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3. An electric heater is used to heat a slab, and the following model has been derived to predict the slab temperature: dT - = Q(t) – a(T* –T,*) dt where T is the slab temperature in °R, Q(t) is the rate of heat input in Btu/h which is an input variable, C = 250 Btu/oR, T = 530°R and a = 5x10-8 Btu/h.°R4. (a) Obtain a linearized model around a slab steady state temperature of 650°R. (b) Obtain the transfer function for the process relating the slab temperature to the heating rate. Determine the time constant and steady state gain of the linearized model.

3. An electric heater is used to heat a slab, and the following model has been derived to predict the slab temperature: dT - = Q(t) – a(T* –T,*) dt where T is the slab temperature in °R, Q(t) is the rate of heat input in Btu/h which is an input variable, C = 250 Btu/oR, T = 530°R and a = 5x10-8 Btu/h.°R4. (a) Obtain a linearized model around a slab steady state temperature of 650°R. (b) Obtain the transfer function for the process relating the slab temperature to the heating rate. Determine the time constant and steady state gain of the linearized model.

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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Process Dynamics and Control, Third Edition or Fourth Edition, by D. E. Seborg, T. F. Edgar, D. A. Mellichamp, F. J. Doyle III, John Wiley & Sons, Inc, 2011

3. An electric heater is used to heat a slab, and the following model has been derived to predict the slab temperature: dT C - = Q(t) – a(T* -T,*) dt where T is the slab temperature in R, Q(t) is the rate of heat input in Btu/h which is an input variable, C = 250 Btu/OR, T = 530°R and a = 5x10-8 Btu/h-ºR4. (a) Obtain a linearized model around a slab steady state temperature of 650°R. (b) Obtain the transfer function for the process relating the slab temperature to the heating rate. Determine the time constant and steady state gain of the linearized model.
Transcribed Image Text:3. An electric heater is used to heat a slab, and the following model has been derived to predict the slab temperature: dT C - = Q(t) – a(T* -T,*) dt where T is the slab temperature in R, Q(t) is the rate of heat input in Btu/h which is an input variable, C = 250 Btu/OR, T = 530°R and a = 5x10-8 Btu/h-ºR4. (a) Obtain a linearized model around a slab steady state temperature of 650°R. (b) Obtain the transfer function for the process relating the slab temperature to the heating rate. Determine the time constant and steady state gain of the linearized model.
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