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

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Języki publikacji
EN
Abstrakty
EN
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-Pade 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.
Rocznik
Strony
1--7
Opis fizyczny
Bibliogr. 19 poz., rys., tab., wykr.
Twórcy
  • University of the Limpopo, Applied Mathematics Department, Private Bag X1106, Sovenga 0727, South Africa
Bibliografia
  • [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.
  • [6] A. J. Guttamann. Asymptotic analysis of power - series expansions, Phase Transitions and Critical Phenomena. C. Domb and J. K. Lebowitz, eds. Academic Press, New York, pp. 1-234, 1989.
  • [7] C. Hunter and B. Guerrieri. Deducing the properties of singularities of functions from their Taylor series coefficients. SIAM J. Appl. Math., 39:, 248-263, 1980.
  • [8] D. L. Hunter and G. A. Baker. Methods of series analysis III: Integral approximant methods. Phys. Rev. B, 19: 3808-3821, 1979.
  • [9] P. L. Leider and R. B. Bird. Squeezing flow between parallel plates I. Theoretical analysis. Indust. Engn. Chem. Fundam., 13: 336-341, 1974.
  • [10] O. D. Makinde. Extending the utility of perturbation series in problems of laminar flow in a porous pipe and a diverging channel. Jour. of Austral. Math. Soc. Ser. B, 41: 118-128, 1999.
  • [11] O. D. Makinde. Heat and mass transfer in a pipe with moving surface: Effects of viscosity variation and energy dissipation. Quaestiones Mathematicae, 24: 97-108, 2001.
  • [12] R. E. Shafer..On quadratic approximation. SIAM J. Numer. Anai, 11: 447-460, 1974.
  • [13] T. Shonhiwa and M. B. Zaturska. Disappearance of criticality in thermal ignition for a simple reactive viscous flow. Jour. Appl. Math. Phy. ZAMP, 37: 632-635, 1986.
  • [14] A.Y. Sergeyev. A recursive algorithm for Pade-Hermite approximations. U.S.S.R. Comput. Math. Phys., 26: 17-22, 1986.
  • [15] A. Y. Sergeyev and A. Z. Goodson. Summation of asymptotic expansions of multiple-valued functions using algebraic approximants: Application to anharmonic oscillators. J. Phys., A: Math. Gen., 31: 4301-4317, 1998.
  • [16] K. Taira. A mathematical analysis of thermal explosions. IJMMS, 1-26, 2001.
  • [17] Z. Warnatz, U. Maas and R. W. Dibble. Combustion, 2nd ed., Springer-Verlag, Berlin 1999.
  • [18] M. B. Zaturska. Critical conditions for thermal explosion in reactive viscous flows. Combustion Flame, 41: 201-211, 1981.
  • [19] Ya. B. Zeldovich, G. I. Barenblatt, Y. B. Librovich and G. M. Makhviladze. The mathematical theory of combustion and explosions. Consultants Bureau, New York, London 1985.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB1-0013-0007
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