Assume we have following system. A heater is heating the right chamber with a thermal flow
rate qin, Assuming the fluid in the right chamber has a thermal capacitance c1 and a temperature
theta1, the fluid in the left chamber has a thermal capacitance C2 and a temperature theta2. The
thermal resistance for the side walls of the chambers is R1, R2 and R3, respectively. The
atmosphere temperature is theta a and is a 1own value. Two insulation layers on top and bottom
of the chambers do not have any heat exchange with surrounding environment. a. Please find out
the state equations for this system.
Solution
To write its state equations first of all we try to draw its thermal ckt. diagram
Qin heat get divided in two sides, one of them toward R3 wall and other toward R2 wall. R1
wall resistance is in series with R2 wall resistance but there is some enthalpy in left chamber i.e.
therefore the total heat that passes through resistance R2 will be Q'1 + Q2.
Now we will write the equation
First of all Qin = Q1 +Q'1