Authors : T. O. Sarumo; R. A. Oderinu; S. O. Salawu

Volume/Issue : Volume 11 - 2026, Issue 1 - January

Google Scholar : https://tinyurl.com/yd7bc3ay

Scribd : https://tinyurl.com/7jm3dxef

DOI : https://doi.org/10.38124/ijisrt/26jan1321

Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.

Abstract : In contrast to existing studies on thermal criticality, which are limited to single-cylinder configurations, this study examines bimolecular exothermic reactions in finite concentric cylinders subject to asymmetric and Neumann boundary conditions. The nonlinear energy equation is first nondimensionalised and then solved using the Weighted Residual Collocation Method (WRCM) with a six-term polynomial trial function implemented in Maple. The accuracy and convergence of the WRCM are verified by comparison with the classical fourth-order Runge–Kutta (RK4) method, yielding errors below 10−7 throughout the computational domain. The results indicate that an increase in the Frank– Kamenetskii parameter causes a rapid rise in temperature, leading to eventual thermal runaway at criticality values of 0.780 for asymmetric conditions and 1.650 for Neumann conditions. Higher heat-loss parameters improve thermal stability by enhancing boundary heat dissipation, whereas the initiation parameter significantly influences reaction sensitivity and temperature gradients near the core. Furthermore, asymmetric boundary conditions generate higher peak temperatures than Neumann conditions, owing to reduced heat removal. These findings provide useful design insights for combustion chambers, catalytic reactors, and energy storage systems, highlighting how appropriate control of heat dissipation can mitigate thermal runaway and improve operational safety.

Keywords : Combustion; Concentric Cylinder; Bimolecular Kinetics; Thermal Criticality; Heat Loss.

References :

1. Kareem, I., Yusuf, A., and Chen, Z. (2024). Convective boundary effects in nonlinear reactive heat transfer systems. Applied Thermal Engineering, 242, 121056.
2. Lebelo, R., Mahlobo, R., & Moloi, K. (2018). Thermal stability analysis in a Two-Step reactive cylindrical stockpile. American Journal of Applied Sciences, 15(2), 124–131.
3. Alhassan, B., and Musa, K. (2025). Thermal runaway in catalytic converters: A nonlinear heat transfer analysis. Energy Reports, 11(1), 118–130.
4. Ohaegbue, A.D., Oderinu, R. A., and Salawu, S.O. (2024). Thermal criticality and diffusion–reaction behavior in exothermic media. International Journal of Heat and Mass Transfer, 226, 125833.
5. Frank-Kamenetskii, D. A. (1969). Diffusion and Heat Transfer in Chemical Kinetics. Plenum Press.
6. Zhang, H., and Li, J. (2022). Criticality of nonlinear bimolecular reactions under heat loss. Chemical Engineering Science, 262, 118029.
7. Thosago, K. F., Banjo, P. O., Rundora, L., and Adesanya, S. O. (2024). Thermal stability and entropy generation in combustible reactive flows: Spectral analysis approach. Applied Sciences, 14(24), 11491.
8. Mohan, R., and Suresh, V. (2024). Numerical modeling of nonlinear boundary-value problems using Python-based iterative solvers. SoftwareX, 26, 101725.
9. Alma, A., Bello, A., and Ige, O. (2023). Stability analysis of heat-generating media in cylindrical coordinates. International Communications in Heat and Mass Transfer, 142, 107740.
10. Alma’asfa, S.I., Aziz, M.S.A., Khor, C., and Fraige, F.Y. (2025). Thermal management of cylindrical Li-ion batteries using fin–PCM configurations: A numerical study. Journal of Thermal Analysis and Calorimetry, 150, 12643–12662.
11. Ferreira, P., Tang, S.-X., and Kim, H. (2025). Investigating thermal behavior in cylindrical energy systems under convective boundaries. Scientific Reports, 15(2), 30830.
12. Singh, A., and Patel, R. (2023). Application of Python for solving nonlinear heat transfer equations using Newton-Raphson and Runge–Kutta methods. Computational Thermal Sciences, 15(4), 355–366.
13. Adewale, A.R., Saka, A., and Ajiboye, T. (2022). Nonlinear thermal stability of exothermic reactions in cylindrical reactors. Journal of Thermal Engineering, 8(5), 922–935.
14. Ajadi, S.O.; Gol’dshtein, V. (2009). Critical behaviour in a three-step reaction kinetics model. Combust. Theory Model. 13, 1–16.
15. Salawu, S.O.; Okoya, S.S, (2020). On criticality for a branched-chain thermal reactive-diffusion in a cylinder. Combust. Sci. Technol., 192, 1–16.
16. Ajadi, S.O.( 2011). Approximate analytic solution for critical parameters in thermal explosion problem. Appl. Math. Comput., 218, 2005–2010.
17. Yusuf, A., Kareem, I., and Adebayo, L.O. (2024). Semi-analytical modeling of thermal instability in reactive cylindrical systems. Heat and Mass Transfer Journal, 61(7), 3412–3426.
18. Okonkwo, J., Bello, A., and Ige, O. (2023). Stability analysis of heat-generating media in cylindrical coordinates. International Communications in Heat and Mass Transfer, 142, 107740.
19. Monagan, M.B., Geddes, K.O., Heal, K.M., Labahan, G. Vorkoetter, S.M., McCarron, j. and DeMarco, P.(2009), Maple introductory programming guide, Waterloon Maple Inc, 15-16
20. Al-Kandari, H., and Ahmad, M. (2024). Symbolic–numeric implementation of nonlinear heat transfer models using Maple. Journal of Computational and Applied Mathematics, 440, 115702.
21. Das, R., and Roy, S. (2023). Maple-based numerical framework for nonlinear reaction–diffusion problems in cylindrical coordinates. Case Studies in Thermal Engineering, 45, 102598.
22. Rahman, K., Hassan, A., and Zhou, Q. (2025). Nonlinear thermal stability and symbolic computation of exothermic reactive systems in Maple. Energy Reports, 11(1), 325–339.
23. Shampine, L. F. (2023). Boundary value problems and the use of Runge–Kutta methods as reference solvers. Applied Numerical Mathematics, 194, 1–15.
24. Abdulle, A., & Lubich, C. (2024). Error analysis of collocation and Runge–Kutta methods for nonlinear boundary value problems. Numerische Mathematik, 146(3), 567–598.
25. Wang, Y., Li, X., & Chen, Z. (2025). Convergence properties of weighted residual and collocation methods for nonlinear differential equations. Nonlinear Analysis: Modelling and Control, 30(1), 89–110
26. Zhu, J., Li, X., and Chen, L. (2021). Ignition delay and initiation effects in bimolecular reactive systems. International Journal of Thermal Sciences, 170, 107119.
27. Li,S., Peng, J., and Huang, Z. (2025). Critical ignition and heat-loss modeling in catalytic tubular reactors. Chemical Engineering Journal, 485, 149761.
28. Cheng, L., Zhang, Y., and Li, H. (2025). Modeling ignition sensitivity in nonlinear combustion systems with convective losses. Journal of Thermal Science and Engineering Applications, 17(3), 045301. https://doi.org/10.1115/1.4064392
29. Oderinu, R. A., Salawu, S. O., and Ohaegbue, C. I. (2025). Thermal management and critical ignition in dual-layer exothermic reactors. International Journal of Heat and Mass Transfer, 224, 125733.
30. Yu, P., Wang, T., and Chen, X. (2023). Convective heat-loss optimization for preventing thermal runaway in reactive systems. Energy Conversion and Management, 296, 117361.
31. Zeldovich, Y.B.; Barenblatt, G.I.; Librovich, V.B.; Makhviladze, G.M. The Mathematical Theory of Combustion and Explosions; Consultants Bureau: New York, NY, USA, 1985.