2. 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/°R, Ts = 530°R and a = 5x10-8 Btu/h-°R*. (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.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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2. An electric heater is used to heat a slab, and the following model has been derived to predict
the slab temperature:
dT
C3Q(t)- a(T – T)
dt
%3D
|
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, Ts = 530°R and a = 5x10-8 Btu/h-°R*.
%3D
%3D
%3D
(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:2. An electric heater is used to heat a slab, and the following model has been derived to predict the slab temperature: dT C3Q(t)- a(T – T) dt %3D | 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, Ts = 530°R and a = 5x10-8 Btu/h-°R*. %3D %3D %3D (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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