereqd:=fsolve(eq3,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkpVGltZXJlcWRHNiIkIitiJlI5SSchIik=">JCIrYiZSOUknISIp</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Alternatively, one can find the steady state value of the temperature analytically by applying the 'limit' command on T3 instead of TT3.</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T3steadystate:=limit(T3,t=infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkuVDNzdGVhZHlzdGF0ZUc2Ii1JJmxpbWl0RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQsLiosIyIiIiIiI0YuKUkmYWxwaGFHRiRGL0YuKUkidEdGJEYvRi4tSSRleHBHRic2IywkKiYsJkYxRi5JJWJldGFHRiRGLkYuRjNGLiEiIkYuLCYiIz9GLiomRjlGOywmKiZGPUYuRjFGLkYuKiYiJF0jRi5GOkYuRi5GLkY7Ri5GLioqRjFGLkYzRi5GNEYuLChGPUYuKihGMUYuKUY5Ri9GO0Y/Ri5GOyooRkJGLkY5RjtGOkYuRjtGLkYuKiZGNEYuLCpGPUYuKihGMEYuKUY5IiIkRjtGP0YuRjsqKkZCRi5GMUYuRkZGO0Y6Ri5GO0ZHRjtGLkYuRkpGLkZNRi5GR0YuL0YzSSlpbmZpbml0eUdGKA==">LUkmbGltaXRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwuKiwjIiIiIiIjRiwpSSZhbHBoYUdGJ0YtRiwpSSJ0R0YnRi1GLC1JJGV4cEdGJDYjLCQqJiwmRi9GLEklYmV0YUdGJ0YsRixGMUYsISIiRiwsJiIjP0YsKiZGN0Y5LCYqJkY7RixGL0YsRiwqJiIkXSNGLEY4RixGLEYsRjlGLEYsKipGL0YsRjFGLEYyRiwsKEY7RiwqKEYvRiwpRjdGLUY5Rj1GLEY5KihGQEYsRjdGOUY4RixGOUYsRiwqJkYyRiwsKkY7RiwqKEYuRiwpRjciIiRGOUY9RixGOSoqRkBGLEYvRixGREY5RjhGLEY5RkVGOUYsRixGSEYsRktGLEZFRiwvRjFJKWluZmluaXR5R0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">Maple is unable to find the limit, as it does not know the sign of alpha and beta.  We can specify that alpha and beta are greater than zero by using Maple's 'assume' command:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">assume(alpha&gt;0,beta&gt;0);</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"></Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T3steadystate:=eval(T3steadystate);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkuVDNzdGVhZHlzdGF0ZUc2IiomLCoqKCIkXSgiIiIpSSdhbHBoYXxpckdGJCIiI0YpSSZiZXRhfGlyR0YkRilGKSooRihGKUYrRikpRi1GLEYpRikqJiIkXSNGKSlGLSIiJEYpRikqJiIjP0YpKUYrRjNGKUYpRiksKiokRjZGKUYpKihGM0YpRipGKUYtRilGKSooRjNGKUYrRilGL0YpRikqJEYyRilGKSEiIg==">KiYsKiooIiRdKCIiIilJJ2FscGhhfGlyRzYiIiIjRiZJJmJldGF8aXJHRilGJkYmKihGJUYmRihGJilGK0YqRiZGJiomIiRdI0YmKUYrIiIkRiZGJiomIiM/RiYpRihGMUYmRiZGJiwqKiRGNEYmRiYqKEYxRiZGJ0YmRitGJkYmKihGMUYmRihGJkYtRiZGJiokRjBGJkYmISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Note that the trailing tildes (tildes symbol) indicate that the \316\261 and \316\262 </Font>must be greater than zero.</Text-field>
</Input>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>