MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.
-
Upload
ralph-chase -
Category
Documents
-
view
214 -
download
1
Transcript of MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.
![Page 1: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/1.jpg)
MATHEMATICAL MODELS FOR GENERATING ELECTRICITY
FROM OCEANIC BODY
![Page 2: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/2.jpg)
AbstractIn 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.
![Page 3: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/3.jpg)
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.
![Page 4: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/4.jpg)
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.
![Page 5: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/5.jpg)
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. “
![Page 6: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/6.jpg)
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.
![Page 7: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/7.jpg)
FIG.1This tower was constructed by solving equation below on the 7 th of February 1887;
![Page 8: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/8.jpg)
FIG.2
![Page 9: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/9.jpg)
FIG.3
![Page 10: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/10.jpg)
FIG.4
![Page 11: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/11.jpg)
FIG.5
![Page 12: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/12.jpg)
FIG.6
![Page 13: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/13.jpg)
FIG.7
![Page 14: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/14.jpg)
FIG.9
![Page 15: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/15.jpg)
FIG.10
![Page 16: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/16.jpg)
FIG.11
![Page 17: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/17.jpg)
FIG.12
![Page 18: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/18.jpg)
Because of the violent nature of the sea, we need to impose a system structure that is
•Controllable
•Admissible
•Observable
![Page 19: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/19.jpg)
An admissible system is one to which corrective measures can be administered.
![Page 20: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/20.jpg)
A controllable system is a system that is
mathematical expressed as
that is a system that is bounded below and above.
If there is a finite time and a control
,the state is said to be controllable at time
, which transfers the state
to the origin at time
if all values of are controllable for all the system is completely controllable.
![Page 21: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/21.jpg)
Observable system: is one that is analytic, that is, its first derivative exists within the
interval.
If by observing the output during the finite time interval
.
the state can be determined, the state is said to be
observable at time
![Page 22: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/22.jpg)
Kalman in 1960 showed that a necessary and sufficient condition for controllability and observability is that the system should be a
nonsingular matrix [2]
![Page 23: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/23.jpg)
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.
![Page 24: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/24.jpg)
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)
![Page 25: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/25.jpg)
Let the coefficient of the x(t) and u(t) be and respectively ,such that we 𝛼 𝛾
plot 𝛾 u(t) against 𝛾 x(t) .
Then we can write; 𝛾 x(t) + i 𝛾 u(t) (2)
Multiplying 𝛾 x(t) + i 𝛾 u(t) by its conjugate will give;
It follows that we want to
![Page 26: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/26.jpg)
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
![Page 27: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/27.jpg)
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.
![Page 28: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/28.jpg)
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.
![Page 29: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/29.jpg)
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.
![Page 30: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/30.jpg)
![Page 31: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/31.jpg)
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
,
,
…
![Page 32: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/32.jpg)
Generating Electricity From The Sound of The Sea Wave
FIG.13
![Page 33: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/33.jpg)
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.
![Page 34: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/34.jpg)
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
![Page 35: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/35.jpg)
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
![Page 36: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/36.jpg)
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.
![Page 37: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/37.jpg)
FIG.15
![Page 38: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/38.jpg)
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
![Page 39: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/39.jpg)
![Page 40: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/40.jpg)
![Page 41: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/41.jpg)
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 !
![Page 42: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/42.jpg)
![Page 43: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/43.jpg)
![Page 44: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/44.jpg)
And
![Page 45: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/45.jpg)
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.
![Page 46: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/46.jpg)
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.
![Page 47: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/47.jpg)
![Page 48: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/48.jpg)
![Page 49: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/49.jpg)
![Page 50: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/50.jpg)
![Page 51: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/51.jpg)
![Page 52: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/52.jpg)
![Page 53: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/53.jpg)
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;
![Page 54: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/54.jpg)
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
![Page 55: MATHEMATICAL MODELS FOR GENERATING ELECTRICITY FROM OCEANIC BODY.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697c0111a28abf838ccba60/html5/thumbnails/55.jpg)
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.