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MATHEMATICAL
MODELS FOR
GENERATING
ELECTRICITY
FROM OCEANIC
BODY
Abstract
In this paper we present some mathematical models for
the generation of electrical energy from sea bodies and
thunder strikes.
Pictorial models are presented and their mathematical
analyses are given.
Introduction
It is said that for Nigeria to be industrialized, she will
need about 120,000 kilo waltz of electricity as against the
present 3to 5 thousand kilo waltz of electricity generated in
the country.
Thus for a quick industrialization of the country, we would
need to depend on nuclei fusion to be able to generate the
expected 120,000 kilo waltz of electricity.
However, generating electricity from nuclei fusion has the
following disadvantages:
•It will place Nigeria at a position of high nuclei risk which could
be as a result of earthquake as it happened in Japan and China,
thus leading to problem of nuclei radiation ;
•Terrorist gaining control over such nuclei reactor could hold the
nation to ransom;
•It will aggravate the problem of Global warming if most nations
would have to depend on nuclei fusion for electricity generation.
Consequent upon these and coupled with the quest for
industrialization, we need to think and design modalities for the
generation of the 120,000 kilo waltz of electricity that is needed.
Hence the need for the topic “mathematical models for
generating electricity from oceanic body. “
Generating Electricity From The Sea Wave
Our aim is to be able to control the sea water and wave in a way to optimize
it for electricity generation. But there are some constraints to be considered
before the issues of electricity generation can be possible.
The constraints are;
•The violent nature of the sea;
•The sea coast low level;
•The sandy nature of the sea; and
•The salty nature of the sea.
FIG.1
This tower was constructed by solving equation below on the 7th of February 1887;
FIG.2
FIG.3
FIG.4
FIG.5
FIG.6
FIG.7
FIG.9
FIG.10
FIG.11
FIG.12
Because of the violent nature of the sea, we need to impose
a system structure that is
•Controllable
•Admissible
•Observable
An admissible system is one to which
corrective measures can be administered.
A controllable system is a system that is
mathematical expressed as
that is a system that is bounded below and above.
, which transfers the state
If there is a finite
time and a control
to the origin at time ,the state is said to be controllable at time
if all values of
controllable.
are controllable for all
the system is completely
.
Observable system:
is one that is analytic, that is, its first derivative exists within the
interval.
If by observing the output
the state
observable at time
during the finite time interval
can be determined, the state
is said to be
Kalman in 1960 showed that a necessary and sufficient condition for
controllability and observability is that the system should be a
nonsingular matrix [2]
This is a system that is subject to us in a way thus
successfully bypassing the turbulent and violent nature
of the sea.
Another concern is the salty nature of the ocean water.
This can be prevented by coating the propeller with
polythene material.
Our intention can be conceptualized as follows;
We want to optimize the ocean →
Optimize electricity generation=
Objective is to generate electricity= (Z)
Subject to;
•The violent nature of the sea;
•The low land of sea coast;
•The sandy nature of the sea; and
•The salty nature of the sea.
The state variable is the wave of the sea = x(t);
The control variable is the structure that is introduced into the sea to control it
flow= u(t)
Let the coefficient of the x(t) and u(t) be 𝛼 and 𝛾 respectively ,such that we
plot 𝛾 u(t) against 𝛼 x(t) .
Then we can write;
𝛼 x(t) + i 𝛾 u(t)
Multiplying 𝛼 x(t) + i 𝛾 u(t) by its conjugate will give;
It follows that we want to
(2)
Thus we now have an optimization problem as;
Subject to;
•The violent nature of the sea;
•The low land of sea coast;
•The sandy nature of the sea; and
•The salty nature of the sea
Analysis of the Control Structure
For us to obtain the control structure and to be able to examine its
functionality (what goes on in the structure), we make use of the finite
element method.
This is because the stiffness matrix is defined in the fluid flow problem
to relate nodal volumetric fluid-flow to nodal potentials, and in structure
problem the stiffness matrix is defined to relate nodal forces to nodal
displacement.
For the discretized structure in Fig.10, we want to derive
the element stiffness matrix and equation by using one
dimensional finite element formulation.
This will enable us to determine;
•the potential at the junctions;
•the velocities in each section of the structure and;
•the volumetric flow rate.
It follows that for a smooth pipe [], the permeability coefficient,
.
We find that the element stiffness matrices are:
Where the units of are meters for fluid flowing through a structure
and
is the area of each portion of the discretized structure.
If a structure is discretized into parts then there will be
nodal potentials or fluid heads.
The determinant given as
,
,
…
The fluid velocity in element 1 is
The Volumetric flow rates
Generating Electricity From The Sound of The Sea Wave
FIG.13
HOW THE STRUCTURE IN FIG.13 WORKS
(i)The dish receives the sound of the sea wave;
(ii) the sound sensitive material receives the sound and amplify it;
(iii) a piezoelectric transducer converts the sound signal into an
electrical signal;
(iv) an ultrasonic transducer converts the electrical signal into an
ultrasonic sound signal;
(v) again the amplified ultrasonic sound signal is converted into an
electric signal via a
Piezoelectric transducer
(vi)an amplifier that will be able to amplify electrical signal is
needed at this point and the found one is a Biomolecular Transistor
called Microtubules (MTs).
MICROTUBULES (MTs):
Taxol-stabilized Microtubules (MTs) behave as Biomolecular
Transistors capable of amplifying electrical signal.
We want all these structures to be isomorphic, that is, to hold together as one.
Then we are to invoke an integration such that;
represents the transformer
If the electrical energy is very high, we will nee d
to be a step down transformer such that
But if the electrical energy is low, we will need
to bust it to the order of our desire such that
Thus (10) becomes;
For a step up case. While (10) becomes
It is obvious that since
systems of operations,
can be written as matrices which must be square and all of equal order.
This will allow for easy multiplication.
FIG.15
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If the human’s ears are viewed as 2 cylinders, then the volume of air that goes
into the brain is given as
By also considering air flow to the brain through the noisy as a cylinder the volume of
air flow is
Thus the volume of air flow to the brain is
It follows that if one wears an ear piece on the two ears, the air flow is reduced to
This is dangerous to the brain !
And
Generating Electricity From Thunder Strike
Electrons are emitted when there is a thunder strike. To overcome the
problem of electricity generation, it is high time we considered how to
gather the electrons that are emitted. There is an existing technology by
which these electrons can be gathered. This is by using a thunder catcher.
A Mathematical View of Thunder Strike and a Thunder Catcher
In Mathematics, the thunder catcher can be viewed as a point of
convergence because the electrons significantly meet on the thunder
catcher.
By using an approximate Mathematical Method, one can represent the
pictures of the thunder strikes by graph theory as follows;
(i) Fig.17 and fig. 19 can be represented approximately as binary and
ternary trees respectively;
(ii) Fig.18 can be studied using the Scattering velocity or complex
system Analysis;
(iii)the Schrodinger Equation for n electrons can be used and it is given
as;
According to the data collected in this month of April 2013 in
Ado-Ekiti, there was only one thunder strike in my area as shown
below.
14/4/2013
Thunder strike
18/4/2013
lightening but no thunder strike
19/4/2013
no thunder strike
20/4/2013
no thunder strike
25/4/2013
no thunder strike
28/4/2013
no thunder strike
The steps by which electricity from thunder strikes can be generated are
as follows;
•first find a means of measuring the electrons emitted when there is a
thunder strike;
•we are to make use of some thunder catcher that are connected to some
capacitors since capacitors can receive and store electrons,
• if the quantity of electrons trapped by the thunder catcher is
as the capacitors serve as electrons banks, we envisage that the electrons
harvested therein could be stored until the next raining season since
thunder strikes do not always occur every time it rained.