Rishi Transform for Determining the Concentrations of the Chemical Compounds in First Order Successive Chemical Reaction
Abstract
Understanding chemical reactions is crucial for solving engineering and applied science issues including photosynthesis, nuclear reactors, heat transport, radioactive decay, and photon emission. The main goal of this paper is to use the Rishi transform to ascertain the chemical compound concentrations in first-order successive chemical reactions. The goal of this study is to maximize production by removing waste or unnecessary products during the transitional stage of a chemical reaction. According to the results, the Rishi transform is a useful analytical tool for determining the concentrations of the chemical compounds in a first order sequential chemical process. The paper's findings also show that the Rishi transform can produce precise results without requiring laborious computing.
References
1. Aggarwal, S., Gupta, A.R., Singh, D.P., Asthana, N. and Kumar, N., Application of Laplace transform for solving population growth and decay problems, International Journal of Latest Technology in Engineering, Management & Applied Science, 7(9), 141-145, 2018.
2. Aggarwal, S., Gupta, A.R., Asthana, N. and Singh, D.P., Application of Kamal transform for solving population growth and decay problems, Global Journal of Engineering Science and Researches, 5(9), 254-260, 2018.
3. Aggarwal, S., Pandey, M., Asthana, N., Singh, D.P. and Kumar, A., Application of Mahgoub transform for solving population growth and decay problems, Journal of Computer and Mathematical Sciences, 9(10), 1490-1496, 2018.
4. Aggarwal, S., Sharma, N. and Chauhan, R., Solution of population growth and decay problems by using Mohand transform, International Journal of Research in Advent Technology, 6(11), 3277-3282, 2018.
5. Aggarwal, S., Asthana, N. and Singh, D.P., Solution of population growth and decay problems by using Aboodh transform method, International Journal of Research in Advent Technology, 6(10), 2706-2710, 2018.
6. Aggarwal, S., Singh, D.P., Asthana, N. and Gupta, A.R., Application of Elzaki transform for solving population growth and decay problems, Journal of Emerging Technologies and Innovative Research, 5(9), 281-284, 2018.
7. Aggarwal, S., Sharma, S.D. and Gupta, A.R., Application of Shehu transform for handling growth and decay problems, Global Journal of Engineering Science and Researches, 6(4), 190-198, 2019.
8. Aggarwal, S. and Bhatnagar, K., Sadik transform for handling population growth and decay problems, Journal of Applied Science and Computations, 6(6), 1212-1221, 2019.
9. Singh, G.P. and Aggarwal, S., Sawi transform for population growth and decay problems, International Journal of Latest Technology in Engineering, Management & Applied Science, 8(8), 157-162, 2019.
10. Aggarwal, S., Sharma, S.D., Kumar, N. and Vyas, A., Solutions of population growth and decay problems using Sumudu transform, International Journal of Research and Innovation in Applied Science, 5(7), 21-26, 2020.
11. Priyanka and Aggarwal, S., Solution of the model of the bacteria growth via Rishi transform, Journal of Advanced Research in Applied Mathematics and Statistics, 7(1 & 2), 5-11, 2022.
12. Bansal, S., Kumar, A. and Aggarwal, S., Application of Anuj transform for the solution of bacteria growth model, GIS Science Journal, 9(6), 1465-1472, 2022.
13. Sharma, N. and Aggarwal, S., Laplace transform for the solution of Abel’s integral equation, Journal of Advanced Research in Applied Mathematics and Statistics, 4(3&4), 8-15, 2019.
14. Aggarwal, S. and Sharma, S.D., Application of Kamal transform for solving Abel’s integral equation, Global Journal of Engineering Science and Researches, 6(3), 82-90, 2019.
15. Aggarwal, S., Sharma, S.D. and Gupta, A.R., A new application of Mohand transform for handling Abel’s integral equation, Journal of Emerging Technologies and Innovative Research, 6(3), 600-608, 2019.
16. Aggarwal, S. and Sharma, S.D., Solution of Abel’s integral equation by Aboodh transform method, Journal of Emerging Technologies and Innovative Research, 6(4), 317-325, 2019.
17. Aggarwal, S. and Gupta, A.R., Sumudu transform for the solution of Abel’s integral equation, Journal of Emerging Technologies and Innovative Research, 6(4), 423-431, 2019.
18. Aggarwal, S. and Gupta, A.R., Shehu transform for solving Abel’s integral equation, Journal of Emerging Technologies and Innovative Research, 6(5), 101-110, 2019.
19. Aggarwal, S. and Bhatnagar, K., Solution of Abel’s integral equation using Sadik transform, Asian Resonance, Vol. 8 No. 2, (Part-1), 57-63, 2019.
20. Aggarwal, S. and Upadhyaya, L.M., An application of the Laplace-Carson transform method for the solution of the generalized Abel’s integral equation, Bulletin of Pure and Applied Sciences-Math & Stat. 40E(2), 155-163, 2021.
21. Debnath, L. and Bhatta, D., Integral transforms and their applications, 2nd ed., Chapman & Hall/CRC, Boca Raton.
22. Spiegel, M.R., Schaum’s outline of theory and problems of Laplace transforms, McGraw-Hill, USA, 1965.
23. Higazy, M., Aggarwal, S. and Hamed, Y.S., Determination of number of infected cells and concentration of viral particles in plasma during HIV-1 infections using Shehu transform, Journal of Mathematics, 2020, 1-13, 2020. https://doi.org/10.1155/2020/6624794
24. Kumar, A., Bansal, S., Aggarwal, S., Determination of the blood glucose concentration of a patient during continuous intravenous injection using Anuj transform, Neuroquantology, 19(12), 303-306, 2021.
25. Higazy, M., Aggarwal, S. and Taher, A.N., Sawi decomposition method for Volterra integral equation with application, Journal of Mathematics, 2020, 1-13, 2020. https://doi.org/10.1155/2020/6687134
26. Kumar, A., Bansal, S. and Aggarwal, S., A new novel integral transform “Anuj transform” with application, Design Engineering, 2021(9), 12741-12751, 2021.
27. Kumar, R., Chandel, J. and Aggarwal, S., A new integral transform “Rishi Transform” with application, Journal of Scientific Research, 14(2), 521-532, 2022.
28. Aggarwal, S., Sharma, N. and Chauhan, R., Duality relations of Kamal transform with Laplace, Laplace-Carson, Aboodh, Sumudu, Elzaki, Mohand and Sawi transforms, SN Applied Sciences, 2(1), 135, 2020. https://doi.org/10.1007/s42452-019-1896-z
29. Aggarwal, S. and Gupta, A.R., Dualities between Mohand transform and some useful integral transforms, International Journal of Recent Technology and Engineering, 8(3), 843-847, 2019.
30. Aggarwal, S. and Gupta, A.R., Dualities between some useful integral transforms and Sawi transform, International Journal of Recent Technology and Engineering, 8(3), 5978-5982, 2019.
31. Aggarwal, S., Bhatnagar, K. and Dua, A., Dualities between Elzaki transform and some useful integral transforms, International Journal of Innovative Technology and Exploring Engineering, 8(12), 4312-4318, 2019.
32. Chauhan, R., Kumar, N. and Aggarwal, S., Dualities between Laplace-Carson transform and some useful integral transforms, International Journal of Innovative Technology and Exploring Engineering, 8(12), 1654-1659, 2019.
33. Aggarwal, S. and Bhatnagar, K., Dualities between Laplace transform and some useful integral transforms, International Journal of Engineering and Advanced Technology, 9(1), 936-941, 2019.
34. Chaudhary, R., Sharma, S.D., Kumar, N. and Aggarwal, S., Connections between Aboodh transform and some useful integral transforms, International Journal of Innovative Technology and Exploring Engineering, 9(1), 1465-1470, 2019.
35. Mishra, R., Aggarwal, S., Chaudhary, L. and Kumar, A., Relationship between Sumudu and some efficient integral transforms, International Journal of Innovative Technology and Exploring Engineering, 9(3), 153-159, 2020.
36. Higazy, M. and Aggarwal, S., Sawi transformation for system of ordinary differential equations with application, Ain Shams Engineering Journal, 12(3), 3173-3182, 2021. https://doi.org/10.1016/j.asej.2021.01.027
37. Murphy, R.D., Exact solution of rate equations for consecutive first and second order reactions, Indian Journal of Chemistry, 32A, 381-382, 1993.
38. Lin, S.H., Consecutive chemical reactions in an annular reactor with non Newtonian flow, Applied Scientific Research, 30, 113-126, 1974.
39. Chrastil, J., Determination of the first order consecutive reaction rate constants from final product, Computers & Chemistry, 12(4), 289-292, 1988.
40. Westman, A.E.R. and DeLury, D.B., The differential equations of consecutive reactions, Canadian Journal of Chemistry, 34(8), 1134-1138, 1956.
41. Erdogdn, F. and Sahmurat, F., Mathematical fundamentals to determine the kinetic constants of first-order consecutive reactions, Journal of Food Process Engineering, 30(4), 407-420, 2007.
42. Aggarwal, S., Kumar, R. and Chandel, J., Exact solution of non-linear Volterra integral equation of first kind using Rishi transform, Bulletin of Pure and Applied Sciences, Section-E-Mathematics & Statistics, 41E(2), 159-166, 2022.
43. Aggarwal, S., Kumar, R. and Chandel, J., Solution of linear Volterra integral equation of second kind via Rishi transform, Journal of Scientific Research, 15(1), 111-119, 2023. http://dx.doi.org/10.3329/jsr.v15i1.60337
2. Aggarwal, S., Gupta, A.R., Asthana, N. and Singh, D.P., Application of Kamal transform for solving population growth and decay problems, Global Journal of Engineering Science and Researches, 5(9), 254-260, 2018.
3. Aggarwal, S., Pandey, M., Asthana, N., Singh, D.P. and Kumar, A., Application of Mahgoub transform for solving population growth and decay problems, Journal of Computer and Mathematical Sciences, 9(10), 1490-1496, 2018.
4. Aggarwal, S., Sharma, N. and Chauhan, R., Solution of population growth and decay problems by using Mohand transform, International Journal of Research in Advent Technology, 6(11), 3277-3282, 2018.
5. Aggarwal, S., Asthana, N. and Singh, D.P., Solution of population growth and decay problems by using Aboodh transform method, International Journal of Research in Advent Technology, 6(10), 2706-2710, 2018.
6. Aggarwal, S., Singh, D.P., Asthana, N. and Gupta, A.R., Application of Elzaki transform for solving population growth and decay problems, Journal of Emerging Technologies and Innovative Research, 5(9), 281-284, 2018.
7. Aggarwal, S., Sharma, S.D. and Gupta, A.R., Application of Shehu transform for handling growth and decay problems, Global Journal of Engineering Science and Researches, 6(4), 190-198, 2019.
8. Aggarwal, S. and Bhatnagar, K., Sadik transform for handling population growth and decay problems, Journal of Applied Science and Computations, 6(6), 1212-1221, 2019.
9. Singh, G.P. and Aggarwal, S., Sawi transform for population growth and decay problems, International Journal of Latest Technology in Engineering, Management & Applied Science, 8(8), 157-162, 2019.
10. Aggarwal, S., Sharma, S.D., Kumar, N. and Vyas, A., Solutions of population growth and decay problems using Sumudu transform, International Journal of Research and Innovation in Applied Science, 5(7), 21-26, 2020.
11. Priyanka and Aggarwal, S., Solution of the model of the bacteria growth via Rishi transform, Journal of Advanced Research in Applied Mathematics and Statistics, 7(1 & 2), 5-11, 2022.
12. Bansal, S., Kumar, A. and Aggarwal, S., Application of Anuj transform for the solution of bacteria growth model, GIS Science Journal, 9(6), 1465-1472, 2022.
13. Sharma, N. and Aggarwal, S., Laplace transform for the solution of Abel’s integral equation, Journal of Advanced Research in Applied Mathematics and Statistics, 4(3&4), 8-15, 2019.
14. Aggarwal, S. and Sharma, S.D., Application of Kamal transform for solving Abel’s integral equation, Global Journal of Engineering Science and Researches, 6(3), 82-90, 2019.
15. Aggarwal, S., Sharma, S.D. and Gupta, A.R., A new application of Mohand transform for handling Abel’s integral equation, Journal of Emerging Technologies and Innovative Research, 6(3), 600-608, 2019.
16. Aggarwal, S. and Sharma, S.D., Solution of Abel’s integral equation by Aboodh transform method, Journal of Emerging Technologies and Innovative Research, 6(4), 317-325, 2019.
17. Aggarwal, S. and Gupta, A.R., Sumudu transform for the solution of Abel’s integral equation, Journal of Emerging Technologies and Innovative Research, 6(4), 423-431, 2019.
18. Aggarwal, S. and Gupta, A.R., Shehu transform for solving Abel’s integral equation, Journal of Emerging Technologies and Innovative Research, 6(5), 101-110, 2019.
19. Aggarwal, S. and Bhatnagar, K., Solution of Abel’s integral equation using Sadik transform, Asian Resonance, Vol. 8 No. 2, (Part-1), 57-63, 2019.
20. Aggarwal, S. and Upadhyaya, L.M., An application of the Laplace-Carson transform method for the solution of the generalized Abel’s integral equation, Bulletin of Pure and Applied Sciences-Math & Stat. 40E(2), 155-163, 2021.
21. Debnath, L. and Bhatta, D., Integral transforms and their applications, 2nd ed., Chapman & Hall/CRC, Boca Raton.
22. Spiegel, M.R., Schaum’s outline of theory and problems of Laplace transforms, McGraw-Hill, USA, 1965.
23. Higazy, M., Aggarwal, S. and Hamed, Y.S., Determination of number of infected cells and concentration of viral particles in plasma during HIV-1 infections using Shehu transform, Journal of Mathematics, 2020, 1-13, 2020. https://doi.org/10.1155/2020/6624794
24. Kumar, A., Bansal, S., Aggarwal, S., Determination of the blood glucose concentration of a patient during continuous intravenous injection using Anuj transform, Neuroquantology, 19(12), 303-306, 2021.
25. Higazy, M., Aggarwal, S. and Taher, A.N., Sawi decomposition method for Volterra integral equation with application, Journal of Mathematics, 2020, 1-13, 2020. https://doi.org/10.1155/2020/6687134
26. Kumar, A., Bansal, S. and Aggarwal, S., A new novel integral transform “Anuj transform” with application, Design Engineering, 2021(9), 12741-12751, 2021.
27. Kumar, R., Chandel, J. and Aggarwal, S., A new integral transform “Rishi Transform” with application, Journal of Scientific Research, 14(2), 521-532, 2022.
28. Aggarwal, S., Sharma, N. and Chauhan, R., Duality relations of Kamal transform with Laplace, Laplace-Carson, Aboodh, Sumudu, Elzaki, Mohand and Sawi transforms, SN Applied Sciences, 2(1), 135, 2020. https://doi.org/10.1007/s42452-019-1896-z
29. Aggarwal, S. and Gupta, A.R., Dualities between Mohand transform and some useful integral transforms, International Journal of Recent Technology and Engineering, 8(3), 843-847, 2019.
30. Aggarwal, S. and Gupta, A.R., Dualities between some useful integral transforms and Sawi transform, International Journal of Recent Technology and Engineering, 8(3), 5978-5982, 2019.
31. Aggarwal, S., Bhatnagar, K. and Dua, A., Dualities between Elzaki transform and some useful integral transforms, International Journal of Innovative Technology and Exploring Engineering, 8(12), 4312-4318, 2019.
32. Chauhan, R., Kumar, N. and Aggarwal, S., Dualities between Laplace-Carson transform and some useful integral transforms, International Journal of Innovative Technology and Exploring Engineering, 8(12), 1654-1659, 2019.
33. Aggarwal, S. and Bhatnagar, K., Dualities between Laplace transform and some useful integral transforms, International Journal of Engineering and Advanced Technology, 9(1), 936-941, 2019.
34. Chaudhary, R., Sharma, S.D., Kumar, N. and Aggarwal, S., Connections between Aboodh transform and some useful integral transforms, International Journal of Innovative Technology and Exploring Engineering, 9(1), 1465-1470, 2019.
35. Mishra, R., Aggarwal, S., Chaudhary, L. and Kumar, A., Relationship between Sumudu and some efficient integral transforms, International Journal of Innovative Technology and Exploring Engineering, 9(3), 153-159, 2020.
36. Higazy, M. and Aggarwal, S., Sawi transformation for system of ordinary differential equations with application, Ain Shams Engineering Journal, 12(3), 3173-3182, 2021. https://doi.org/10.1016/j.asej.2021.01.027
37. Murphy, R.D., Exact solution of rate equations for consecutive first and second order reactions, Indian Journal of Chemistry, 32A, 381-382, 1993.
38. Lin, S.H., Consecutive chemical reactions in an annular reactor with non Newtonian flow, Applied Scientific Research, 30, 113-126, 1974.
39. Chrastil, J., Determination of the first order consecutive reaction rate constants from final product, Computers & Chemistry, 12(4), 289-292, 1988.
40. Westman, A.E.R. and DeLury, D.B., The differential equations of consecutive reactions, Canadian Journal of Chemistry, 34(8), 1134-1138, 1956.
41. Erdogdn, F. and Sahmurat, F., Mathematical fundamentals to determine the kinetic constants of first-order consecutive reactions, Journal of Food Process Engineering, 30(4), 407-420, 2007.
42. Aggarwal, S., Kumar, R. and Chandel, J., Exact solution of non-linear Volterra integral equation of first kind using Rishi transform, Bulletin of Pure and Applied Sciences, Section-E-Mathematics & Statistics, 41E(2), 159-166, 2022.
43. Aggarwal, S., Kumar, R. and Chandel, J., Solution of linear Volterra integral equation of second kind via Rishi transform, Journal of Scientific Research, 15(1), 111-119, 2023. http://dx.doi.org/10.3329/jsr.v15i1.60337
Published
2023-08-29
How to Cite
AGGARWAL, Sudhanshu; KUMAR, Rishi; CHANDEL, Jyotsna.
Rishi Transform for Determining the Concentrations of the Chemical Compounds in First Order Successive Chemical Reaction.
Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 8, n. 1&2, p. 10-17, aug. 2023.
ISSN 2455-7021.
Available at: <http://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/819>. Date accessed: 21 dec. 2024.
Section
Research Article
