> restart;

This is the equation for T(x) as derived in Section 9.4

> T:=x->(x/b+mu*V^2*x*(1-x/b)/(2*k*(Tb-To)*b))*(Tb-To)+To;

> Ts:=simplify(T(x));

The derivative of T with respect to x at the maximum temperature is equal to 0.

> ans:=simplify(diff(Ts,x)=0);

> omega:=8097*rev/m; rev:=2*pi; pi:=3.14159; m:=60*s; R:=6.05*cm; b:=.072*cm; Tb:=70*C; To:=70*C; mu:=92.3*cp; cp:=.01*g/cm/s; rho:=1.22*g/cm^3; k:=.0055*cal/s/cm/C; cal:=4.184e7*g*cm^2/s^2; V:=R*omega;

> Ts;

Solve the derivative for x, the location of the maximum temperature.

> xmax:=solve(ans,x);

> x:=xmax;

Plug in the maximum distance into our T(x) equation.

> Ts;

This converts to 181.75*F