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<Text-field style="Heading 3" layout="Heading 3"><Font italic="false">Example 3.3</Font></Text-field>
</Input>
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<Input>
<Text-field style="Text" layout="Normal">Consider diffusion with a first order reaction in a semi-infinite plane:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZlcS1JI21vR0YkNi1RIn5GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGQ0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrLUkjbWlHRiQ2JVEjRDFGJy8lJ2l0YWxpY0dGNEYvLUkmbWZyYWNHRiQ2KC1GIzYnLUYsNi1RMCZEaWZmZXJlbnRpYWxEO0YnRi8vRjNRJnVuc2V0RicvRjZGVS9GOEZVL0Y6RlUvRjxGVS9GPkZVL0ZARlVGQUZELUkjbW5HRiQ2JVEiMkYnLyUsc3VwZXJzY3JpcHRHUSV0cnVlRidGLy1GLDYuRi5Gam5GL0YyRjVGN0Y5RjtGPUY/RkFGRC1GRzYlUSJDRidGSkYvRi8tRiM2JkZRLUZHNiVRInhGJ0ZKRi8tRkc2JkZpbkZKRmpuRi9GLy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXnAvJSliZXZlbGxlZEdGNEYrLUYsNi1RKiZ1bWludXMwO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yMjIyMjIyZW1GJy9GRUZncC1GRzYlUSNrQ0YnRkpGL0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGKy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUZnbjYkUSUzLjExRidGL0YvRi9GLw==</Equation></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred">C<Equation executable="false" style="Text" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkobWZlbmNlZEdGJDYkLUYjNiQtSSNtbkdGJDYkUSIwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjRGNC1JI21vR0YkNi1RIj1GJ0Y0LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRjE2JFEiMUYnRjQtRjg2LVEifkYnRjRGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZWLUY4Ni5RJGFuZEYnLyUlYm9sZEdGPUY0RjtGPkZARkJGREZGRkhGVUZXRlItSSNtaUdGJDYlUSJDRicvJSdpdGFsaWNHRj1GNC1GLDYkLUYjNiQtRjg2LVEoJmluZmluO0YnRjRGO0Y+RkBGQkZERkZGSEZVRldGNEY0RlItRmhuNiVRI2lzRidGW29GNEZSLUZobjYlUShkZWZpbmVkRidGW29GNEY0</Equation></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
<Text-field style="Text" layout="Normal">where C is the dimensionless concentration, D1 is the diffusion and k is the rate constant.  This equation is solved below using the procedure described above.</Text-field>
</Input>
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<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
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<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):with(plots):</Text-field>
</Input>
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<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIiIw==">IiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(C(x),x$2)-k/D1*C(x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIsJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJDR0YkNiNJInhHRiQtSSIkR0YoNiRGLSIiIyIiIiooSSJrR0YkRjJJI0QxR0YkISIiRipGMkY2">LCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYkNiQtSSJDRzYiNiNJInhHRitGLUYtIiIiKihJImtHRitGLkkjRDFHRishIiJGKUYuRjI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal262">A:=matrix(N,N,[0,1,k/D1,0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyQ3JCIiISIiIjckKiZJImtHRiRGK0kjRDFHRiQhIiJGKg==">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</Equation></Text-field>
</Output>
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<Group labelreference="L7" 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="PkkkbWF0RzYiLUknbWF0cml4R0YkNiM3JDckLCYqJiMiIiIiIiNGLS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjKihJI0QxR0YkISIiKSomRjZGLUkia0dGJEYtRixGLUkieEdGJEYtRi1GLSomRixGLS1GMDYjLCRGNUY3Ri1GLSwkKipGLEYtRjZGLSwmRj1GN0YvRi1GLUY4RjdGLTckLCQqKkYsRi1GOkYtRkJGLUY4RjdGLUYq">[encoded data, 4532 characters]</Equation></Text-field>
</Output>
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<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal262">Y0:=matrix(N,1,[1,c[1]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWTBHNiItSSdtYXRyaXhHRiQ2IzckNyMiIiI3IyZJImNHRiQ2I0Yq">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=evalm(mat&amp;*Y0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkc29sRzYiLUknbWF0cml4R0YkNiM3JDcjLCgqJiMiIiIiIiNGLS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjKihJI0QxR0YkISIiKSomRjZGLUkia0dGJEYtRixGLUkieEdGJEYtRi1GLSomRixGLS1GMDYjLCRGNUY3Ri1GLSosRixGLUY2Ri0sJkY9RjdGL0YtRi1GOEY3JkkiY0dGJDYjRi1GLUYtNyMsJioqRixGLUY6Ri1GQUYtRjhGN0YtKiYsJkYrRi1GPEYtRi1GQkYtRi0=">[encoded data, 7000 characters]</Equation></Text-field>
</Output>
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<Group labelreference="L10" 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="PkkiQ0c2IiwoKiYjIiIiIiIjRigtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyooSSNEMUdGJCEiIikqJkYxRihJImtHRiRGKEYnRihJInhHRiRGKEYoRigqJkYnRigtRis2IywkRjBGMkYoRigqLEYnRihGMUYoLCZGOEYyRipGKEYoRjNGMiZJImNHRiQ2I0YoRihGKA==">LCgqJiMiIiIiIiNGJS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKihJI0QxR0YsISIiKSomRi9GJUkia0dGLEYlRiRGJUkieEdGLEYlRiVGJSomRiRGJS1GKDYjLCRGLkYwRiVGJSosRiRGJUYvRiUsJkY2RjBGJ0YlRiVGMUYwJkkiY0dGLDYjRiVGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> This can be rewritten as</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C:=collect(C,exp(1/D1*(D1*k)^(1/2)*x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQ0c2IiwoKiYsJiMiIiIiIiNGKSoqRihGKUkjRDFHRiRGKSkqJkYsRilJImtHRiRGKUYoISIiJkkiY0dGJDYjRilGKUYpRiktSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyooRixGMEYtRilJInhHRiRGKUYpRikqJkYoRiktRjU2IywkRjpGMEYpRikqLEYoRilGLEYpRi1GMEY9RilGMUYpRjA=">LCgqJiwmIyIiIiIiI0YmKipGJUYmSSNEMUc2IkYmKSomRilGJkkia0dGKkYmRiUhIiImSSJjR0YqNiNGJkYmRiZGJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGKjYjKihGKUYuRitGJkkieEdGKkYmRiZGJiomRiVGJi1GMzYjLCRGOEYuRiZGJiosRiVGJkYpRiZGK0YuRjtGJkYvRiZGLg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C:=collect(C,exp(-1/D1*(D1*k)^(1/2)*x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQ0c2IiwmKiYsJiMiIiIiIiNGKSoqRihGKUkjRDFHRiRGKSkqJkYsRilJImtHRiRGKUYoISIiJkkiY0dGJDYjRilGKUYwRiktSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKihGLEYwRi1GKUkieEdGJEYpRjBGKUYpKiYsJkYoRilGK0YpRiktRjU2I0Y7RilGKQ==">LCYqJiwmIyIiIiIiI0YmKipGJUYmSSNEMUc2IkYmKSomRilGJkkia0dGKkYmRiUhIiImSSJjR0YqNiNGJkYmRi5GJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGKjYjLCQqKEYpRi5GK0YmSSJ4R0YqRiZGLkYmRiYqJiwmRiVGJkYoRiZGJi1GMzYjRjlGJkYm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> Since C is finite as x tends to infinity, the second parenthesis must go to zero because exp(x) goes to infinity as x goes to infinity.  Consequently, the equation for c<Font subscript="true">1</Font> can be found by setting the coefficient of the second term equal to zero:</Text-field>
</Input>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqbc:=coeff(C,exp(1/D1*(D1*k)^(1/2)*x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZXFiY0c2IiwmIyIiIiIiI0YnKipGJkYnSSNEMUdGJEYnKSomRipGJ0kia0dGJEYnRiYhIiImSSJjR0YkNiNGJ0YnRic=">LCYjIiIiIiIjRiQqKkYjRiRJI0QxRzYiRiQpKiZGJ0YkSSJrR0YoRiRGIyEiIiZJImNHRig2I0YkRiRGJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">c[1]:=solve(eqbc,c[1]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJImNHNiI2IyIiIiwkKiZJI0QxR0YlISIiKSomRipGJ0kia0dGJUYnI0YnIiIjRidGKw==">LCQqJkkjRDFHNiIhIiIpKiZGJCIiIkkia0dGJUYpI0YpIiIjRilGJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Thus, the desired solution for C is simply:</Text-field>
</Input>
</Group>
<Group labelreference="L18" 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="PkkiQ0c2Ii1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqKEkjRDFHRiQhIiIpKiZGLSIiIkkia0dGJEYxI0YxIiIjRjFJInhHRiRGMUYu">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJCooSSNEMUdGJyEiIikqJkYrIiIiSSJrR0YnRi8jRi8iIiNGL0kieEdGJ0YvRiw=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Plots can be made by substituting values for the parameters D1 and k:</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={D1=1e-5,k=1};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kia0dGJCIiIi9JI0QxR0YkJEYoISIm">PCQvSSJrRzYiIiIiL0kjRDFHRiUkRiYhIiY=</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..1e-2,labels=[x,&quot;C&quot;],thickness=4,axes=boxed,title=&quot;Figure Exp. 3.1.6.&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="L30" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">New plots can be made by substituting different values for the paramters.</Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={D1=1e-7,k=1};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kia0dGJCIiIi9JI0QxR0YkJEYoISIo">PCQvSSJrRzYiIiIiL0kjRDFHRiUkRiYhIig=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(subs(pars,C),x=0..1e-2,labels=[x,&quot;C&quot;],thickness=4,axes=boxed,color=black,title=&quot;Figure Exp. 3.1.7.&quot;);</Text-field>
</Input>
<Output>
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<Text-field style="Text" layout="Normal">We observe that as the diffusion coefficient decreases mass transfer limitations increase the length of the diffusion layer (distance required for C to drop to approximately 0) which decreases as expected.</Text-field>
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