Example 11.4-3: Part a: checking on the viscosity approximation: 11.4-18 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. 2.2-3 Temperature also only varies in the x direction. Thus vz(x) and T(x) and all terms on the left of eq. B.9-1 are zero. Note that Table B.9 only requires that rho and k be constant: not mu. On the right side we have the first term as the only important one if we can neglect viscous dissipation and variations of thermal conductivity with temperature. > restart; > s:=dsolve({diff(T(x),x,x),T(0)=T0,T(delta)=Td},T(x)): Simplified form of eq B.9-1 > assign(s); > T:=unapply(T(x),x); > mu17:=x->mu0*exp(B*(1/T(x)-(1/T0))); eq. 11.4-17. > mu17(x); > mu17(0); > mud:=mu17(delta); > A:=mud/mu0; > mu19:=x->mu0*A^(x/delta); > mu19(0); > mu19(delta); > mu19(delta/2); Data for water from plot and fit of data in Table 1.1-2 > B:=1868.6; mu0:=1.787; T0:=273.15; Td:=373.15; > mu17(.6*delta); > mu19(.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 (or mPa*s). > 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([mu17(x*delta),mu19(x*delta)],x=0...1,color=[red,green]): > display([p1,p2]); The red curve is the value from eq 17, the green one from the approximate of this: eq. 19 and the circles are the data in the Table.
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