ABE 436 Spring 2014
leegill2
Assignment #1
1. In the 1970s, it was predicted that the oil supply would last for about 20 years. In
the 1990s, some people predicted again that the oil supply would last for about
ABE 436 Spring 2014
Assignments 1:
1. In the 1970s, it was predicted that the oil supply would last for about 20 years. In the
1990s, some people predicted again that the oil supply would last for about 20 years. In
the textbook, At current consumption ra
ARE 436 Solar Energy and Solar Radiation
HW#2
1. Find the local solar time (LST) on August 21 for the following local times and
locations:
a) 9:00 A.M. EDST, Norfolk, VA
b) 1:00 P.M. CDST, Lincoln, NE
c) 10:00 A.M. MDST, Casper, WY
d) 3:00 P.M. PDST, Pend
In this lecture we begin by computing the Laplace transforms of discontinuous functions and more generally of functions dened, through branching, by
dierent formulas. The basis of such a computation is the formula:
Lcfw_u(t a)f (t) = eas Lcfw_f (t + a)
wh
We will solve the following initial-boundary value problem:
u
2u
= 3 2 0 < x < , t > 0
t
x
u(0, t) = u(, t) = 0 t > 0
u(x, 0) = sin x + 3 sin(2x)
We begin by seeking nonzero functions of the form u(x, t) = X(x)T (t) that
satisfy the rst two conditions. In
We dene the inverse Laplace transform of a function F (s) as the function
f (t) that has F as its Laplace transform. Usually we deal with rational functions
of s in which case we use partial fraction decomposition in order to write them
as sums of simple
In this lecture we begin by computing the Laplace transforms of discontinuous functions and more generally of functions dened, through branching, by
dierent formulas. The basis of such a computation is the formula:
Lcfw_u(t a)f (t) = eas Lcfw_f (t + a)
wh
The Fourier coecients of a 2l - periodic function are given by:
an =
1
l
l
f (x) cos
l
nx
dx
l
bn =
1
l
l
f (x) sin
l
nx
dx
l
Then, the Fourier series of f (x) is given by:
+
ao
nx
nx
+ bn sin
)
+
(an cos
2
l
l
n=1
In this lecture, we also introduce to th
A function f , whose domain of denition includes an interval of the form
(a, +) is called of exponential order if there exists a T > 0 and a constant
C such that:
|f (t)| Cet
for all t > T .
A function will be called of exponential order if it is of expon
We begin by looking at the method of reduction of degree which allows
to nd a solution to a linear homogeneous equation of the second order when
one solution is already known. In this case the new solution will be linearly
independent of the rst one.
Supp
In this lecture we begin by analyzing a little more equations of the form:
y + by + cy = 0
where the auxiliary equation
t2 + bt + c = 0
has negative determinant. Then, the equation has two complex roots + i
and i. It turns out that the two linearly indepe
In this lecture we review the method of undetermined coecients and show
how it can be used even if the right hand side is of a more general form. The
idea is the following. Suppose that we have the dierential equation:
ay + by + cy = f1 (x) + f2 (x)
Then
We will now describe a method that enables us to nd a particular solution
in the case that the right hand side is not of the form that was dealt with in
the method of undetermined coecients. In other words, we are interested in
the equation of the form:
a
In this lecture we discuss the formalism of operational calculus for the solution of systems of dierential equations. Here, we introduced the dierentiation
operator D and we saw how a system like:
y + 2y + x x
2y y + x + 3x
= ex
= cos x
can be rewritten a
A dierential equation of the form
P (x, y) + Q(x, y)
dy
=0
dx
F
is called exact if one can nd a function F = F (x, y) such that P =
and
x
F
. Because of their close connection with dierentials of functions of two
Q=
y
variables, we often rewrite the diere
In this lecture we begin with a special type of rst degree dierential equations: separable equations. These are equations of the form:
dy
= p(x)q(y)
dx
In other words, in the traditional equation y = f (x, y), f (x, y) can be
expressed in the form p(x)q(y
We begin this lecture by giving an improved approach to Eulers method.
Recall that Eulers method allows us to nd approximations to solutions of the
initial value problem:
y = f (x, y) y(xo ) = yo
In particular, one uses the recursion formula yn+1 = yn + f
We begin by reviewing equations of the form:
M (x, y)dx + N (x, y)dy = 0
that are not necessarily exact. In general we would hope that we can make
them exact by multiplying by an appropriate integrating factor (x, y) as in
the case of linear equations. Ho
Example 3
A house owner in Champaign, IL (at 88 deg W longitude and 40 deg N latitude) installed a solar
PV panel (10 m2) for his home. The panel is set on roof facing south and titled at 40 deg. What
is the power of the PV panel at 3:00 pm CST on Feb. 21
Example 1
A CSP plant has a two-tank thermal energy storage system using molten-salt: Cold" storage
tank: 288 C (550 F); Hot storage tank 566 C (1,051 F). A 100-megawatt turbine would need
two tanks of about 30 feet (9.1 m) tall and 80 feet (24 m) in diam
Geothermal Energy
Question of the Day
How much heat can be extracted from 1m3 of rock
from 1000C to 300C?
Lecture 15.1
Topics of the Day
Earth Heat
Applications of Geothermal Energy
Power Generation
Ideal Rankine Cycle
Direct Use
Heat Mining
Lecture 15.2
Example 1
A PV module is made of 36 identical cells, all wired in a series. Each cell has a parallel
resistance RP = 6.6 and a series resistance RS = 0.005 . With 1-sun insolation (1000 w/m2) at
25C, each cell has a short-circuit current Isc = 3.4 A and i
Ground Source Heat Pump
Question of the Day
Why are GSHPs more efficient than other HVAC
equipment?
Lecture 16.1
Topics of the Day
Principle of heat pump
Ground source heat pump
Configurations and design of GSHP
Lecture 16.2
Refrigeration
Qo
W
Qi
Lectu
Example 2
Find the soar altitude, , and azimuth, , and the incident angle, , of a vertical window facing
east at 10:30 a.m. CDST on June 21 at Champaign at 88 deg W longitude and 40 deg N latitude.
Solution:
Champaign, IL (40 deg N, 88 deg W)
From Table 7
Economics of Heat Pump
Question of the Day
What is the biggest benefit for a ground source heat pump
system?
What does an ENERGY STAR label mean to a Heat
Pump?
Lecture 17.1
Topics of the Day
Definitions of efficiency
Cost Comparison
Lecture 17.2
EER
E
Solar Photovoltaics Systems
Question of the Day:
How do we optimize the power output of a PV system?
Lecture 8.1
Topics of the Day
Types of PV systems
Operating point of the PVs
PV system sizing
Cost of PVs
Lecture 8.2
Types of PV systems
Grid-tied PV sy
SYLLABUS
ABE 436 - Renewable Energy Systems
Spring 2014
Instructor: Dr. Xinlei Wang, Room 332C, Agr. Engr Science Bldg,
Office Ph: 333-4446, email: xwang2@illinois.edu.
Office hours: 11:00 a.m. -12:00 p.m. Monday and Wednesday, other times by appointment
Energy and Environment
Question of the Day
What are the major pollutants from
conventional energy production and use?
Lecture 2.1
Topics of the Day
Pollutant and Environmental Effects
Emission Sources
Global Warming
CO2 Sequestration
Lecture 2.2
Pollutant
Solar Heating
Question of the Day
How much energy is needed for heating your home per
year? How can the solar energy be utilized for heating?
NCSU Solar House
Lecture 5.1
Topics of the Day
Thermal radiation
Active solar heating Solar water heater
Types of
Solar Time and Solar Angle
How much solar radiation is available in the west wall of
the Agricultural Engineering Sciences Building at 3p.m.,
March 30?
Lecture 3.1
Topics of the Day
Earths motion about the sun
Solar time
Solar angle
Lecture 3.2
Example