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
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 abo
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
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 i
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,
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
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 i
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
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 functio
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 sol
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 roo
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 di
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
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 +
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 func
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 =
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 p
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 integrati
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
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 o
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
I
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,
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
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.
So
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
Definit
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
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
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 rad
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 abo