Non-linear Convection in Couple Stress Fluid with Non-classical Heat Conduction Under Magnetic Field Modulation

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Computational Sciences - Modelling, Computing and Soft Computing (CSMCS 2020)

Abstract

A theoretical examination of thermal convection for a couple stress fluid which is electrically conducting and possessing significant thermal relaxation time is explored under time dependent magnetic field. Fourier’s law fails for a diverse area of applications such as fluids subjected to rapid heating, strongly confined fluid and nano-devices and hence a non-classical heat conduction law is employed. The heat transport in the system is examined and quantified employing the Lorenz model. The Nusselt number is deduced to quantitate the transfer of heat.

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References

  1. Bhadauria, B.S., Kiran, P.: Weak nonlinear analysis of magneto-convection under magnetic field modulation. Phys. Scr. 89, 095209 (2014)

    Article  Google Scholar 

  2. Cattaneo, C.: Sulla condizione del calore. Atti Del Semin. Matem. E Fis. Della Univ. Modena. 3, 83–101 (1948)

    Google Scholar 

  3. Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford (1961)

    MATH  Google Scholar 

  4. Christov, C.I.: On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction. Mech. Res. Commun. 36, 481–486 (2009)

    Article  MathSciNet  Google Scholar 

  5. Cokelet, G.R.: Biomechanics, Its Foundation and Objectives. Prentice-Hall, Hoboken (1963)

    Google Scholar 

  6. Goldsmith, H.L., Skalak, R.: Hemodynamics. Annu. Rev. Fluid Mech. 7, 231–247 (1975)

    Article  Google Scholar 

  7. Kiran, P., Bhadauria, B.S., Narasimhulu, Y.: Oscillatory magneto-convection under magnetic field modulation. Alexandria Eng. J. 57, 445–453 (2018)

    Article  Google Scholar 

  8. Kumar, A., Vanita, Gupta, V.K.: Study of heat and mass transport in couple-Stress liquid under g-jitter effect. Ain Shams Eng. J. Online 9(4), 973–984 (2016)

    Google Scholar 

  9. Maxwell, J.C.: On the dynamical theory of gases. Phil. Trans. Royal Soc. 157, 49–88 (1867)

    Article  Google Scholar 

  10. Pranesh, S., George, S.: Effect of magnetic field on the onset of Rayleigh- Bénard convection in Boussinesq-Stokes Suspensions with time periodic boundary temperatures. Int. J. Appl. Math. Mech. 6(16), 38–55 (2010)

    Google Scholar 

  11. Pranesh, S., Kiran, R.V.: Study of Rayleigh-Bénard magneto convection in a micropolar fluid with Maxwell-Cattaneo law. Appl. Math. 1, 470–480 (2010)

    Article  Google Scholar 

  12. Ramesh, K.: Effects of slip and convective conditions on the peristaltic flow of couple stress fluid in an asymmetric channel through porous medium. Comput. Methods Programs Biomed. 135, 1–14 (2016)

    Article  Google Scholar 

  13. Siddheshwar, P.G., Pranesh, S.: An analytical study of linear and non-linear convection in Boussinesq-Stokes suspensions. Int. J. Non-Linear Mech. 39(1), 165–172 (2004)

    Article  Google Scholar 

  14. Stokes, V.K.: Couple stresses in fluids. Phys. Fluids 9(9), 1709–1715 (1966)

    Article  Google Scholar 

  15. Stranges, D.F., Khayat, R.E., Albaalbaki, B.: Thermal convection of non-Fourier fluids. Linear Stability. Int. J. Therm. Sci. 74, 14–23 (2013)

    Article  Google Scholar 

  16. Stranges, D.F., Khayat, R.E., Debruyn, J.: Finite thermal convection of non-Fourier fluids. Int. J. Therm. Sci. 104, 437–447 (2016)

    Article  Google Scholar 

  17. Straughan, B.: Porous convection with Cattaneo heat flux. Int. J. Heat Mass Transf. 53, 2808–2812 (2010)

    Article  Google Scholar 

  18. Straughan, B.: Thermal convection with the Cattaneo-Christov model. Int. J. Heat Mass Transf. 53, 95–98 (2010)

    Article  Google Scholar 

  19. Straughan, B., Franchi, F.: Bénard convection and the Cattaneo law of heat conduction. Proc. Royal Soc. Edinburgh 96A, 175–178 (1984)

    Article  Google Scholar 

  20. Venezian, G.: Effect of modulation on the onset of thermal convection. J. Fluid Mech. 35(2), 243–254 (1969)

    Article  Google Scholar 

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Correspondence to Maria Thomas .

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Thomas, M., George, K.S., Pranesh, S. (2021). Non-linear Convection in Couple Stress Fluid with Non-classical Heat Conduction Under Magnetic Field Modulation. In: Awasthi, A., John, S.J., Panda, S. (eds) Computational Sciences - Modelling, Computing and Soft Computing. CSMCS 2020. Communications in Computer and Information Science, vol 1345. Springer, Singapore. https://doi.org/10.1007/978-981-16-4772-7_18

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  • DOI: https://doi.org/10.1007/978-981-16-4772-7_18

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