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An annular chemical reactor consists of a packed bed of catalyst between two coaxial cylinders. The inner and outer cylinders have radii of ro and ri, respectively. It is reasonable to assume that there is no heat transfer through the surface of the inner cylinder, which is at a constant temperature To. The catalytic reaction releases heat at a uniform volumetric rate, S, throughout the reactor, whose effective thermal conductivity k may be considered constant. Neglect the temperature gradients in the axial direction. a) Derive a second-order differential equation to describe the radial temperature distribution in the annular reactor starting with a shell thermal energy balance.

An annular chemical reactor consists of a packed bed of catalyst between two coaxial cylinders. The inner and outer cylinders have radii of ro and ri, respectively. It is reasonable to assume that there is no heat transfer through the surface of the inner cylinder, which is at a constant temperature To. The catalytic reaction releases heat at a uniform volumetric rate, S, throughout the reactor, whose effective thermal conductivity k may be considered constant. Neglect the temperature gradients in the axial direction. a) Derive a second-order differential equation to describe the radial temperature distribution in the annular reactor starting with a shell thermal energy balance.

Introduction to Chemical Engineering Thermodynamics
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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An annular chemical reactor consists of a packed bed of catalyst between two coaxial cylinders. The inner and outer cylinders have radii of ro and ri, respectively. It is reasonable to assume that there is no heat transfer through the surface of the inner cylinder, which is at a constant temperature To. The catalytic reaction releases heat at a uniform volumetric rate, S, throughout the reactor, whose effective thermal conductivity k may be considered constant. Neglect the temperature gradients in the axial direction. a) Derive a second-order differential equation to describe the radial temperature distribution in the annular reactor starting with a shell thermal energy balance.
Transcribed Image Text:An annular chemical reactor consists of a packed bed of catalyst between two coaxial cylinders. The inner and outer cylinders have radii of ro and ri, respectively. It is reasonable to assume that there is no heat transfer through the surface of the inner cylinder, which is at a constant temperature To. The catalytic reaction releases heat at a uniform volumetric rate, S, throughout the reactor, whose effective thermal conductivity k may be considered constant. Neglect the temperature gradients in the axial direction. a) Derive a second-order differential equation to describe the radial temperature distribution in the annular reactor starting with a shell thermal energy balance.
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