Magneto-Nanofluid Dynamics in Convergent-Divergent Channel and its Inherent Irreversibility

Abstract:

The effects of Cu-nanoparticles on the entropy generation of steady magnetohydrodynamic incompressible flow with viscous dissipation and Joule heating through convergent-divergent channel are analysed in this paper. The basic nonlinear partial differential equations are transformed into a system of coupled ordinary differential equations using suitable transformations which are then solved using power series with Hermite- Padé approximation technique. The velocity profiles, temperature distributions, entropy generation rates, Bejan number as well as the rate of heat transfer at the wall are presented in convergent-divergent channels for various values of nanoparticles solid volume fraction, Eckert number, Reynolds number and channel angle. A stability analysis has been performed for the shear stress which signifies that the lower solution branch is stable and physically realizable, whereas the upper solution branch is unstable. It is interesting to remark that the entropy generation of the system increases at the two walls as well as the heat transfer irreversibility is dominant there whereas the fluid friction irreversibility is dominant along the centreline of the channel.

• Periodical: Defect and Diffusion Forum (Volume 377)
• Pages: 95-110
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.377.95
• Online since: September 2017
• Authors: Md. Sarwar Alam*, Md. Abdul Hakim Khan, Oluwole Daniel Makinde
• Keywords: Convergent-Divergent Channel, Hermite-Padé Approximation, Irreversibility Analysis, Magnetic Field, Nanofluid

References

[1] G.B. Jeffery, The two-dimensional steady motion of a viscous fluid, Phil. Mag., 6 (1915) 455-46.

[2] G. Hamel, Spiralförmige Bewgungen Zäher Flüssigkeiten, Jahresbericht der Deutschen Math. Vereinigung, 25 (1916) 34-60.

[3] L. Rosenhead, The steady two-dimensional radial flow of viscous fluid between two inclined plane walls, Proc. R. Soc. A, 175 (1940) 436-467.

DOI: 10.1098/rspa.1940.0068

[4] G. K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press: Cambridge, (1967).

[5] R. Sadri, Channel entrance flow, Ph.D. thesis, Dept. Mechanical Engineering, University of Western Ontario, (1997).

[6] M. Hamadiche, J. Scott, D. Jeandel, Temporal stability of Jeffery-Hamel flow, J. Fluid Mech., 268 (1994) 71-88.

DOI: 10.1017/s0022112094001266

[7] L. E. Fraenkel, Laminar flow in symmetrical channels with slightly curved walls. I: On the Jeffery-Hamel solutions for flow between plane walls, Proc. R. Soc. London, 267 (1962) 119 - 138.

DOI: 10.1098/rspa.1962.0087

[8] I. J. Sobey, P. G. Drazin, Bifurcations of two-dimensional channel flows, J. Fluid Mech., 171 (1986) 263-287.

DOI: 10.1017/s0022112086001441

[9] O. D. Makinde, Steady flow in a linearly diverging asymmetrical channel, Comp. Assist. Mech. and Eng. Sci., 4 (1997) 157 - 165.

[10] O. D. Makinde, P. Y. Mhone, Hermite-Pade' Approximation approach to Hydromagnetic flows in convergent-divergent channels, Appl. Math. and Comp., 181(2) (2006) 966 - 972.

DOI: 10.1016/j.amc.2006.02.018

[11] O. D. Makinde, P. Y. Mhone, Temporal stability of small disturbances in MHD Jeffery-Hamel flows, Comp. & Math. with Appl., 53 (2007) 128 - 136.

DOI: 10.1016/j.camwa.2006.06.014

[12] O. D. Makinde, Effect of arbitrary magnetic Reynolds number on MHD flows in convergent-divergent channels, Int. J. of Num. Meth. for Heat & Fluid Flow, 18(6) (2008) 697 - 707.

DOI: 10.1108/09615530810885524

[13] S. U. S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, In Proceedings of the 1995 ASME Int. Mech. Eng. Cong. and Exposition, 66, San Francisco, USA, (1995) 99-105.

[14] M. Sheikholeslami, D. D. Ganji, H. R. Ashorynejad, H. B. Rokni, Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method, Appl. Math. Mech. Engl. Ed, 33 (2012) 25-36.

DOI: 10.1007/s10483-012-1531-7

[15] A. Moradi, A. Alsaedi, T. Hayat, Investigation of heat transfer and viscous dissipation effects on the Jeffery-Hamel flow of nanofluids, Thermal Sci., 19(2) (2015) 563-578.

DOI: 10.2298/tsci120410208m

[16] G. S. Seth, M. K. Singh, Combined free and forced convection MHD flow in a rotating channel with perfectly conducting wall, Ind. J. Theo. Phys., 56 (2008) 203-222.

[17] T. M. Syed, U. Khan, N. Ahmed, W. Sikander, A study of Velocity and Temperature slip effects on flow of water based nanofluids in Converging and Diverging Channels, Int. J. Appl. Comp. Math, (2015) DOI 10. 1007/s40819-015-0032-z.

DOI: 10.1007/s40819-015-0032-z

[18] A. Bejan, Entropy-generation minimization, CRC Press, New York, (1996).

[19] A. Bejan, A study of entropy generation in fundamental convective heat transfer, J. Heat Trans., 101 (1979) 718-725.

DOI: 10.1115/1.3451063

[20] S. Das, S. Chakraborty, R. N. Jana, O. D. Makinde, Entropy analysis of unsteady magneto-nanofluid flow past accelerating stretching sheet with convective boundary condition, Appl. Math. and Mech., 36(12) (2005) 1593-1610.

DOI: 10.1007/s10483-015-2003-6

[21] H. Padé, Sur la représentation approchée d'une fonction pour des fractions rationnelles, Ann. Sci. École Norm. Sup. Suppl., 9 (1892) 1-93.

DOI: 10.24033/asens.378

[22] C. Hermite, Sur la généralisation des fractions continues algébriques, Annali. di. Math. Pura e Applicata, 21(2) (1893) 289-308.

DOI: 10.1007/bf02420446

[23] P.G. Drazin, Y. Tourigny, Numerically study of bifurcation by analytic continuation of a function defined by a power series, SIAM J. of Appl. Math., 56 (1996) 1-18.

DOI: 10.1137/s0036139994272436

[24] M.A.H. Khan, High-Order Differential Approximants, J. of Comp. and Appl. Math., 149 (2002) 457-468.

[25] M. M. Rahman, A New Approach to Partial Differential Approximants, M. Phil, Bangladesh University of Engineering & Technology, Dhaka, (2004).

[26] L.C. Woods, Thermodynamics of Fluid Systems, Oxford University Press, Oxford, UK, (1975).