The porous catalyst pellet shown in Figure 1 has an overall radius R and a thermal conductivity k (which may be assumed constant). Because of the chemical reaction occurring within the porous pellet, heat is generated at a constant rate of S, cal/cm³ - s. Heat is lost at the outer surface of the pellet to a gas stream at a constant temperature T, by convective heat transfer coefficient h. Figure I. Sphere with internal heat generation Gas temperature T, Answer the following questions (a) Make a list of assumptions that apply to the above situation. (b) Set up the differential equation by making a shell energy balance. Show the units for all variables that are used. (c) Specify the proper boundary conditions. (d) Integrate the differential equation with the above boundary conditions to obtain an expression for the temperature profile, and make a sketch of the function profile T(r). (e) What is the limiting form of T(r) when h -→ ? () What is the maximum temperature in the system? (g) Briefly explain at what point in the derivation of the model equation would one modify the procedure to account for variable k and S- (h) What dimensionless groups could be defined to transform the primitive form of the solution to one that contains these groups?

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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Transcribed Image Text:The porous catalyst pellet shown in Figure 1 has an overall radius R and a thermal conductivity k (which may be assumed constant). Because of the chemical reaction occurring within the porous pellet, heat is generated at a constant rate of S, cal/cm³ - s. Heat is lost at the outer surface of the pellet to a gas stream at a constant temperature T, by convective heat transfer coefficient h. Figure I. Sphere with internal heat generation Gas temperature T, Answer the following questions (a) Make a list of assumptions that apply to the above situation. (b) Set up the differential equation by making a shell energy balance. Show the units for all variables that are used. (c) Specify the proper boundary conditions. (d) Integrate the differential equation with the above boundary conditions to obtain an expression for the temperature profile, and make a sketch of the function profile T(r). (e) What is the limiting form of T(r) when h -→ ? () What is the maximum temperature in the system? (g) Briefly explain at what point in the derivation of the model equation would one modify the procedure to account for variable k and S- (h) What dimensionless groups could be defined to transform the primitive form of the solution to one that contains these groups?

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