The thermal analysis in a cylindrical pipe with surface cooling and possible heat loss

References

• Adesanya, S. O. 2013. Thermal stability analysis of reactive hydro-magnetic third grade fluid through a channel with convective cooling. Journal of the Nigerian Mathematical Society 32:61–72.
   Google Scholar
• Biyadi, H., M. Er-Riani, and K. Chetehouna. 2015. Hermite-padé approximation approach to exothermic explosions with heat loss. Annals of the University of Craiova-Mathematics and Computer Science Series 42 (1):140–47.
   Web of Science ®Google Scholar
• Boddington, T., C. G. Feng, and P. Gray. 1983. Thermal explosions, criticality and the disappearance of criticality in systems with distributed temperatures i, arbitrary biot number and general reaction-rate laws. In Proceedings of the royal society of London a: Mathematical, physical and engineering sciences, Vol. 390, 247–64. London: The Royal Society.
   Google Scholar
• Boddington, T., C. G. Feng, and P. Gray. 1984. Thermal explosions, criticality, and the disappearance of criticality in systems with distributed temperatures ii: An asymptotic analysis of criticality at the extremes of biot number ((), ()) for general reaction rate-laws. In Proceedings of the royal society of London A: Mathematical, physical and engineering sciences, Vol. 392, 301–22. London: The Royal Society.
   Google Scholar
• Hamza, B., E. S. Massawe, C. W. Mahera, and O. D. Makinde. 2012. On thermal stability analysis for a reacting slab. International Journal of Theoretical and Mathematical Physics 2 (4):91–95. doi:10.5923/j.ijtmp.20120204.06.
   Google Scholar
• Hasan, Y. Q., and L. M. Zhu. 2008. Modified adomian decomposition method for singular initial value problems in the second-order ordinary differential equations. Surveys in Mathematics and Its Applications 3:183–93.
   Google Scholar
• Hassan, A. R., and J. A. Gbadeyan. 2014. Thermal stability of a reactive hydromagnetic poiseuille fluid flow through a channel. American Journal of Applied Mathematics 2 (1):14–20. doi:10.11648/j.ajam.20140201.13.
   Google Scholar
• Hayat, T., Q. Hussain, and T. Javed. 2009. The modified decomposition method and pade approximants for the mhd flow over a non-linear stretching sheet. Nonlinear Analysis: Real World Applications 10 (2):966–73. doi:10.1016/j.nonrwa.2007.11.020.
   Web of Science ®Google Scholar
• Kechil, S. A., and I. Hashim. 2009. Approximate analytical solution for mhd stagnation-point flow in porous media. Communications in Nonlinear Science and Numerical Simulation 14 (4):1346–54. doi:10.1016/j.cnsns.2008.02.007.
   Web of Science ®Google Scholar
• Makinde, O. D. 2005. Strongly exothermic explosions in a cylindrical pipe: A case study of series summation technique. Mechanics Research Communications 32 (2):191–95. doi:10.1016/j.mechrescom.2004.02.008.
   Web of Science ®Google Scholar
• Makinde, O. D. 2012a. Computational modelling of thermal stability in a reactive slab with reactant consumption. In Abstract and applied analysis, Vol. 2012. Hindawi: Hindawi Publishing Corporation.
   Google Scholar
• Makinde, O. D. 2012b. On the thermal decomposition of reactive materials of variable thermal conductivity and heat loss characteristics in a long pipe. Journal of Energetic Materials 30 (4):283–98. doi:10.1080/07370652.2011.566598.
   Web of Science ®Google Scholar
• Makinde, O. D. 2014. Thermal analysis of a reactive generalized couette flow of power law fluids between concentric cylindrical pipes. The European Physical Journal Plus 129 (12):1–9. doi:10.1140/epjp/i2014-14270-4.
   Web of Science ®Google Scholar
• Okoya, S. S. 2016. Flow, thermal criticality and transition of a reactive third-grade fluid in a pipe with Reynolds’ model viscosity. Journal of Hydrodynamics, Series B 28 (1):84–94. doi:10.1016/S1001-6058(16)60610-8.
   Web of Science ®Google Scholar
• Seydel, R. 2009. Practical bifurcation and stability analysis, Vol. 5. New York: Springer Science & Business Media.
   Google Scholar
• Thomas, P. H. 1958. On the thermal conduction equation for self-heating materials with surface cooling. Transactions of the Faraday Society 54:60–65. doi:10.1039/tf9585400060.
   Google Scholar
• Wazwaz, A. M. 1999. A reliable modification of adomian decomposition method. Applied Mathematics and Computation 102 (1):77–86. doi:10.1016/S0096-3003(98)10024-3.
   Web of Science ®Google Scholar
• Wazwaz, A. M. 2006. Padé approximants and adomian decomposition method for solving the Flierl–Petviashivili equation and its variants. Applied Mathematics and Computation 182 (2):1812–18. doi:10.1016/j.amc.2006.06.018.
   Web of Science ®Google Scholar
• Wazwaz, A. M. 2015. A first course in integral equations. New Jersey: World Scientific Publishing Co Inc.
   Google Scholar