ME109 Heat Transfer
Final Exam; Instructor: Prof. A. Majumdar
December 18, 2004; Time: 12:30-3:30 pm; Maximum Points = 100
NOTE: This is an open book, open notes exam.
Transmissivity, tl
Reflectivity, rl
1. Give brief answers with explanation and reasonin
Calculate, using the numerical finite difference procedure for one dimensional conduction, the steady state temperature in a long flat plate of 1m thickness (and also 1m width) with a uniform energy generation of 4 x 104W/m3 The surface at x = 0 is a
UC Berkeley Department of Mechanical Engineering
ME 109 Heat Transfer (CCN 55509)
Spring 2016
Wednesday January 20th to Friday May 6th, 2016
Instructor:
Dr. David Rich
([email protected], [email protected])
Office: 60 A Hesse Hall
Office Hours
ME 132
Solutions # 6
1 PI position control for a DC Motor
First observe that the motor dynamics in transfer function notation are given by
1600
1.9
u
TL
=
s(s + 0.97)
s(s + 0.97)
Next, our PI controller has the form
sKP + KI
u=
(r )
s
Combining these equa
Practice Problems for Midterm 1
(Homework Assignment #5)
ME 109 Heat Transfer
University of California, Berkeley
Fall 2016
Assigned:
September 21, 2016
Due:
NO DUE DATE
Topics
Transient (Lumped) Conduction
Transient (Non-Lumped) Conduction Fourier Series
ME 132
Solutions # 2
1 Model Properties
Many of you had difficulty with this problem, particularly part (c).
(a) This model is memoryless, nonlinear, time-invariant, causal.
(b) This model is memoryless, nonlinear (because of the affine term b), time-inva
ME 132
Solutions # 1
1 Structure of Control Systems
Shown below is a block diagram for the temperature control system in a refrigerator. A relay is
an on-off switch, and is often the most elementary actuation in control systems. Not shown are
humidity eff
ME 132
Solutions # 11
1 Observers
(a) A state-space realization
0
x 1
x 2 = 0
y
1
of the plant model is
1 0
x1
0
0 1 x2 + 0 n
u
1
0 0
If the desired characteristic polynomial for A + LC is s2 + 1 s + 0 , the observer gain K is
T
1
found using the pro
ME 132
Solutions # 4
1 Finding Transfer functions
(a) To find the transfer function of the cascade connection:
y (2) + 3y (1) + 10y = v (1) 5v
100v (1) + v = u
we first rewrite these equations using the transfer function notation:
y=
s2
s5
v,
+ 3s + 10
v=
ME 132
Solutions # 09
1 State-space realizations
(a) We can write down the controllable canonical from realization by inspection.
0 1 0
0
0 0
x1
x 1
x 2 0 0 1
0
0 0 x2
1
0 0 x3
x 3 0 0 0
x = 0 0 0
0
1 0
x4
4
x 3 0 2 7 6 1 x
5
5
u
y
1 0 0
3
PROBLEM 5.5
KNOWN: Geometries of various objects. Material and/or properties. Cases (a) through (d):
Convection heat transfer coefficient between object and surrounding fluid. Case (e): Emissivity of
sphere, initial temperature, and temperature of surroun
Homework Assignment #7
ME 109 Heat Transfer
University of California, Berkeley
Fall 2016
Assigned:
October 12, 2016
Due:
Wednesday, October 19, by 4:00 pm,
Turn in to the ME109 homework box (box #4) on the 3rd floor of Etcheverry Hall.
Topics
Numerical Me
Homework Assignment #6
ME 109 Heat Transfer
University of California, Berkeley
Fall 2016
Assigned:
October 6, 2016
Due:
THURSDAY, October 13, by 4:00 pm,
Turn in to the ME109 homework box (box #4) on the 3rd floor of Etcheverry Hall.
Topics
Single Term Fo
Homework Assignment #4
ME 109 Heat Transfer
University of California, Berkeley
Fall 2016
Assigned:
September 21, 2016
Due:
Wednesday, September 28, by 4:00 pm,
Turn in to the ME109 homework box (box #4) on the 3rd floor of Etcheverry Hall.
Topics
Fins
Sha
Homework Assignment #8
ME 109 Heat Transfer
University of California, Berkeley
Fall 2016
Assigned:
October 19, 2016
Due:
Wednesday, October 26, by 4:00 pm,
Turn in to the ME109 homework box (box #4) on the 3rd floor of Etcheverry Hall.
Topics
Convection C
ME 132
Solutions # 8
1 Realizations
(a) The state and output equation for the system from v to r is
x = Ax + BY v
r = XCx + XDY v
so a state-space representation of the cascaded system is (A, BY, XC, XDY ).
(b) First write the integrator as 1/s. Next, we
ME 132
Solutions # 3
1 First-order Systems
(a) The first-order system y + ay = bu is stable if and only if a > 0. In this case, a = 1 hence
the system is stable.
(b) The time constant is =
(c) The DC gain is uy =
b
a
1
a
=1
= 2
(d) The response to the giv
ME 109 Heat Transfer HW Chapters 6 and 7: Assigned Monday 3/7/16, Due Friday 3/18/16
Problem 1:
Appendix E of your text provides the following energy equation:
Chapter 6, Equation 6.29 presents a reduced form of equation E.4 as follows:
a) Walk through th
ME 109, HEAT TRANSFER (3)
Spring 2015
MWF 2-3 105 North Gate
Costas P. Grigoropoulos, Professor
Text: Fundamentals of Heat and Mass Transfer
6177 Etcheverry Hall
Incropera and De Witt, 7th