Fixed an error in the left hand terms conduction terms

While revising the equations for one dimensional heat transfer (see mtiller#53), I recognized that there was an error in the equations in these models. One term included the effects of length while the other didn't.
adrian-nilsson-fcc · Apr 11, 2014 · a87d4af · a87d4af
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Showing 4 changed files with 11 additions and 11 deletions.
diff --git a/ModelicaByExample/ArrayEquations/HeatTransfer/Rod_ArrayComprehensions.mo b/ModelicaByExample/ArrayEquations/HeatTransfer/Rod_ArrayComprehensions.mo
@@ -30,7 +30,7 @@ model Rod_ArrayComprehensions
 initial equation
   T = linspace(200,300,n);
 equation
-  rho*V*C*der(T[1]) = -h*(T[1]-Tamb)-k*A/(L/n)*(T[1]-T[2]);
-  rho*V*C*der(T[2:n-1]) = {-k*(L/n)*(T[i]-T[i-1])-k*A/(L/n)*(T[i]-T[i+1]) for i in 2:(n-1)};
-  rho*V*C*der(T[end]) = -h*(T[end]-Tamb)-k*A/(L/n)*(T[end]-T[end-1]);
+  rho*V*C*der(T[1]) = -h*(T[1]-Tamb)-k*A*(T[1]-T[2])/(L/n);
+  rho*V*C*der(T[2:n-1]) = {-k*A*(T[i]-T[i-1])/(L/n)-k*A*(T[i]-T[i+1])/(L/n) for i in 2:(n-1)};
+  rho*V*C*der(T[end]) = -h*(T[end]-Tamb)-k*A*(T[end]-T[end-1])/(L/n);
 end Rod_ArrayComprehensions;
diff --git a/ModelicaByExample/ArrayEquations/HeatTransfer/Rod_ForLoop.mo b/ModelicaByExample/ArrayEquations/HeatTransfer/Rod_ForLoop.mo
@@ -29,9 +29,9 @@ model Rod_ForLoop "Modeling heat conduction in a rod using a for loop"
 initial equation
   T = linspace(200,300,n);
 equation
-  rho*V*C*der(T[1]) = -h*(T[1]-Tamb)-k*A/(L/n)*(T[1]-T[2]);
+  rho*V*C*der(T[1]) = -h*(T[1]-Tamb)-k*A*(T[1]-T[2])/(L/n);
   for i in 2:(n-1) loop
-    rho*V*C*der(T[i]) = -k*A/(L/n)*(T[i]-T[i-1])-k*A/(L/n)*(T[i]-T[i+1]);
+    rho*V*C*der(T[i]) = -k*A*(T[i]-T[i-1])/(L/n)-k*A*(T[i]-T[i+1])/(L/n);
   end for;
-  rho*V*C*der(T[end]) = -h*(T[end]-Tamb)-k*A/(L/n)*(T[end]-T[end-1]);
+  rho*V*C*der(T[end]) = -h*(T[end]-Tamb)-k*A*(T[end]-T[end-1])/(L/n);
 end Rod_ForLoop;
diff --git a/ModelicaByExample/ArrayEquations/HeatTransfer/Rod_VectorNotation.mo b/ModelicaByExample/ArrayEquations/HeatTransfer/Rod_VectorNotation.mo
@@ -30,7 +30,7 @@ model Rod_VectorNotation
 initial equation
   T = linspace(200,300,n);
 equation
-  rho*V*C*der(T[1]) = -h*(T[1]-Tamb)-k*A/(L/n)*(T[1]-T[2]);
-  rho*V*C*der(T[2:n-1]) = -k*(L/n)*(T[2:n-1]-T[1:n-2])-k*A/(L/n)*(T[2:n-1]-T[3:n]);
-  rho*V*C*der(T[end]) = -h*(T[end]-Tamb)-k*A/(L/n)*(T[end]-T[end-1]);
+  rho*V*C*der(T[1]) = -h*(T[1]-Tamb)-k*A*(T[1]-T[2])/(L/n);
+  rho*V*C*der(T[2:n-1]) = -k*A*(T[2:n-1]-T[1:n-2])/(L/n)-k*A*(T[2:n-1]-T[3:n])/(L/n);
+  rho*V*C*der(T[end]) = -h*(T[end]-Tamb)-k*A*(T[end]-T[end-1])/(L/n);
 end Rod_VectorNotation;
diff --git a/ModelicaByExample/ArrayEquations/HeatTransfer/Rod_VectorNotationNoSubscripts.mo b/ModelicaByExample/ArrayEquations/HeatTransfer/Rod_VectorNotationNoSubscripts.mo
@@ -33,7 +33,7 @@ model Rod_VectorNotationNoSubscripts
 initial equation
   T = linspace(200,300,n);
 equation
-  Qleft = {if i==1 then -h*(T[i]-Tamb) else -k*A/(L/n)*(T[i]-T[i-1]) for i in 1:n};
-  Qright = {if i==n then -h*(T[i]-Tamb) else -k*A/(L/n)*(T[i]-T[i+1]) for i in 1:n};
+  Qleft = {if i==1 then -h*(T[i]-Tamb) else -k*A*(T[i]-T[i-1])/(L/n) for i in 1:n};
+  Qright = {if i==n then -h*(T[i]-Tamb) else -k*A*(T[i]-T[i+1])/(L/n) for i in 1:n};
   rho*V*C*der(T) = Qleft+Qright;
 end Rod_VectorNotationNoSubscripts;