THERMAL INSTABILITY IN REACTIVE VISCOUS PLANE POISEUILLE / COUETTE FLOWS FOR TWO EXTREME THERMAL BOUNDARY CONDITIONS

  • 투고 : 2009.02.12
  • 심사 : 2009.04.25
  • 발행 : 2009.06.25

초록

The problem of thermal stability of an exothermic reactive viscous fluid between two parallel walls in the plane Poiseuille and Couette flow configurations is investigated for different thermal boundary conditions. Neglecting reactant consumption, the closed-form solutions obtained from the momentum equation was inserted into the energy equation due to dissipative effect of viscosity. The resulting energy equation was analyzed for criticality using the variational method technique. The problem is characterized by two parameters: the Nusselt number(N) and the dynamic parameter($\Lambda$). We observed that the thermal and dynamical boundary conditions of the wall have led to a significant departure from known results. The influence of the variable pre-exponential factor, due to the numerical exponent m, also give further insight into the behavior of the system and the results expressed graphically and in tabular forms.

키워드

참고문헌

  1. S.O. Ajadi: A note on the thermal stability of a reactive non-Newtonian flow in a cylindrical pipe, Int. Comm. Heat mass Transfer 36(2009),63-68. https://doi.org/10.1016/j.icheatmasstransfer.2008.09.005
  2. S.O. Ajadi and V.Gol'dshtein: Critical behaviour in a three step reactions kinetics model Combustion Theory and Modelling 13(2009),1-16. https://doi.org/10.1080/13647830802337289
  3. S.O. Ajadi: Thermal Instability in a Model Chain Branching-Chain Breaking Kinetics, MATCH Commun. Math. Comput. Chem. 53(2005), 347-356.
  4. S.O. Ajadi and S. S. Okoya: The Effect of Variable Pre - Exponential Factors on the Ignition Time of a Homogeneous System, Int. Comm. Heat mass Transfer, 31(2004), 143-150. https://doi.org/10.1016/S0735-1933(03)00209-4
  5. S. Chen, Z. Liu, C. Zhang, Z. He, and Z. Tian: A novel coupled lattice Boltzmann model for low Mach number combustion simulation, Applied Mathematics and Computation 193(2007), 266284. https://doi.org/10.1016/j.amc.2007.03.087
  6. T. Fang: A note on the incompressible couette flow with porous walls, Int. Comm. Heat Mass Transfer, 31(2004), 31-41. https://doi.org/10.1016/S0735-1933(03)00199-4
  7. J.G. Graham - Eagle and G.C.Wake, The theory of thermal explosions with simultaneous parallel reaction III. Disappearance of critical behaviour with one exothermic and one endothermic reaction, Proc. R. Soc. Lond. A 407(1986), 183 - 198.
  8. J.F. Griffiths and J.A. Barnardand, Flame and Combustion, Blackie Academic and Professional, Chapman and Hall(third edition), London, 1995.
  9. G.S.S. Ludford: Combustion: basic equations and peculiar asymptotics, Journal de Mecanique, 16(1977), 531 - 551
  10. G.S.S. Ludford: Reacting flows: Combustion and Chemical Reactors ( G. S. S. Ludford, ed), American Mathematical Society Publication, 24(1986),129-161.
  11. O.D. Makinde: Thermal criticality in viscous reactive flows through channels with a sliding wall: An exploitation of the Hermite-Pade' approximation method, Mathematics and Computer Modelling 47(2008), 312-317. https://doi.org/10.1016/j.mcm.2007.05.003
  12. O.D. Makinde: Thermal Ignition in a reactive Viscous Flow Through a Channel Filled with a Porous Medium, Journal of Heat Transfer, 128(2006), 601-604. https://doi.org/10.1115/1.2188511
  13. A. Majda and K.G. Lamb, Simplified equations for low Mach number combustion with strong heat release, in: Fife, P. C., A. Linan, F. A. Williams(Eds), Dynamical Issues in Combustion Theory, Springer, 1991.
  14. S.S. Okoya: Thermal Stability for a Reactive Viscous Flow in a Slab, Mechanics Research Communications 33(2006), 728-733. https://doi.org/10.1016/j.mechrescom.2005.11.004
  15. S.S. Okoya: Reactive-diffusive equation with variable pre-exponential factor, Mechanics Research Communications 31(2004), 263-267. https://doi.org/10.1016/j.mechrescom.2003.08.001
  16. S.S. Okoya and S. O. Ajadi: Critical Parameters for Thermal Conduction Equations, Mechanics Research Communications, 26(1999), 363-370. https://doi.org/10.1016/S0093-6413(99)00035-X
  17. J.R. Rodoia and J.F. Osterle: Finite Difference Analysis of Plane Poiseuille and Couette flow developments, Appl. Sci. Res., 10(1960), 265-276.
  18. Ya.B. Zeldovich, G.I. Barenblatt, V.B. Librovich and G.M. Makhviladze, The mathematical Theory of Combustion and Explosion, Plenum Publishing Corp., New York, 1985.