electric power generation. Some are Wind-mills, Hydro-electric power (falling water) plants, Fossil-fuels plant and Solar cell plants.

5. Wind-Mill Plant

This plant is device for tapping the energy of the wind by means of sails mounted on a rotating shafts. It is generally less reliable than the water power, but where water is deficient wind power is an attractive substitute. Wind-mill-plant can be use in areas that suffer from draught or from a shortage of surface water and also in a low-lying area where rivers offer little energy. They were mostly used, converting the energy of the wind into mechanical energy for grinding grain, pumping water and drainage. They produced less energy for electricity [5].

6. Hydro-Electric Power

It is the electricity produced from generators driven by water turbines that convert the potential energy in falling or fast-flowing water to mechanical energy. They are usually located in dams that impound rivers; especially in areas with heavy rain fall and hilly or mountainous region. In generation, water is collected or stored at a higher elevation and led downward through large pipes or tunnels to a lower elevation. At the end of its passage down the pipes, the falling water causes turbines to rotate which in turn drive generators which convert the turbines mechanical energy into electricity [6]. Although hydroelectric power plants are not hazardous as the fossil fuels, but it may not meet the electricity demand of a country as fossil fuels would. Also if there are not enough water impounded in a reservoirs during the dry season, the falling water would not be enough to cause the turbine to turn to generate electricity.

7. Fossil-Fuels

The production of steam by fossil-fuels, produce the greatest amount of electrical energy compared to hydroelectric and wind-mills. Fossil-fuels are coal, petroleum, natural gas, oil shales, bitumens, tar sands and heavy oil. All contain carbon and were formed as a result of geologic processes acting on the remains of organic matter produced by photosynthesis. All fossil-fuels can be burned in air or with oxygen to provide heat. The heat may be utilized to produce steam to drive generators that can supply electricity [7]. The use of fossil-fuels is very hazardous to human health as a result of environmental pollutant from burning of the fuels.

8. Solar Cell Plants

This is the best plant that can only be conveniently use on satellites and space where the flow of energy out of the sun (the solar wind) can be harnessed without interference from the atmosphere or the rotation of the earth [8]. Although this type of non-nuclear power plant can also be use on earth, but cannot produce the desire electricity because of the changes in atmospheric conditions and rotation of the earth [9].

9. Advantages of Nuclear Plant over Non-Nuclear Plant

All the non-nuclear power generation discussed above produced low electricity compared to the nuclear reactors. The nuclear reactor released a large amount of energy during the process of fission. Most of this energy released takes form of heat, which is used to produce steam. The steam drives a turbine, the mechanical energy of which is converted to electricity by a generator. The whole process takes place in a safety environment that is not hazardous to the human. The nuclear reactor eliminates most of the disadvantages of the non-nuclear energy by generating enough energy for consumption; does not involved emission of carbon which is very dangerous to the environment; does not involved burning of coal and oils that are the causes of all manners of lung ailments and also does not dependent on fossil-fuels.

10. Main Result

There were three major nuclear reactor accidents they are the three mole island in Pennsylvania, USA in 1979 [3], the Chernobyl RBMK in Soviet Union in 1986 [10] and Fukushima nuclear reactor accident in Tokyo, Japan in 2011 [11].

With the above analysis on nuclear accidents, nuclear technology is necessary for power generation if the safety concerns can be adequately addressed and that is why this work is purely devoted to the safety aspect and not to the weapons production. The fission from the reactors produce energy in form of heat that releases steam to turn turbine to generate electricity, therefore it is necessary to find equations for rate of heat that can be use for the purpose of our work. See [12-14].

11. The Energy Balance for Reactors

The following results were obtained through energy balance equation and were arranged in terms of rate of heats of the reactors (i.e. batch, continuous stirred tank, semi batch and plug flow). See [15,16].

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

(32)

(33)

(34)

(35)

(36)

If the above thirty-six parametric equations and nuclear tokens can be used for the structure model for the construction of nuclear reactors, then the safety will be maximized and disaster minimized. This will later be structured into mathematical model in form of quadratic functional. The model will be solved using Conjugate Gradient Method algorithm, with MATLAB as a support soft-ware. See [17,18].

In particular, we shall use the following quadratic functional for further work.

where i.e. X = (x1x2 x3x4x5x6)T, a = (111111)T, f0 = 1 and

where are the rate of heat of the reactors, and i, j = 1, 2, 3, 4, 5, 6. See [19].

12. Nomenclature

The following nomenclatures are the nuclear tokens.

A = heat transfer area Cj = concentration of species j

= feed concentration of species j

= steady-state concentration of species j

= constant-pressure heat capacity

= partial molar heat capacity

= heat capacity per volume

= constant-pressure heat capacity per mass

= constant-volume heat capacity per mass

= heat capacity change on reaction,

E = total energy

= total energy per mass

= partial molar enthalpy

= enthalpy per unit mass

= enthalpy change on reaction,

= reaction rate constant for reaction i

= reaction rate constant evaluated at mean temperature Tm

= equilibrium constant for reaction i

= kinetic energy per unit mass

= total mass fow of stream k n = reaction order

= moles of species j,

= number of reactions in the reaction network

ns = number of species in the reaction network

P = pressure

Pj = partial pressure of component j

Q = volumetric flow rate Qf = feed volumetric flowrate

= heat transfer rate to reactor

= reaction rate for i th reaction

= production rate for j th species

= time

= temperature

= temperature of heat transfer medium

= mean temperature at which k is evaluated

= overall heat transfer coefficient

= internal energy per mass

= velocity of stream k

= reactor volume variable

= partial molar volume of species j

= reactor volume

= change in volume upon reaction i,

= rate work is done on the system

= coefficient of expansion of the mixture,

= reactor residence time,

= stoichiometric coefficient for species j in reaction i

= mass density

= mass density of stream k

REFERENCES

  1. A. C. Kadak, et al., “A Response to the Environmental and Economic Challenge of Global Warming,” Massachusetts Institute of Technology, Massachusetts, 1998, pp. 1-6.
  2. IAEA Austria, “Structure of Nuclear Power Plant Design Characteristics in the IAEA Power reactor Information System(PRIS),” International Atomic Energy Agency (IAEA), Vienna, 2007, pp. 9-17.
  3. S. Frank, “Nuclear Reactors,” Kennesaw State University, Kennesaw, 2009, pp. 1-13. http//www.chemcases.com/nuclear/nc-10.html
  4. Wikipedia, “Boiling Water Reactor Safety System,” The Free Encyclopedia, 2011, pp. 2-9. http://en.wikipedia.org/wiki/Boiling-water-reator-safety-systems
  5. Encyclopaedia Britannica, “Windmill Power,” (Ultimate Refrence Suite) Chicago Encyclopaedia Britannica, Chicago, 2010.
  6. Encyclopaedia Britannica, “Hydroelectric Power,” (Ultimate Refrence Suite) Chicago Encyclopaedia Britannica, Chicago, 2010.
  7. C. K. Otto, “Fossil Fuel Power,” University of Tennessee, Ultimate Reference Suite Chicago Encyclopaedia Britannica, Knoxville, 2011.
  8. S. Ashok, “Solar Energy,” Department of Engineering, Pennsylvania State University: Ultimate Reference Suite Chicago Encyclopaedia Britannica, Chicago, 2011.
  9. J. S. Walker, “The Three Mile Island: ANuclear Crises in Historical Perspective. Berkeley,” University of California Press, Berkeley, 2004, pp. 216-265.
  10. “The Chernobyl Facts,” 2011. http://www.chernobyl-interntional.org/documents/chernobylfacts2.pdf
  11. Wikipedia, “The Free Encyclopedia,” Fukushima Daiichi Nuclear Reactor Disaster, Fukushima, 2011, pp. 5-27. http://en.wikipedia.org/wiki/Fukushima-Daiichi-nclear-disaster
  12. Wikipedia, “The Free Encyclopedia,” Energy in Japan, 2009, p. 1. http://www.en.wikipedia.org/wiki/Electricity-sector-in-Japan
  13. “Nuclear Fuel Behaviour in Loss-of-Coolant-Accident (LOCA) Conditions,” Nuclear Energy Agency (NEA), 2009, p. 141. http://wwwoecd-nea.org/nsd/reports/2009/nea6846-LOCA.pdf
  14. “Mitigation of Hydrogen Hazard in Water Cooled Power Reactors,” International Atomic Energy Agency (IAEA), 2001, pp. 3-10. http://www-pub.iaea.org/MTCD/publicatuion/PDF/te-1196-prn.pdf
  15. “The Enargy Balance for Chemical Reactors,” Nob Hill Publishing, LLC., Adison Wisconsin, 2011, pp. 1-182. http://jbrwww.che.wisc.edu/home/jbraw/chemreacfun/chb/slides-enbal.pdf
  16. G. H. Brian, “Energy Equations for Reactors,” Department of Chemical Engineering and Material Science, University of California, Davis: Lecture Note, Berkeley, 2010, pp. 9-13.
  17. J. O. Omolehin, “On the Control of Reaction Diffusion Equation,” Ph.D. Thesis, University of Ilorin, Ilorin, 1991.
  18. J. O. Omolehin, K. Rauf and D. J. Evans, “Conjugate Gradient Method Approach to Queue Theory,” International Journal of Computer Mathematics, Vol. 82, No. 7, 2005, pp. 829-835. http://www.tandf.co.uk/journals doi:10.1080/00207160412331296670
  19. J. O. Omolehin, L. Aminu and K. Rauf, “Computational Results on Quadratic Functional Model for the Tokens of Nuclear Safety,” American Journal of Computational Mathematics, 2012 (submitted for publication). http://www.scirp.org/journals/ajcm

NOTES

*Corresponding author.

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