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<Text-field style="Heading 3" layout="Heading 3"><Font italic="false">Example 3.2</Font></Text-field>
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<Text-field style="Text" layout="Normal">Diffusion with a convection and simultaneous first orderrreaction in a rectangular plate can be simulated using the program described above by using minor modifications.  Consider the composition profile in a packed tube reactor undergoing isothermal linear kinetics with axial diffusion.  The equation is</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="Text" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYkLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjRGNC1JI21vR0YkNi1RIj1GJ0Y0LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRjE2JFEiMEYnRjRGNA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNiMtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjQtSSNtb0dGJDYtUSI9RidGNC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYxNiRRIjBGJ0Y0</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Solving this boundary value problem by hand is difficult and the solution for this problem is very long.  This boundary value problem is solbed below easilty by following the procedure described earlier.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):with(plots):</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=2;</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(C(x),x$2)-Pe*diff(C(x),x)-Ha*C(x);</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal262">A:=matrix(N,N,[0,1,Ha,Pe]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyQ3JCIiISIiIjckSSNIYUdGJEkjUGVHRiQ=">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=exponential(A,x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkbWF0RzYiLUknbWF0cml4R0YkNiM3JDckLCQqKCMiIiIiIiNGLSwqKiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKihGLEYtLCZJI1BlR0YkRi0qJCksJiokKUY6Ri5GLUYtKiYiIiVGLUkjSGFHRiRGLUYtRixGLUYtRi1JInhHRiRGLUYtRi1GPEYtRi0qJkY6Ri0tRjI2IywkKihGLEYtLCZGOkYtRjshIiJGLUZDRi1GLUYtRi0qJkY6Ri1GMUYtRkoqJkZFRi1GPEYtRi1GLUY8RkpGLSwkKiYsJkZFRi1GMUZKRi1GPEZKRko3JCwkKihGQkYtRk9GLUY8RkpGSiwkKihGLEYtLCpGMEZKRkRGLUZLRkpGTEZKRi1GPEZKRko=">[encoded data, 15820 characters]</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Note that for this boundary value problem both  C and <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>at x=0 are not known.  However, using the boundary condition at x=0,  <Equation executable="false" style="2D Math" input-equation="" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JJW1yb3dHRiQ2JS1JI21vR0YkNi1RMCZEaWZmZXJlbnRpYWxEO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZGLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EmZmFsc2VGJ0YyRjItRiw2JkYuLUYvNi1RIn5GJ0YyL0Y2Rk8vRjlGTy9GO0ZPL0Y9Rk8vRj9GTy9GQUZPL0ZDRk9GREZHLUZKNiVRInhGJ0ZNRjJGMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXm8vJSliZXZlbGxlZEdGTw==">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</Equation> can be written in terms of the unknown constant c<Font subscript="true">1</Font>, which is the concentration at x=0.</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal262">Y0:=matrix(N,1,[c[1],-Pe*(1-c[1])]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWTBHNiItSSdtYXRyaXhHRiQ2IzckNyMmSSJjR0YkNiMiIiI3IywkKiZJI1BlR0YkRi0sJkYtRi1GKiEiIkYtRjM=">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=evalm(mat&amp;*Y0):</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C:=sol[1,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQ0c2IiwmKiojIiIiIiIjRigsKiomLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJCooRidGKCwmSSNQZUdGJEYoKiQpLCYqJClGNUYpRihGKComIiIlRihJI0hhR0YkRihGKEYnRihGKEYoSSJ4R0YkRihGKEYoRjdGKEYoKiZGNUYoLUYtNiMsJCooRidGKCwmRjVGKEY2ISIiRihGPkYoRihGKEYoKiZGNUYoRixGKEZFKiZGQEYoRjdGKEYoRihGN0ZFJkkiY0dGJDYjRihGKEYoKiosJkZARihGLEZFRihGN0ZFRjVGKCwmRihGKEZIRkVGKEYo">LCYqKiMiIiIiIiNGJSwqKiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkKihGJEYlLCZJI1BlR0YuRiUqJCksJiokKUYzRiZGJUYlKiYiIiVGJUkjSGFHRi5GJUYlRiRGJUYlRiVJInhHRi5GJUYlRiVGNUYlRiUqJkYzRiUtRio2IywkKihGJEYlLCZGM0YlRjQhIiJGJUY8RiVGJUYlRiUqJkYzRiVGKUYlRkMqJkY+RiVGNUYlRiVGJUY1RkMmSSJjR0YuNiNGJUYlRiUqKiwmRj5GJUYpRkNGJUY1RkNGM0YlLCZGJUYlRkZGQ0YlRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dCdx:=sol[2,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZENkeEc2IiwmKipJI0hhR0YkIiIiLCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKigjRigiIiNGKCwmSSNQZUdGJEYoKiQpLCYqJClGNUYzRihGKComIiIlRihGJ0YoRihGMkYoISIiRihJInhHRiRGKEYoRigtRis2IywkKihGMkYoLCZGNUYoRjZGKEYoRj5GKEYoRj1GKEY3Rj0mSSJjR0YkNiNGKEYoRj0qLEYyRigsKiomRj9GKEY3RihGPSomRjVGKEYqRihGKComRjVGKEY/RihGPSomRipGKEY3RihGPUYoRjdGPUY1RigsJkYoRihGREY9RihGKA==">LCYqKkkjSGFHNiIiIiIsJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCQqKCNGJiIiI0YmLCZJI1BlR0YlRiYqJCksJiokKUYzRjFGJkYmKiYiIiVGJkYkRiZGJkYwRiYhIiJGJkkieEdGJUYmRiZGJi1GKTYjLCQqKEYwRiYsJkYzRiZGNEYmRiZGPEYmRiZGO0YmRjVGOyZJImNHRiU2I0YmRiZGOyosRjBGJiwqKiZGPUYmRjVGJkY7KiZGM0YmRihGJkYmKiZGM0YmRj1GJkY7KiZGKEYmRjVGJkY7RiZGNUY7RjNGJiwmRiZGJkZCRjtGJkYm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">To find c<Font subscript="true">1</Font>, we can use the known boundary condition at  x=0.</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=subs(x=1,dCdx)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLywmKipJI0hhR0YkIiIiLCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywmKiYjRikiIiNGKUkjUGVHRiRGKUYpKiZGM0YpKSwmKiQpRjVGNEYpRikqJiIiJUYpRihGKUYpRjNGKSEiIkYpLUYsNiMsJkYyRilGNkYpRj1GKUY3Rj0mSSJjR0YkNiNGKUYpRj0qLEYzRiksKiomRj5GKUY3RilGPSomRjVGKUYrRilGKSomRjVGKUY+RilGPSomRitGKUY3RilGPUYpRjdGPUY1RiksJkYpRilGQUY9RilGKSIiIQ==">LywmKipJI0hhRzYiIiIiLCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IywmKiYjRiciIiNGJ0kjUGVHRiZGJ0YnKiZGMUYnKSwmKiQpRjNGMkYnRicqJiIiJUYnRiVGJ0YnRjFGJyEiIkYnLUYqNiMsJkYwRidGNEYnRjtGJ0Y1RjsmSSJjR0YmNiNGJ0YnRjsqLEYxRicsKiomRjxGJ0Y1RidGOyomRjNGJ0YpRidGJyomRjNGJ0Y8RidGOyomRilGJ0Y1RidGO0YnRjVGO0YzRicsJkYnRidGP0Y7RidGJyIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The equation for c<Font subscript="true">1</Font> can be solved easily by using Maple's 'solve' command.</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">c[1]:=solve(bc2,c[1]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJImNHNiI2IyIiIiooSSNQZUdGJUYnLCoqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCYqJiNGJyIiI0YnRilGJ0YnKiZGNEYnKSwmKiQpRilGNUYnRicqJiIiJUYnSSNIYUdGJUYnRidGNEYnRidGJ0Y3RichIiIqJkYpRictRi02IywmRjNGJ0Y2Rj5GJ0YnKiZGKUYnRixGJ0Y+KiZGQEYnRjdGJ0Y+RicsLiooRjVGJ0Y9RidGQEYnRicqKEY1RidGPUYnRixGJ0Y+KihGKUYnRixGJ0Y3RidGPiomRjpGJ0ZARidGJyomRjpGJ0YsRidGPiooRilGJ0ZARidGN0YnRj5GPg==">KihJI1BlRzYiIiIiLCoqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCYqJiNGJSIiI0YlRiNGJUYlKiZGMEYlKSwmKiQpRiNGMUYlRiUqJiIiJUYlSSNIYUdGJEYlRiVGMEYlRiVGJUYzRiUhIiIqJkYjRiUtRik2IywmRi9GJUYyRjpGJUYlKiZGI0YlRihGJUY6KiZGPEYlRjNGJUY6RiUsLiooRjFGJUY5RiVGPEYlRiUqKEYxRiVGOUYlRihGJUY6KihGI0YlRihGJUYzRiVGOiomRjZGJUY8RiVGJSomRjZGJUYoRiVGOiooRiNGJUY8RiVGM0YlRjpGOg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Now that we have c<Font subscript="true">1, </Font>the complete solution can be determined for C by using Maple's 'eval' command:</Text-field>
</Input>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C:=eval(C);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, one can plot the concentration profile by substituting values for the parameters Ha and Pe:</Text-field>
</Input>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={Ha=1,Pe=10};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kjSGFHRiQiIiIvSSNQZUdGJCIjNQ==">PCQvSSNIYUc2IiIiIi9JI1BlR0YlIiM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(subs(pars,C),x=0..1,thickness=4,axes=boxed,labels=[x,&quot;C&quot;],title=&quot;Figure Exp. 3.1.3.&quot;);</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="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">New plots can be made for different sets of parameters such as:</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={Ha=1,Pe=50};</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(subs(pars,C),x=0..1,thickness=4,axes=boxed,labels=[x,&quot;C&quot;],color=green,title=&quot;Figure Exp. 3.1.4.&quot;);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kjSGFHRiQiIiIvSSNQZUdGJCIjXQ==">PCQvSSNIYUc2IiIiIi9JI1BlR0YlIiNd</Equation></Text-field>
</Output>
<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="false">[encoded data, 7952 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">When we get weird plots, we can solve this problem by increasing the number of digits as:</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Digits:=30;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknRGlnaXRzRzYiIiNJ">IiNJ</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(subs(pars,C),x=0..1,thickness=4,axes=boxed,labels=[x,&quot;C&quot;],color=gold,title=&quot;Figure Exp. 3.1.5.&quot;);</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="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>