Jiec
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- 1
- Homework Statement
- Built the physical model (considering lumped capacitance mthod) of the three-layer wall, using one node for each layer placed at the centre of the latter, one node for the inner surface and one node for the outer surface.
The layers have conductivity k_i (for i=1:3) and thickness l_i (for i=1:3) and cross-sectional area A, only layer number 2 has a heat capacitance C2. The temperature of the inner and outer surface are assigned.
Then write the equations of the mathematical model.
- Relevant Equations
- R=l_i/(k_i*A)
Q=(T_i-T_j)/R
dQ=C_i*(dT/dt)
Hello,
I have some doubt on the representation of the physical model. I'm not sure about the number and value of the capacitance to be used.
I solved the exercise using this model (see figure) and i would like to know if the solution is correct or if there is something to fix.
Regarding the solution:
- R_a= R1/2
- R2_a=R1/2+R2/2
- R2_b=R2/2+R3/2
- R_b=R3/2
where R1, R2, R3 are the thermal resistance of each layer
- C2=l_2*A*c2
where c2 is hte specific heat of the second layer
For the mathematical model the equations are the following:
- (Ti-T1)/R_a-(T1-T2)/R2_a=0
- ( (T1-T2)/R2_a-(T2-T3)/R2_b )=C2*dT2/dt where dT2/dt is the derivative of T2 with respect to the time
- (T2-T3)/R2_b-(T3-Te)/R_b=0
I have some doubt on the representation of the physical model. I'm not sure about the number and value of the capacitance to be used.
I solved the exercise using this model (see figure) and i would like to know if the solution is correct or if there is something to fix.
Regarding the solution:
- R_a= R1/2
- R2_a=R1/2+R2/2
- R2_b=R2/2+R3/2
- R_b=R3/2
where R1, R2, R3 are the thermal resistance of each layer
- C2=l_2*A*c2
where c2 is hte specific heat of the second layer
For the mathematical model the equations are the following:
- (Ti-T1)/R_a-(T1-T2)/R2_a=0
- ( (T1-T2)/R2_a-(T2-T3)/R2_b )=C2*dT2/dt where dT2/dt is the derivative of T2 with respect to the time
- (T2-T3)/R2_b-(T3-Te)/R_b=0