Example 10.5-2: Part a
Steady Flow of a non-isothermal film: The only component of velocity is the z component. It only changes in the x direction as shown in Fig. 2.2-2 Temperature also only varies in the x direction. > restart; > s:=dsolve({diff(T(x),x,x),T(0)=T0,T(delta)=Td},T(x)): > assign(s); > T:=unapply(T(x),x); > mu:=proc(x) eq. 10.5-19a > local T1;global T, B; > T1:=T(x); > mu0*exp(B*((1/T1)-(1/T0))); > end: > mu(0); > mud:=mu(delta); > A:=mud/mu0; > muapp:=proc(x) eq. 10.5-19c > global delta, mu, mu0, A; > mu0*A^(x/delta); > end: > muapp(0); > muapp(delta); > muapp(delta/2); Data for water from plot and fit of data in Table 1.1-1 > B:=1868.6; mu0:=1.787; T0:=273.15; Td:=373.15; > muapp(.6*delta);
> mu(.6*delta); From Table 1.1-1 it should be .4665 at 60C
> mus:=[1.787,1.0019,0.6530,0.4665,0.3548,0.2821]; From Table 1.1-1 mu in cp. > Ts:=[0,20,40,60,80,100]; The temperatures in the table in C. > Tmus:=[[Ts[n]/100,mus[n]]$n=1...6]; Making a list of lists. > with(plots): > p1:=plot(Tmus,style=point,symbol=circle): > p2:=plot([mu(x*delta),muapp(x*delta)],x=0...1,color=[red,green]): > display([p1,p2]); The red curve is the value from mu, the green one from the approximate one and the circles are the data in the Table.
>