The surface of a radiation shield facing a black hot wall at 400 K has a reflectivity of 0.95. Attached to the back side of the shield is a 25-mm-thick sheet of insulating material having a thermal conductivity of 0.016 W/m ⋅ K . The overall heat transfer coefficient (convection and radiation) at the surface exposed to the ambient air and surroundings al 300 K is 10 W/m 2 ⋅ K . (a) Assuming negligible convection in the region between the wall and the shield, estimate the heat loss per unit area from the hot wall. (b) Perform a parameter sensitivity analysis on the insulation system, considering the effects of shield reflectivity, ρ s , and insulation thermal conductivity, k . What influence do these parameters have on the heat loss from the hot wall? What is the effect of an increased overall coefficient on the heal loss? Show the results of your analysis in a graphical format.
The surface of a radiation shield facing a black hot wall at 400 K has a reflectivity of 0.95. Attached to the back side of the shield is a 25-mm-thick sheet of insulating material having a thermal conductivity of 0.016 W/m ⋅ K . The overall heat transfer coefficient (convection and radiation) at the surface exposed to the ambient air and surroundings al 300 K is 10 W/m 2 ⋅ K . (a) Assuming negligible convection in the region between the wall and the shield, estimate the heat loss per unit area from the hot wall. (b) Perform a parameter sensitivity analysis on the insulation system, considering the effects of shield reflectivity, ρ s , and insulation thermal conductivity, k . What influence do these parameters have on the heat loss from the hot wall? What is the effect of an increased overall coefficient on the heal loss? Show the results of your analysis in a graphical format.
Solution Summary: The author explains how to perform the energy balance on shield and the wall.
The surface of a radiation shield facing a black hot wall at 400 K has a reflectivity of 0.95. Attached to the back side of the shield is a 25-mm-thick sheet of insulating material having a thermal conductivity of
0.016
W/m
⋅
K
. The overall heat transfer coefficient (convection and radiation) at the surface exposed to the ambient air and surroundings al 300 K is
10
W/m
2
⋅
K
.
(a) Assuming negligible convection in the region between the wall and the shield, estimate the heat loss per unit area from the hot wall. (b) Perform a parameter sensitivity analysis on the insulation system, considering the effects of shield reflectivity,
ρ
s
, and insulation thermal conductivity, k. What influence do these parameters have on the heat loss from the hot wall? What is the effect of an increased overall coefficient on the heal loss? Show the results of your analysis in a graphical format.
100
As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the
spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a
damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is
subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in
a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement:
• Analytically (hand calculations)
Creating Simulink Model
Plot solutions for first two, three and four non-zero terms as well as the Simulink solution on the same graph
for the first 15 sec. The graph must be fully formatted by code.
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set
in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its
equilibrium position a distance 2 m and then releasing both masses. if m₁ = m² = 1 kg, k₁ = 3 N/m and
k₂ = 2 N/m.
(y₁ = 0)
www
k₁ = 3
Jm₁ = 1
k2=2
www
(Net change in
spring length
=32-31)
(y₂ = 0)
m₂ = 1
32
32
System in
static
equilibrium
System in
motion
Figure Q3 - Coupled mass-spring system
Determine the equations of motion y₁ (t) and y₂(t) for the two masses m₁ and m₂ respectively:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Produce an animation of the system for all solutions for the first minute.
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank
A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each
tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of
6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If,
initially, tank A contains pure water and tank B contains 20 kg of salt.
A
6 L/min
0.2 kg/L
x(t)
100 L
4 L/min
x(0) = 0 kg
3 L/min
1 L/min
B
y(t)
100 L
y(0) = 20 kg
2 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t≥ 0:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Plot all solutions on the same graph for the first 15 min. The graph must be fully formatted by code.
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