Conductivity
4. RESULTS AND DISCUSSION
4.3 Heat Transfer Rate Analysis at the Sphere Surface
Fig. 8. on temperature
Fig. 9. Bi on temperature
Contrary to what has happened, we observe that a combined increment in the parameters (heat loss) and (temperature biot number) results with a decline in the temperature profiles, as illustrated in Figs. 8 - 9. An increase in means that the rate of heat loss at the surface of the sphere is increased, hence the temperature of the system’s reduction. The same is observed with the increase in , that there is a decline in the temperature of the system. This is due to increased rate of heat loss due to convection at the surface of the sphere. The last two parameters, are good for discouraging the exothermic chemical reaction from taking place to control self-ignited fires.
increase in temperature profiles. We see a different picture in Tables 5 – 6, where an increase in the values of the parameters (heat loss) and (temperature biot number) show a decrease in the temperature of the system, as indicated in Figs. 7 - 8, meaning that the rate of heat release at the surface of the sphere is more, and therefore there is reduction on the exothermic chemical reaction to reduce the heat release during combustion under the effects of the parameters under discussion. The tables are presented below to demonstrate how the method of Slope Linear Regression (SLP) is used to indicate the effects of selected parameters on the gradients of the temperature at the surface of the sphere.
Table 1. Effects of on (Fig. 4)
0.1 0.0297921110627965
0.3 0.0982017773962830
0.5 0.183562649501951
SLP 0.384426346
Table 2. Effects of on (Fig. 5)
0.1 0.0297921110627965
0.7 0.0301022900136715
2 0.0307851856168397
SLP 0.000523094
Table 3. Effects of on (Fig. 6)
0.1 0.0297921110627965
0.3 0.0305842707861642
0.5 0.0324552293904337
SLP 0.00140768
Table 4. Effects of on (Fig. 7)
0.5 0.0297921110627965
0 0.0297367439132690
-2 0.0295183937637705
SLP 0,000109398
Table 5. Effects of α on Nu (Fig. 8)
1 0.0297921110627965
2 0.0219449805598255
3 0.0174049587746782
SLP -0.006193576
Table 6. Effects of Bi on Nu (Fig. 9)
1 0.0297921110627965
2 0.0343007502359461
3 0.0361241407790109
SLP 0.003166015
5. CONCLUSION
The analysis of heat transfer in a combusting stockpile of reactive materials modeled in a spherical domain of variable thermal conductivity was presented in this article. It was discovered that some parameters encourage exothermic chemical reaction, whilst others discourage the reaction from taking place in stockpiles of combustible materials. The parameters , , and were found to favor the acceleration of the exothermic chemical reaction. The occurrence of the exothermic chemical reaction releases more heat into the combusting sphere, and the accumulation of heat causes the raising up of the temperature gradient during combustion. It is better to keep these parameters very low to reduce self-ignition process in stockpiles of combustible materials. On the other hand, it was found out that the parameters and favor the reduction of the temperature during the combustion.
These parameters should be kept high to avoid self-ignited fires from explosions. This study was done theoretically to make the understanding of the combustion process in a cheaper and a quicker way compared to the experimental one. The understanding of the imbedded parameters on heat transfer can help in the control of self-ignition process in the storage of reactive materials. This study can be extended to two-step exothermic chemical reaction processes.
COMPETING INTERESTS
Author has declared that no competing interests exist.
REFERENCES
1. Makinde OD. Strongly exothermic explosions in a cylindrical pipe: A case study of series summation technique, Mech. Res. Commun. 2005;32:191–195.
2. Lebelo RS. Numerical investigation of CO2 emission and thermal stability of a convective and radiative stockpile of reactive material in a cylindrical pipe of variable thermal conductivity, AIP Conference Proceedings. 2014;1621(60):60–68.
3. Arisoy A, Beamish BB, Cetezen E. Modelling spontaneous combustion of coal. Turkish J. Eng.
Env. Sci. 2006;30:193–201.
4. Arisoy A, Beamish BB, Cetegen E. Modelling spontaneous combustion of coal. Turk J Eng Env Sci. 2006;30:193–201.
5. Lebelo RS. Numerical investigation of CO2 emission and thermal stability of a convective and radiative stockpile of reactive material in a cylindrical pipe of variable thermal conductivity. AIP Conf Proc 2014;1621:60–68.
6. Lebelo RS, Makinde OD, Chinyoka T. Thermal decomposition analysis in a sphere of combustible materials. Advances in Mechanical Engineering. 2017;9(2):1687814017692515.
7. Chinyoka T, Makinde OD. Computational analysis of CO2 emission, O2 depletion and thermal decomposition in a cylindrical pipe filled with reactive materials, Commun. Nonlinear Sci. Num.
Sim. 2013;18:2448–2461.
8. Bowes PC. Self-heating: Evaluating and controlling the hazards. Elsevier, Amsterdam; 1984.
9. Balakrishnan E, Swift A, Wake GC. Critical values for some non-class A geometries in thermal ignition theory, Math. Comp. Model. 1996;24:1–10.
10. Lebelo RS. Transient heat analysis in a spherical domain of combustible material, J. Commun.
Compt. 2016;13:159-163.
11. Lebelo RS, Makinde OD, Chinyoka T. Thermal decomposition analysis in a sphere of combustible materials. Adv. Mech. Eng. 2017;9:1–14.
12. Lacey AA, Wake GC. Thermal ignition with variable thermal conductivity. J. Appl. Math. 1982;
28:23–39.
13. Moise A, Pritchard HO. Thermal explosion with variable thermal conductivity. C. R. Exp. S. Sci.
Canada, M3J, 1P3. 1981;165-167.
Biography of author(s)
Ramoshweu Solomon Lebelo
Vaal University of Technology, Mathematics Department, Adries Potgieter Blvd, Vanderbijlpark, 1911, South Africa.
He is an Educator and Researcher in the Department of Education at the Vaal University of Technology. He is offering Mathematics and Educational Studies to the B.Ed students and his research areas are in Computational Fluid Dynamics (CFD) and Mathematics Education. He has published extensively in the areas of CFD in International Peer-Reviewed Journals indexed in Scopus and ISI and to date has presented his work in a total of 19 Conferences. He is a reviewer for over 15 Peer- Reviewed Journals, and he sits on the Editorial Board of three international Peer-reviewed Journals. He was a Guest Editor for the Special Issue “Mathematical Application and Computing in Mechanical Engineering” of the Peer-Reviewed Advances in Mechanical Engineering Journal published by SAGE (2016 – 2017). He is presently Editing a Special Issue “Computational Fluid Dynamic and Mathematical Modeling” for Defect and Diffusion Forum Journal published by Scientific.Net. He co-authored the textbook “Mathematics for Engineering students” ISBN: 9781485122326, Publisher: Juta & Company (Pty) Ltd and authored the research book “Mathematical Approach to Transient Heat Analysis” ISBN: 978-3-330-03882-0, Publisher: Lambert Academic Publishing. He has also authored a Spiritual Book “Suffer with Christ” ISBN: 978-1-4836-6118-6, Publisher: Xlibris Publishing.
_________________________________________________________________________________
© Copyright (2021): Author(s). The licensee is the publisher (Book Publisher International).
DISCLAIMER
This chapter is an extended version of the article published by the same author(s) in the following journal.
Materials Science and Engineering, 269: 012062, 2017.
_____________________________________________________________________________________________________
1EEE Department, Dr. MGR Educational & Research Institute, Maduravoyal, Chennai-95, India.
2Department of Electrical and Electronics Engineering, Vels institute of Science, Technology and Advanced Studies, Chennai, India.
3CSE Department, SRM Institute of Science and Technology, Kattankulathur, India.
4Chemical Engg Department, Dr. MGR Educational & Research Institute, Maduravoyal, Chennai-95, India.
5EEE Department, Meenakshi College of Engineering, Chennai, India.