Numerical Methods with Chemical Engineering Applications 1st. Edition by Kevin D. Dorfman, Prodromos Daoutidis | 9781107135116 | 1107135117 | Holooly

Numerical Methods

Numerical Methods with Chemical Engineering Applications

102 SOLVED PROBLEMS

Question: 7.PS.1

2D Reaction–Diffusion In this last case study, we will consider a basic question about reaction–diffusion problems. We will look at the solution to the steady state reaction–diffusion equation D∇^2c = R(c) (7.5.1) in a box of size L × L, where R(c) is the rate of consumption of the reactant. We ...

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We will discretize the domain into an n × n grid, ...

Question: 6.PS.2

Coupled Heat and Mass Transfer Let’s now consider the problem of calculating the steady state concentration and temperature profile for the system in Fig. 6.15. The concentration of reactant on the left is c(0) = 0, while the concentration on the right is fixed at c(L) = c_0. The steady state mass ...

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Dimensionless Formulation Let’s first convert the ...

Question: 6.PS.1

Reaction–Diffusion in a Packed Bed We consider a packed bed reactor, shown in Fig. 6.12. At the left edge of the bed, x = 0, the concentration of the reactant is equal to the bulk concentration, c = c_0. There is a wall at the right edge of the bed, x = l, with the corresponding no-flux boundary ...

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If we are going to work in terms of a Thiele modul...

Question: 5.PS.1

Non-Isothermal CSTR In Chapter 4, we presented two case studies of chemical reactors. In Section 4.4, we looked at a continuous stirred tank reactor with a fluctuating inlet. This problem was dynamic, since the independent variable was time, and one-dimensional since the only dependent variable in ...

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Steady States If we want to look for the steady st...

Question: 8.5

Simplify Eq. (8.2.32) for evenly spaced data. ...

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With

x_2 = x_0 + 2h

and

x_1 ...

Question: 8.6

Simply Eq. (8.2.33) for evenly spaced data. ...

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We can begin by applying Eq. (8.2.52) to get conve...

Question: 8.2

Compute the third divided difference using the recursion relationship Eq. (8.2.28). ...

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The recursion relationship gives us

f[x_3, ...

Question: 8.7

To test our claim about the accuracy of these methods, use Program 8.4 to calculate the integral I=(m+1)∫0^1 x^m dx (8.3.22) which we know has the value I = 1 for any positive integer m. ...

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Table 8.1 shows the results up to m = 6. There are...

Question: 8.8

Use the multiple trapezoidal rule to determine how the error in the integral I =∫0^1/2 cos πxdx (8.4.8) depends on the number of trapezoids. ...

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We know that the integral is

I = π^{−1}[/la...

Question: 8.PS.1

Concentrated Differential Distillation In this final case study, we will consider the case of differential distillation of benzene and toluene from our colleague Ed Cussler’s book Diffusion, which is illustrated schematically in Fig. 8.10.In this system, we have a saturated liquid feed of 3500mol/h ...

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The first item of business is to determine a relat...

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