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4. Gas temperature T R A spherical catalyst pellet has a radius R and a thermal conductivity k (which may be assumed constant) [see the image to the right]. Because of the chemical reaction occurring within the porous pellet, heat is generated at a rate Sc cal/(cm³.s). Heat is lost at the outer surface of the pellet to a gas stream at constant temperature Tg by convective heat transfer with heat-transfer coefficient h. Find the steady-state temperature profile, assuming that Sc is constant throughout. a) Set up the differential equation by making a shell energy balance. b) Integrate the differential equation to get the temperature profile.

4. Gas temperature T R A spherical catalyst pellet has a radius R and a thermal conductivity k (which may be assumed constant) [see the image to the right]. Because of the chemical reaction occurring within the porous pellet, heat is generated at a rate Sc cal/(cm³.s). Heat is lost at the outer surface of the pellet to a gas stream at constant temperature Tg by convective heat transfer with heat-transfer coefficient h. Find the steady-state temperature profile, assuming that Sc is constant throughout. a) Set up the differential equation by making a shell energy balance. b) Integrate the differential equation to get the temperature profile.

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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4. Gas temperature T R A spherical catalyst pellet has a radius R and a thermal conductivity k (which may be assumed constant) [see the image to the right]. Because of the chemical reaction occurring within the porous pellet, heat is generated at a rate Sc cal/(cm³.s). Heat is lost at the outer surface of the pellet to a gas stream at constant temperature Tg by convective heat transfer with heat-transfer coefficient h. Find the steady-state temperature profile, assuming that Sc is constant throughout. a) Set up the differential equation by making a shell energy balance. b) Integrate the differential equation to get the temperature profile.
Transcribed Image Text:4. Gas temperature T R A spherical catalyst pellet has a radius R and a thermal conductivity k (which may be assumed constant) [see the image to the right]. Because of the chemical reaction occurring within the porous pellet, heat is generated at a rate Sc cal/(cm³.s). Heat is lost at the outer surface of the pellet to a gas stream at constant temperature Tg by convective heat transfer with heat-transfer coefficient h. Find the steady-state temperature profile, assuming that Sc is constant throughout. a) Set up the differential equation by making a shell energy balance. b) Integrate the differential equation to get the temperature profile.
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