9.5 Heat Conduction with Chemical Heat Source

First we will derive eq. 9.5-24

>  restart;
>  Sc:=T->Sc1*(T-To)/(T1-To);  eq. 9.5-1
>  A:=Pi*R^2;  The bed area is constant
>  Qcond:=z->A*qz(z);  The rate of heat conduction at position z
>  Qconv:=z->A*rho1*v1*Cp*(T(z)-T0);  The rate of thermal heat 
convection at position z
>  LHS:=limit((Qcond(z+dz)-Qcond(z)+Qconv(z+dz)-Qconv(z))/(A*dz),dz=0); Deriving the Left Hand Side of eq. 9.5-8
>  de:=simplify(LHS=Sc(T(z)));  eq. 9.5-8 with eq. 9.5-1 for Sc  
>  qz:=z->-keff*D(T)(z);  Fourier's Law assuming an effective 
thermal conductivity
>  de;  This looks like eq 9.5-11
>  with(PDEtools,dchange);  Used in DEs to change variables. 
New in Vr5.
>  transf:={z=Z*L,T=To+Theta*(T1-To)};  A set that gives the 
transformation to get  old  variables from the  new  ones. 
Note the use of {} to make a set.
>  Newde:=dchange(transf,de,[Theta(Z),Z]); Arguments in dchange:
1) the set of transformations
2) the differential equation
3) the new functional relation
>  v1:=B*keff/(rho1*Cp*L);  eq. 9.5-21 to replace v1 with B
>  Sc1:=N*rho1*v1*Cp*(T1-To)/L;  eq. 9.5-22 to replace Sc1 with N
>  Newde;
>  eq24:=simplify(Newde*L^2/(B*keff*(T1-To)));  Canceling out the common
terms in the expression, we get eq. 9.5-24

>