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1)The film-penetration model, Gas-absorption systems are usually modeled by assuming a film thickness and steady-state diffusion

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1)The film-penetration model, Gas-absorption systems are usually modeled by assuming a film thickness and steady-state diffusion. In an attempt to modify this picture one can assume a finite film but allow for a transient diffusion in the film. This model is known as the film-penetration model. Perform a scaling analysis for this system and develop a useful relationship to correlate the data on absorption. 

2)Apply scaling analysis for gas absorption with first-order reaction based on the film model. Derive a relation for the depth of penetration of the gas for a fast reaction. Using this relation, verify the following model prediction: RA = CA,s DAk1

3)Roasting of a turkey: scaling analysis. It is required to find the cooking time of a large turkey. Experimental data are available for a small turkey of mass ms, and the time is ts. Suggest the cooking time, tL, for a larger turkey of mass mL by dimensionless and scaling analysis.

4)In correlating the diameter of drops formed at the orifice, the viscosity is to be included as the core group rather than density as done in the text. Form groups with do, ρ, and μ as the core groups and surface tension and drop diameter as the variables.

5)Simple pendulum: time of oscillation. The time of oscillation t of a simple pendulum is expected to be a function of the mass of the pendulum, its length L, and the gravitational constant. How many dimensionless groups can be formed? Show that the key dimensionless group is t √g/L. Hence conclude that t should be proportional to √L/g but is independent of the mass of the pendulum from purely dimensional considerations without invoking any physics. Note that the constant of proportionality is 2π, but this value cannot be determined from dimensionless analysis. A physics model is needed for this.

6)The temperature effect in a porous catalyst. The effectiveness factors for a porous catalyst in the presence of significant temperature gradients can be larger than one. Explain why. Your goal is to generate such a plot of η as a function of φ for the following set of parameters: β = 1/3, γ = 27, Bim = 300, and Bih = 100. Vary φ as a parameter gradually and generate a plot of the effectiveness factor. Careful continuation of parameters based on a good starting solution is needed in order to track the profile. An alternative method is the arc-length continuation discussed in Section 16.2.2.

7)Condensation with reaction. Now consider the above problem for a case where a reaction between the condensing vapor A and the relatively non-condensing gas B can take place in the liquid according to A + B → C Model the system and study the effect of reaction on the condensation rate.

8)Condensation of the binary gas mixture with an inert species. The condensation of a binary mixture A and B in the presence of an inert species C can be analyzed in the same manner. The liquid side has only A and B, and hence the composition on the liquid side is calculated by the same set of equations. The composition on the vapor side should now include the presence of the inert species.Extend the analysis of Section 13.6.3 for condensation of a ternary mixture of A, B, and C.

9)Examine the sensitivity of the results of Problem 1 to changes in the transport parameters by ±20% on either side and tabulate the results for the predicted values of the condensation rate, heat transfer rate, and interface temperature. Which of the three transport parameters is the most influential?

10)Condensation of a pure vapor. Water is condensing on a surface at 310 K. The gas mixture has 65% water vapor and is at a temperature of 370 K. The total pressure is 1 atm. Calculate the rate of condensation. Look for and use numerical values of physical properties from the web or other books. Use the following values for the transport coefficients. The gas-side heat transfer coefficient is 12 W/m2.K. The gas-side mass transfer coefficient is 0.009 m/s. Neglect the heat-transport resistance in the condensing film.

11)The thermodynamic wet-bulb temperature is defined as the temperature at which water evaporates and brings the air to equilibrium conditions. Show that the thermodynamic wet-bulb temperature is the same as the wet-bulb temperature shown in the text, which is derived from transport considerations, if the Lewis number is equal to one. What is the difference between the values computed by using the two definitions if the Lewis number is not unity?

12)Viscosity variation. Extend the analysis in Section 13.4 to a power-law fluid. Compare the changes in the nature of the profile with varying power-law index.A dryer for solid with benzene. At a point in a dryer benzene is evaporating from a solid. The air temperature is 80 ?C and the pressure is 1 atm. The relative humidity of benzene in air is 65%. Find the wet-bulb temperature.

13)The Brinkman problem with constant wall flux. Reexamine the problem of laminar flow with heat generation. Now do the analysis for a constant heat flux at the walls. How should the dimensionless temperature θ be defined here? How is the Brinkman problem defined for this case? Does the problem have an asymptotic solution for large ζ similar to Eq. (12.12) in Section 12.1.3? If so, derive this result and find the value of the Nusselt number. Show some numerical results and compare them with the asymptotic solution.

14)The Brinkman problem: analytical solutions. Owing to the non-homogeneous term in Eq. (13.24), direct separation of variables is not possible. A partial solution has to be found, and the problem has to be solved by the modified method of separation of variables. Develop this analytical model. Plot typical values of the temperature profiles and compare your results with the numerical solution generated by PDEPE. Repeat the analysis for flow in a channel with viscous heat generation.

15)Heat generation due to viscosity: the effect of boundary conditions. Consider again the problem of a highly viscous fluid contained between two parallel plates of gap width d. The top plate is moving with a velocity of V and this generates heat in the system due to viscous dissipation. Develop an equation for the temperature distribution in the system if the upper plate is at T0 while the lower plate is insulated. Assume constant viscosity. What happens to the problem if both plates are insulated?

16)Example: natural convection in water. Water is contained between two vertical plates with a gap width of 2 cm. The temperatures of the plates are 25 and 75 ?C. Find the velocity profile and plot the velocity profile as a function of distance. Also find the maximum velocity in the system. Use the following physical properties, the values of which are evaluated at 50 ?C, the average temperature in the system: density ρ = 988 kg/m3, viscosity μ = 565 × 10−6 Pa ·s, and coefficient of volume expansion 4.54 × 10−4 K−1.

17)Mass transfer in oscillating flow: a case-study problem. Mass transfer can be enhanced by flow oscillation. Your goal in this study is to review the literature and, in particular, examine the following model problem, viz., mass transfer in pipe flow with a dissolving wall. Assume that the flow oscillation is caused by a sinusoidal variation of the inlet pressure. Perform a scaling analysis based on the key time constants to find conditions under which the enhancement is likely and also investigate the problem using numerical tools. How does the time-average Sherwood number vary with the dimensionless amplitude of oscillation?