Effect of Gravity Modulation on Single Component Convection in a Couple Stress Fluid with Maxwell-Cattaneo Law

  • Authors

    • Maria Thomas
    • Sangeetha George K
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.21306
  • Couple stress fluid, Gravity modulation, Maxwell-Cattaneo law, Rayleigh-Bénard convection,

  • Abstract

    The outset of convection in a thin layer of couple stress fluid is analyzed using the linear stability analysis when the fluid is heated from below. In order to assimilate the inertial effects Maxwell-Cattaneo law is used in lieu of the classical Fourier's heat conduction law. The normal mode analysis is used to arrive at the eigenvalues of the perturbed state and a regular perturbation method to find the analytical solutions. The effect of Cattaneo number, couple stress parameter and Prandtl number is discussed and it is concluded that gravity modulation can delay or advance the onset of convection.

     

     

  • References

    1. [1] Bhadauria BS, Siddheshwar PG, Singh AK & Vinod K. Gupta (2016), A local nonlinear stability analysis of modulated double diffusive stationary convection in a couple stress liquid. J. Appl. Fluid Mech. 9(3), 1255-1264.

      [2] Bissell JJ (2015), On oscillatory convection with the Cattaneo-Christov hyperbolic heat-flow model. Proc. R. Soc. A Math. Phys. Eng. Sci 471(2175), 20140845.

      [3] Cattaneo C (1948), Sulla conduzione del calore. Atti Sem. Mat. Fis. Univ. Modena 3, 83–101.

      [4] Jou D, Casas-Vázquez J & Lebon G (2010), Extended Irreversible Thermodynamics, fourth ed., Springer.

      [5] Kiran P (2016), Throughflow and gravity modulation effects on heat transport in a porous medium. J. Appl. Fluid Mech. 9(3), 1105-1113.

      [6] Malashetty MS & Swamy MS (2011), Effect of gravity modulation on the onset of thermal convection in rotating fluid and porous layer. Phys. Fluids 23, 064108.

      [7] Pranesh S & Sangeetha George (2014), Effect of imposed time periodic boundary temperature on the onset of Rayleigh-Bénard convection in a dielectric couple stress fluid. Int. J. Appl. Math. Comput. J. 5(4), 1-13.

      [8] Shivakumara IS & Kumar SN (2014), Linear and weakly nonlinear triple diffusive convection in a couple stress fluid layer. Int. J. Heat Mass Transf. 68, 542-553.

      [9] Stokes VK (1966), Couple stresses in fluids. Phys Fluids 9(9), 1709-1715.

      [10] Straughan B (2010), Thermal convection with the Cattaneo-Christov model. Int. J. Heat Mass Transf. 53(1-3), 95-98.

      [11] Suresh VA, Christov CI & Homsy GM (1999), Resonant thermocapillary and buoyant flows with finite frequency gravity modulation. Phys. Fluids 11(9), 2565–2576.

  • Downloads

  • How to Cite

    Thomas, M., & George K, S. (2018). Effect of Gravity Modulation on Single Component Convection in a Couple Stress Fluid with Maxwell-Cattaneo Law. International Journal of Engineering & Technology, 7(4.10), 657-660. https://doi.org/10.14419/ijet.v7i4.10.21306

    Received date: 2018-10-08

    Accepted date: 2018-10-08

    Published date: 2018-10-02