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<Text-field style="Heading 3" layout="Heading 3"><Font italic="false">Example 4.11  Current Distribution in an Electrochemical Cell</Font></Text-field>
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<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Primary and secondary current distributions in electrochemical cells are governed by the Laplace equation.<Font superscript="true">[8]</Font>  Consider a rectangular geometry governed by the following equation<Font superscript="true">[9]</Font> </Text-field>
<Text-field style="Text" layout="Normal">	</Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>	 </Text-field>
<Text-field style="Text" layout="Normal">	                               </Text-field>
<Text-field style="Text" layout="Normal">                                                                                      u(x,0) =1                                                 (4.1.20)</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>(L,y) = <Font encoding="UTF-8">u(x,\342\210\236) =0 </Font></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">Note that this geometry is of finite dimension in x (L) and semi-infinite in y.  The following transformation is used to combine the variable:</Text-field>
<Text-field style="Text" layout="Normal">	 	                                                       <Font encoding="UTF-8">\316\267 =  </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>                                                    (4.1.21)</Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">The variable u in the new coordinate \316\267 is represented by U.  The boundary conditions for U are:</Font></Text-field>
<Text-field style="Text" layout="Normal">	 	</Text-field>
<Text-field style="Text" layout="Normal">                                                                                     U(0)=1</Text-field>
<Text-field style="Text" layout="Normal">                                                                                                                                                      (4.1.22)</Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">                                                                                    U(\342\210\236)=0</Font></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">Example 4.11 is solved in Maple below.  The program used for example 4.10 can be modified to solve this example.  Only the variable transformation (equation (4.1.21)) has to be modified.  The following results are obtained:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
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<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(student):</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(u(x,y),x$2)+diff(u(x,y),y$2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIsJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1R0YkNiRJInhHRiRJInlHRiQtSSIkR0YoNiRGLSIiIyIiIi1GJzYkRiotRjA2JEYuRjJGMw==">LCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYkNiQtSSJ1RzYiNiRJInhHRitJInlHRitGLUYtIiIiLUYkNiQtRiQ2JEYpRi5GLkYv</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=changevar(u(x,y)=U(eta(x,y)),eq):</Text-field>
</Input>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq1:=(simplify(subs(eta(x,y)=y/(L-x),eq))):</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq1:=subs(y=eta*(L-x),eq1):</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq1:=simplify(eq1*(L-x)^2):</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq2:=convert(eq1,diff);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXEyRzYiLCgqJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJVR0YkNiNJJGV0YUdGJC1JIiRHRik2JEYuIiIjIiIiKUYuRjJGM0YzKihGMkYzLUYoNiRGK0YuRjNGLkYzRjNGJ0Yz">LCgqJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiU2JC1JIlVHNiI2I0kkZXRhR0YsRi5GLiIiIkYuIiIjRi8qJkYoRi9GLkYvRjBGJEYv</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=U(0)=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLy1JIlVHRiQ2IyIiISIiIg==">Ly1JIlVHNiI2IyIiISIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=U(infinity)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLy1JIlVHRiQ2I0kpaW5maW5pdHlHJSpwcm90ZWN0ZWRHIiIh">Ly1JIlVHNiI2I0kpaW5maW5pdHlHJSpwcm90ZWN0ZWRHIiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U:=rhs(dsolve({eq2,bc1,bc2},U(eta)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiVUc2IiomLCZJI1BpRyUqcHJvdGVjdGVkRyIiIiomIiIjRiktSSdhcmN0YW5HNiRGKEkoX3N5c2xpYkdGJDYjSSRldGFHRiRGKSEiIkYpRidGMg==">KiYsJkkjUGlHJSpwcm90ZWN0ZWRHIiIiLUknYXJjdGFuRzYkRiVJKF9zeXNsaWJHNiI2I0kkZXRhR0YrISIjRiZGJCEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U:=expand(U);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiVUc2IiwmIiIiRiYqKCIiI0YmSSNQaUclKnByb3RlY3RlZEchIiItSSdhcmN0YW5HNiRGKkkoX3N5c2xpYkdGJDYjSSRldGFHRiRGJkYr">LCYiIiJGIyomSSNQaUclKnByb3RlY3RlZEchIiItSSdhcmN0YW5HNiRGJkkoX3N5c2xpYkc2IjYjSSRldGFHRixGIyEiIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(U,eta=0..10,thickness=4,title=&quot;Figure Exp. 4.1.23.&quot;,axes=boxed);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" 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="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=expand(subs(eta=y/(L-x),U));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkidUc2IiwmIiIiRiYqKCIiI0YmSSNQaUclKnByb3RlY3RlZEchIiItSSdhcmN0YW5HNiRGKkkoX3N5c2xpYkdGJDYjKiZJInlHRiRGJiwmSSJMR0YkRiZJInhHRiRGK0YrRiZGKw==">LCYiIiJGIyomSSNQaUclKnByb3RlY3RlZEchIiItSSdhcmN0YW5HNiRGJkkoX3N5c2xpYkc2IjYjKiZJInlHRixGIywmSSJMR0YsRiNJInhHRixGJ0YnRiMhIiM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(subs(L=1,u),x=0..1,y=0..2,axes=boxed,title=&quot;Figure Exp. 4.1.24.&quot;,orientation=[30,60],labels=[x,y,&quot;u&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">[encoded data, 13692 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The current distribution at the electrode (y=0) is given by:</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">curr:=subs(y=0,-diff(u,y));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklY3Vyckc2IiwkKigiIiMiIiJJI1BpRyUqcHJvdGVjdGVkRyEiIiwmSSJMR0YkRihJInhHRiRGK0YrRig=">LCQqJkkjUGlHJSpwcm90ZWN0ZWRHISIiLCZJIkxHNiIiIiJJInhHRilGJkYmIiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>