Thermal ignition in a reactive viscous plane-Poiseuille flow: a bifurcation study

  • Oluvole D. Makinde University of the Limpopo

Abstract

Thermal ignition for a reactive viscous flow between two symmetrically heated walls is investigated. The second order nonlinear boundary value problem governing the problem is obtained and solved analytically using a special type of Hermite-Padé approximation technique. We obtained very accurately the critical conditions for thermal ignition together with the two solution branches. It has been observed that an increase in viscous heating due to viscous dissipation can cause a rapid decrease in the magnitude of thermal ignition critical conditions.

Keywords

plane-Poiseuille flow, Hermite-Padé approximants, thermal ignition,

References

[1] R. Aris. The mathematical theory of diffusion and reaction in permeable catalyst, vol. 1, Clarendon Press, London 1975
[2] J . Bebernes and D. Eberly. Mathematical problems from combustion theory, Springer-Verlag, New York 1989.
[3] T. Boddington, P. Gray and G. C. Wake. Criteria for thermal explosions with and without reactant consumption. Proc. Roy. Soc. London Ser. A, 357: 403- 422, 1977.
[4] B. W. Char, K. W. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan and S. M. Watt. Maple V Language Reference Manual. Springer-Verlag, Berlin 1991.
[5] P. G. Drazin, and Y. Tourigny. Numerical study of bifurcations by analytic continuation of a function defined by a power series. SIAM J. Appl. Math., 56: 1-18, 1996.
Published
Dec 8, 2022
How to Cite
MAKINDE, Oluvole D.. Thermal ignition in a reactive viscous plane-Poiseuille flow: a bifurcation study. Computer Assisted Methods in Engineering and Science, [S.l.], v. 12, n. 1, p. 1-7, dec. 2022. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/1002>. Date accessed: 08 dec. 2024.
Section
Articles