Section 10.2 Heat Conduction in a Cylinder with an Electrical Heat Source
A slightly different path from the one in BS&L ed. 2.
>  restart;
>  A:=r-> 2*Pi*r*L;  area of conduction 
>  Q:=r-> - k*A(r)*D(T)(r);  Heat conducted across cylinder of radius r in the direction of increasing r
>  Q(r);  the rate of thermal energy into cylindrical shell at r 
>  Q(r + dr);  rate of thermal energy out across cyllindrical surface at r+dr
>  LHS:=limit((Q(r+dr)-Q(r))/dr,dr=0);  Left hand side of energy balance
>  de:=LHS=A(r)*Se; energy balance, out - in = energy production by electrical dissipation
>  sol:=dsolve({de,T(R)=T0,T(0)=finite},T(r));  Solving the de with BCs 10.2-12 and the equivalent of 10.2-8
>  assign(sol);  Giving T(r) a value
>  T:=unapply(T(r),r);  Making T a function
>  dT:=T(r)-T0;
>  dToverCon:=simplify((dT/(Se*R^2/(4*k))));dTmax:=T(0)-T0;dTavg:=int((T(r)-T0)*r,r=0...R)/int(r,r=0...R); QatR:=Q(R);  Our answers agree with eqs. 10.2-13, 14, 15 and 16

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