Example 3.2.11 Axial Conduction and Diffusion in a Tabular Reactor
Axial diffusion and conduction in an adiabatic tabular reactor can be described by:[6]
(3.2.31)
(0) = θ(0)
1 (3.2.32)
and
(1)=0 (3.2.33)
This coupled boundary value problem is solved in Maple below for the following value of parameters Pe = 10, B0 = 10, E = 18
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Eq[1]:=1/Pe*diff(y(x),x$2)-diff(y(x),x)=4*y(x)*exp(E*(1-1/theta(x))); |
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(1) |
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Eq[2]:=1/Bo*diff(theta(x),x$2)-diff(theta(x),x)=-4*beta*y(x)*exp(E*(1-1/theta(x))); |
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(2) |
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BCs:=[1/Pe*D(y)(0)-y(0)+1,D(y)(1),1/Bo*D(theta)(0)-theta(0)+1,D(theta)(1)]; |
![[`+`(`/`(`*`((D(y))(0)), `*`(Pe)), `-`(y(0)), 1), (D(y))(1), `+`(`/`(`*`((D(theta))(0)), `*`(Bo)), `-`(theta(0)), 1), (D(theta))(1)]](images/Example3.2.11 Rev 1_11.gif) |
(3) |
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pars:={Pe=10,Bo=10,E=18,beta=0.05}; |
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(4) |
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for i to 2 do eq[i]:=subs(pars,Eq[i]);od; |
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(5) |
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(6) |
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(7) |
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bcs:=op(subs(pars,BCs)); |
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(8) |
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sol:=dsolve({eqs,bcs},{vars},type=numeric); |
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(9) |
![[x = 0., theta(x) = 1.01463595348572144, diff(theta(x), x) = .146359534857216172, y(x) = .707280930285567600, diff(y(x), x) = -2.92719069714432400]](images/Example3.2.11 Rev 1_19.gif)
![[x = 0., theta(x) = 1.01463595348572144, diff(theta(x), x) = .146359534857216172, y(x) = .707280930285567600, diff(y(x), x) = -2.92719069714432400]](images/Example3.2.11 Rev 1_20.gif) |
(10) |
![[x = 1., theta(x) = 1.04981039182617586, diff(theta(x), x) = 0., y(x) = 0.379216347648523786e-2, diff(y(x), x) = 0.]](images/Example3.2.11 Rev 1_21.gif) |
(11) |
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odeplot(sol,[x,y(x)],0..1,thickness=4,title="Figure Exp. 3.2.21.",axes=boxed); |
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odeplot(sol,[x,theta(x)],0..1,thickness=4,color=green,title="Figure Exp. 3.2.22.",axes=boxed); |