simulink excercise

Modeling and Analysis of Engineering Systems – SIMULINK Exercise 1 (Due 10/16)

You simply need to submit (hardcopy) what is asked for in bold below. You may

work with others but you must submit your own work under your own name.

(1) A clothes iron has a sole plate weighing 1.75 kg with an exposed area of 0.05 m2.

The sole plate is made of steel, which has a heat capacity of 450 J/kg∙oC, and the heat

transfer coefficient for convection from the iron to the surrounding air (which is at 25 oC)

is 20 J/s∙m2∙oC. The iron is rated at 150 W and is initially at the temperature of the air.

(a) Use SIMULINK to a plot of temperature of the iron versus time. Go out to 5000

seconds in time. Submit the block diagram and the scope.

(b) Using the plot, estimate the steady state temperature of the iron and the time needed

for the iron to reach 100 oC. Compare these to the values obtained analytically in

class. Submit your answers to these as well.

(2) In class, we considered a problem in which a spherical metal pellet was dropped into

a temperature bath in which the bath fluid was assumed to remain at a constant

temperature Tf. Let us reexamine that problem by relaxing this assumption. Now,

assume that there is no heat exchange between the bath and the surroundings but that the

bath temperature can change due to heat released from the pellet. Now both the pellet

temperature T(t) and the bath temperature Tf(t) will vary with time. Take the initial pellet

and bath temperatures to be 100 oC and 25 oC respectively, the mass m, surface area A

and heat capacity C of the pellet to be 0.04 kg, 0.0025 m2 and 800 J/kg oC, and the heat

transfer coefficient h to be 100 J/s m2 oC. The mass mf and heat capacity Cf of the bath

are 0.1 kg and 4000 J/kg oC. The energy balance for the pellet is:

dT/dt = -(hA/MC)(T – Tf) T(0) = 100 oC

And for the bath:

dTf/dt = (hA/MfCf)(T – Tf) Tf(0) = 25 oC

Simulate this system using SIMULINK. It is suggested to use a max step size of 1

second. Choose an appropriate simulation stop time by trial and error. Plot T and Tf

versus time on the same graph. What is the final equilibrium temperature of the system?

Submit your block diagram, the scope showing the results and your answer for the

final equilibrium temperature.