Solve the following questions: 1. Consider a packed-bed catalytic reactor operating at 400 K, where a first-order reaction takes place over a catalyst bed with particles of 2 mm diameter. A reactant gas A flows through the reactor with an inlet concentration of 0.05 mol/L and a superficial velocity of 0.1 m/s. The total length of the reactor is 500 mm, and the bed porosity is 0.35. The diffusion coefficient of A within the pores of the catalyst is 1.2×100 m²/s and the effective diffusion coefficient D=5x10 10m²/s. The rate constant for the first-order reaction on the catalyst surface is k'=0.02 s¹. Determine the concentration profile of reactant A along the reactor length, considering both diffusion and reaction within the catalyst particles. Discuss also ways how to improve the overall rate of reaction for this system. 2. A cylindrical aluminium fin (thermal conductivity k-235 W/m.K with a diameter of 10 mm and a length of 50 mm is attached to a heated wall maintained at 200°C. The fin dissipates heat to the surrounding air at 25°C, with a convective heat transfer coefficient of h=20 W/m2.K. Assume that the heat transfer from the fin tip is negligible. a. Derive the temperature distribution T(x) along the length of the fin. Use the one-dimensional steady-state heat conduction equation for a fin with uniform cross-sectional area and no heat transfer at the tip. b. Calculate the rate of heat transfer from the fin to the surrounding air

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Transcribed Image Text:Solve the following questions: 1. Consider a packed-bed catalytic reactor operating at 400 K, where a first-order reaction takes place over a catalyst bed with particles of 2 mm diameter. A reactant gas A flows through the reactor with an inlet concentration of 0.05 mol/L and a superficial velocity of 0.1 m/s. The total length of the reactor is 500 mm, and the bed porosity is 0.35. The diffusion coefficient of A within the pores of the catalyst is 1.2×100 m²/s and the effective diffusion coefficient D=5x10 10m²/s. The rate constant for the first-order reaction on the catalyst surface is k'=0.02 s¹. Determine the concentration profile of reactant A along the reactor length, considering both diffusion and reaction within the catalyst particles. Discuss also ways how to improve the overall rate of reaction for this system. 2. A cylindrical aluminium fin (thermal conductivity k-235 W/m.K with a diameter of 10 mm and a length of 50 mm is attached to a heated wall maintained at 200°C. The fin dissipates heat to the surrounding air at 25°C, with a convective heat transfer coefficient of h=20 W/m2.K. Assume that the heat transfer from the fin tip is negligible. a. Derive the temperature distribution T(x) along the length of the fin. Use the one-dimensional steady-state heat conduction equation for a fin with uniform cross-sectional area and no heat transfer at the tip. b. Calculate the rate of heat transfer from the fin to the surrounding air

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