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Photochemical reactor modeling: a case-study problem. Although radiation is important in heat transfer, an analogous model can be used in the design of photochemical reactors. The modeling of these reactors requires that the radiation intensity be tracked in the reactor as a function of position and coupled to the kinetics of chemical reaction. The RTE becomes an important sub-model for such reactors. The book by Cassano and Alfabo (1991) is the most valuable source for photochemical reactor modeling. Study this paper or related papers, and set up and solve a case-study example of the light-intensity distribution in a photochemical reactor.

Secondary-emission measurement: a case-study problem. An indirect way of measuring of secondary emission from ponds or large bodies of water used in waste treatment is to measure the concentration and velocity over the surface. The data can then be fitted to a model of the type presented in Section 20.1.4. In a typical experiment benzene concentration and velocity were measured at various locations above the water surface and the data are as follows.

Fit the data to the boundary-layer model and evaluate the rate of emission from the surface. D for benzene is 0.077 cm2/s in air. Usually the data are measured at about six points above the surface, but we use only two points in order to simplify the calculations. Write a critique on this technique of….

Chemical vapor deposition (CVD) on an inclined susceptor: a case-study problem. An important application of convective mass transfer theory is in CVD processes employed to coat surfaces with thin films of metals or semi-conductors. In fact, this turns out to be an example of simultaneous heat and mass transfer with chemical reaction. A flat plate is used as a susceptor to deposit a material for a semi-conductor application. The inclination of the plate is θ to the horizontal. The flow will then be governed by the Falkner–Skan equation described in Section 15.6. Your goal is to set up a mass transfer model and evaluate the variation of the local mass transfer coefficient at various locations in the plate. Usually a constant or nearly constant boundary-layer thickness is preferable…..

A model for a hemodialyser with simulation of the patient–artificial-kidney system: a case-study problem. A useful case study is the paper by Ramachandran and Mashelkar (1980), where a mesoscopic model with axial dispersion was used for the blood side and plug flow was used for the dialysate side. The solution was analytic and was then combined with a compartmental model to simulate the patient–artificial-kidney system. Your goal in this case study is to review the paper and write a comprehensive MATLAB simulation code.

The second task is to do a parametric sensitivity analysis and then suggest how the model can be used to optimize conditions to get the desired end results. This case study combines several key modeling concepts discussed in this text and may be viewed as….

A model for chromatographic separation: a case-study problem. An important application of Taylor dispersion is in chromatography. Here pulses of a mixture of solutes are introduced into one end of a packed-bed reactor containing an adsorbent and washed through the bed with a solvent. Since different species adsorb and diffuse at different rates, we obtain a separation. The axial dispersion will often interfere in the separation (it causes a pulse broadening). Your goal is to set up a model for chromatographic processes wherein you should include the adsorption on the solids as an additional term. You can examine how the dispersion coefficient changes with the adsorption equilibrium constant.

Effect of composition numbering on the Fick matrix K˜. In the matrix representation the species n chosen for elimination is usually referred to as the solvent. The choice of “solvent” species is arbitrary, but it can have an effect on the coefficient and the structure of the resulting form as shown below. A system with a very large variation in binary diffusion values was studied by Wesselingh and Krishna (2000). The three components are hydrogen (1), nitrogen (2), and dichlorodifluoromethane (3). Estimate the binary pair values from Eq. (1.53) given in Chapter 1. Find the K matrix if species (3) is the solvent. Also show that the K matrix has different values if species (2) is the solvent. Although the three matrices look different, show that the eigenvalues….

Diffusion across a porous plug: the effect of a third component (adapted from BSL). When two gases A and B are forced to diffuse through a third gas C, there is a tendency of A and B to separate because of the difference in their diffusivities in gas C. This phenomenon could possibly be used for isotope separation. Consider a “diffusion tube” of diameter d and length L packed with some non-reacting material such as glass wool. One end of the tube, z = 0, the feed side, is maintained at mole fractions of xAf and xBf. The other end, the product end, z = L, is maintained at xAp and xBp. Your task is to model the degree of separation that can be achieved in this system….

Two solutions are separated by a porous sintered disk (1 mm thick) that permits diffusion across the disk. On one side we have a mixture of 1 M HCl and 1 M BaCl2 while on the other side we have pure water. It is required to find the flux across the system. Both salts are completely ionized and diffuse as H+, Cl−, and Ba2+ across the disk. Set up the model to compute the fluxes. From the fluxes, find the effective diffusivities of these ions across the disk. Use for the ionic diffusivity for Ba ions 0.85×10−9 m2/s. For the other ions, use the values in Table 22.1. Use the condition of no net current to solve for the potential. Answers: H, 6.14; Cl, 2.2268; and Ba, 0.271.

Design arrangements in electrophoresis: a case-study problem. Various methods have been developed in order to increase the throughput in electrophoresis. Most of these designs vary in the flow arrangement and the changes in the direction of the electric field. These include the Philpot design, Hanning design, annular design, and rotating annular column, among many others. Discuss these arrangements. A comparison of the performance analysis has been done by Yoshisato et al. (1986), who used the well-studied glycine– glutamic-acid solute pair as a model system. Study this and related papers and do a case study on performance analysis of various designs.

The proton-exchange membrane (PEM) fuel cell: a case-study problem. A hydrogen fuel cell using a PEM consists of a gas-diffusion backing layer with a Pt on C supported catalyst as anode and cathode. The two electrodes are separated by a membrane, which permits selective transport of H+ ions. The protons are released by reaction of hydrogen gas at the anode: H2 → 2H+ + 2e− These protons diffuse across the membrane and react at the cathode with the oxygen (air) gas: 1/2 O2 + 2H+ + 2e− → H2O The overall reaction is simply oxidation of hydrogen to produce water. This reaction is spontaneous with a negative free energy, G◦ = 24 000 kJ/mol at 298 K. An equivalent voltage is generated in the system under conditions of….