The oven shown in the figure has a heating element with appreciable capacitance C. The other capacitance is that of the oven air C. The correspondingtemperatures are T and T, and the outside temperature is To The thermal resistance of the heater-air interface is R; that of the oven wall is R. Identify a modelfor T1 and T2, with input q;, the heat flow rate delivered to the heater mass.Oven airT2C2T.R|T C 19iR2Heatingelementa. Develop the dynamic equations for this system. (submit in Connect)b. Develop the state variable Matrix form of the model in terms of the system parameter variables (not numerical values).c. Using the numerical values for the system parameters provided, use MATLAB to calculate the transfer functions 1 and 2Tand describe the expected behaviorbased on both of these transfer functions.d. Plot the dynamic behavior of the actual temperature of the oven chamber if the heating element is turned on with a constant heat rate of qj. Assume that theentire systems starts at the ambient temperature, and the ambient temperature of the room does not change throughout.When producing your plot from the state variable model, remember that the input will be as a change in qi, and the output will be the increase in temperature, butyou need to plot the actual temperature.System_Parameters =(R| = 5.0 R2= 50.0 C, = 0.1 C2=2.0 q;= 3.0 T,=23.0): C ~W°C

The oven shown in the figure has a heating element with appreciable capacitance C. The other capacitance is that of the oven air C2. The correspond temperatures are T1 and T2, and the outside temperature is To. The thermal resistance of the heater-air interface is R; that of the oven wall is R2. Ider for T1 and T2, with input q, the heat flow rate delivered to the heater mass. Oven air T2 C2 191 R1 R2 Heating 71 |element a. Develop the dynamic equations for this system. (submit in Connect)

The oven shown in the figure has a heating element with appreciable capacitance C. The other capacitance is that of the oven air C2. The correspond temperatures are T1 and T2, and the outside temperature is To. The thermal resistance of the heater-air interface is R; that of the oven wall is R2. Ider for T1 and T2, with input q, the heat flow rate delivered to the heater mass. Oven air T2 C2 191 R1 R2 Heating 71 |element a. Develop the dynamic equations for this system. (submit in Connect)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

The oven shown in the figure has a heating element with appreciable capacitance C. The other capacitance is that of the oven air C. The corresponding
temperatures are T and T, and the outside temperature is To The thermal resistance of the heater-air interface is R; that of the oven wall is R. Identify a model
for T1 and T2, with input q;, the heat flow rate delivered to the heater mass.
Oven air
T2
C2
T.
R|
T C 19i
R2
Heating
element
a. Develop the dynamic equations for this system. (submit in Connect)
b. Develop the state variable Matrix form of the model in terms of the system parameter variables (not numerical values).
c. Using the numerical values for the system parameters provided, use MATLAB to calculate the transfer functions 1 and 2
T
and describe the expected behavior
based on both of these transfer functions.
d. Plot the dynamic behavior of the actual temperature of the oven chamber if the heating element is turned on with a constant heat rate of qj. Assume that the
entire systems starts at the ambient temperature, and the ambient temperature of the room does not change throughout.
When producing your plot from the state variable model, remember that the input will be as a change in qi, and the output will be the increase in temperature, but
you need to plot the actual temperature.
System_Parameters =
(R| = 5.0 R2= 50.0 C, = 0.1 C2=2.0 q;= 3.0 T,=23.0)
: C ~
W
°C

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