×

zbMATH — the first resource for mathematics

Second law analysis for a variable viscosity reactive Couette flow under Arrhenius kinetics. (English) Zbl 1333.76087
Summary: This study investigates the inherent irreversibility associated with the Couette flow of a reacting variable viscosity combustible material under Arrhenius kinetics. The nonlinear equations of momentum and energy governing the flow system are solved both analytically using a perturbation method and numerically using the standard Newton-Raphson shooting method along with a fourth-order Runge-Kutta integration algorithm to obtain the velocity and temperature distributions which essentially expedite to obtain expressions for volumetric entropy generation numbers, irreversibility distribution ratio, and the Bejan number in the flow field.

MSC:
76V05 Reaction effects in flows
80A30 Chemical kinetics in thermodynamics and heat transfer
76M25 Other numerical methods (fluid mechanics) (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge Mathematical Library, Cambridge University Press, Cambridge, Mass, USA, 1999. · Zbl 0958.76001 · doi:10.1017/CBO9780511800955
[2] H. Schlichting and K. Gersten, Boundary-Layer Theory, Springer, Berlin, Germany, 2000. · Zbl 0940.76003
[3] S. Yasutomi, S. Bair, and W. O. Winer, “Application of a free volume model to lubricant rheology. I-dependence of viscosity on temperature and pressure,” ASME Journal of Tribology, vol. 106, no. 2, pp. 291-303, 1984.
[4] A. Aziz, “Entropy generation in pressure gradient assisted Couette flow with different thermal boundary conditions,” Entropy, vol. 8, no. 2, pp. 50-62, 2006. · Zbl 1135.76307 · doi:10.3390/e8020050
[5] W. M. Kays and M. E. Crawford, Convective Heat and Mass Transfer, McGraw-Hill, New York, NY, USA, 1980.
[6] R. I. Tanner, Engineering Rheology, Oxford Science Publications, Oxford University Press, New York, NY, USA, 1985. · Zbl 1171.76300
[7] L. E. Johns and R. Narayanan, “Frictional heating in plane Couette flow,” Proceedings of the Royal Society of London A, vol. 453, no. 1963, pp. 1653-1670, 1997. · Zbl 0886.76020 · doi:10.1098/rspa.1997.0089
[8] O. D. Makinde, “Irreversibility analysis of variable viscosity channel flow with convective cooling at the walls,” Canadian Journal of Physics, vol. 86, no. 2, pp. 383-389, 2008. · doi:10.1139/P07-126
[9] P. C. Bowes, Self-Heating: Evaluating and Controlling the Hazard, Elsevier, Amsterdam, The Netherlands, 1984.
[10] A. Bejan, Entropy Generation through Heat and Fluid Flow, chapter 5, John Wiley < Sons, Canada, 1994.
[11] B. Abu-Hijleh, “Natural convection and entropy generation from a cylinder with high conductivity fins,” Numerical Heat Transfer Part A, vol. 39, no. 4, pp. 405-432, 2001. · doi:10.1080/10407780151063197
[12] A. Bejan, Entropy Generation Minimization, CRC Press, Boca Raton, Fla, USA, 1996. · Zbl 0864.76001
[13] C. G. Carrington and Z. F. Sun, “Second law analysis of combined heat and mass transfer in internal and external flows,” International Journal of Heat and Fluid Flow, vol. 13, no. 1, pp. 65-70, 1992.
[14] G. Ibánez, S. Cuevas, and M. L. de Haro, “Minimization of entropy generation by asymmetric convective cooling,” International Journal of Heat and Mass Transfer, vol. 46, no. 8, pp. 1321-1328, 2003. · Zbl 1025.76545 · doi:10.1016/S0017-9310(02)00420-9
[15] O. D. Makinde, “Irreversibility analysis for a gravity driven non-Newtonian liquid film along an inclined isothermal plate,” Physica Scripta, vol. 74, no. 6, pp. 642-645, 2006. · Zbl 1339.76012 · doi:10.1088/0031-8949/74/6/007
[16] O. D. Makinde, “Hermite-Padé approximation approach to steady flow of a liquid film with adiabatic free surface along an inclined heat plate,” Physica A, vol. 381, no. 1-2, pp. 1-7, 2007. · doi:10.1016/j.physa.2007.03.001
[17] S. H. Tasnim and S. Mahmud, “Entropy generation in a vertical concentric channel with temperature dependent viscosity,” International Communications in Heat and Mass Transfer, vol. 29, no. 7, pp. 907-918, 2002. · doi:10.1016/S0735-1933(02)00411-6
[18] D. A. Frank Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics, Plenum Press, New York, NY, USA, 1969.
[19] http://maplesoft.com/products/maple/technical.aspx.
[20] M. M. Vainberg and V. A. Trenogin, Theory of the Branching of Solutions of Nonlinear Equations, Noordoff, Leyden, Mass, USA, 1974. · Zbl 0274.47033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.