9.2 Heat Conduction in a Cylinder with an Electrical Heat Source

>  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 eq. 9.2-5
>  de:=LHS=A(r)*Se; energy balance, out - in = energy production by 
electrical dissipation giving 9.2-6
>  sol:=dsolve({de,T(R)=T0,T(0)=finite},T(r));  Solving 9.2-6 with 
BC 9.2-8
>  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. 9.2-13, 14, 15 and 16

>