Surface deformation on thermocapillary convection in a binary fluid with internal heat generation and temperature dependent viscosity

  • Authors

    • Nurul Hafizah Zainal Abidin
    • Nor Fadzillah Mohd Mokhtar
    • Nur Zarifah Abdul Hamid
    • Zanariah Abdul Majid
    2018-04-06
    https://doi.org/10.14419/ijet.v7i2.15.11220
  • Binary Fluid, Convection, Internal Heat Generation, Surface Deformation, Temperature Dependent Viscosity.

  • Abstract

    The effects of temperature dependent viscosity and internal heat generation on the onset of steady Bénard-Marangoni convection in a horizontal binary fluid layer heated from below is investigated theoretically. The upper free surface is assumed to be deformable and the lower boundary is considered to be rigid and perfectly insulated to temperature perturbations. The asymptotic solution of the long wavelength is obtained using regular perturbation method with wave number as a perturbation parameter. It is found that the surface deformation of a binary fluid layer enhances the onset of thermocapillary convection while increasing the value of internal heat generation and temperature dependent viscosity will destabilize the binary fluid layer system.

     

  • References

    1. [1] Nield DA (1964), Surface tension and buoyancy effects in cellular convection. Journal of Fluid Mechanics 19, 3, 341-352.

      [2] Davis SH & Homsy GM (1980), Energy stability theory for free-surface problems: buoyancy-thermocapillary layers. Journal of Fluid Mechanics 98, 3, 527-553.

      [3] Nield DA (1967), The thermohaline Rayleigh-Jeffreys problem. Journal of Fluid Mechanics 29, 3, 545-558.

      [4] Machrafi H, Rednikov A, Colinet P & Dauby PC (2010), Bénard instabilities in a binary-liquid layer evaporating into an inert gas. Journal of colloid and interface science 349, 1, 331-353.

      [5] Bergeon A, Henry D, Benhadid H & Tuckerman LS (1998). Marangoni convection in binary mixtures with Soret effect. Journal of Fluid Mechanics 375,143-177.

      [6] Podolny A, Nepomnyashchy AA & Oron A (2008), Long-Wave Coupled Marangoni - Rayleigh Instability in a Binary Liquid Layer in the Presence of the Soret Effect. Math. Model. Nat. Phenom. 3, 1, 1-26.

      [7] Slavtchev S, Simeonov G, Van Vaerenbergh S & Legros JC. (1999), Technical Note Marangoni instability of a layer of binary liquid in the presence of nonlinear Soret effect. International Journal of Heat and Mass Transfer 42, 15, 3007-3011.

      [8] Saravanan S & Sivakumar T (2009), Exact solution of Marangoni convection in a binary fluid with throughflow and Soret effect. Applied Mathematical Modelling. 33, 9, 3674-3681.

      [9] Stengel KC, Oliver DS & Booker JR (1982), Onset of convection in a variable-viscosity fluid. Journal of Fluid Mechanics 120, 411-431.

      [10] Palm E (1960). On the tendency towards hexagonal cells in steady convection. Journal of Fluid Mechanics 8, 2, 183-192.

      [11] Capone F & Gentile M (1994), Nonlinear stability analysis of convection for fluids with exponentially temperature-dependent viscosity. Acta Mechanica 107,1-4, 53-64.

      [12] Char MI & Chen CC (1999), Influence of viscosity variation on the stationary Benard-Marangoni instability with a boundary slab of finite conductivity. Acta Mechanica 135, 3, 181-198.

      [13] Nanjundappa CE, Shivakumara IS & Arunkumar R (2013), Onset of Marangoni-Bénard ferroconvection with temperature dependent viscosity. Microgravity Science and Technology 25: 1-10.

      [14] Torrance KE & Turcotte DL (1971), Thermal convection with large viscosity variations. Journal of Fluid Mechanics 47, 1, 113-125

      [15] Cloot A & Lebon G (1985), Marangoni instability in a fluid layer with variable viscosity and free interface, in microgravity. PhysicoChemical Hydrodynamics 6, 453-462.

      [16] Kozhoukharova Z & Rozé C (1999), Influence of the surface deformability and variable viscosity on buoyant-thermocapillary instability in a liquid layer. The European Physical Journal B-Condensed Matter and Complex Systems 8, 1, 125-135.

      [17] Char MI & Chiang KT (1994), Stability analysis of Benard-Marangoni convection in fluids with internal heat generation. Journal of Physics D: Applied Physics 27, 4 , 748.

      [18] Nanjundappa, C. E., Shivakumara, I. S. & Arunkumar, R. (2011), Onset of Bénard-Marangoni ferroconvection with internal heat generation. Microgravity Science and Technology 23, 1, 29-39.

      [19] Mokhtar, N. F. M. & Uddin, J. (2015), Influence of internal heat source on double-diffusive soret induced convection in a binary fluid. Research and Education in Mathematics (ICREM7) 2015 International Conference on. IEEE, 88-92.

  • Downloads

  • How to Cite

    Hafizah Zainal Abidin, N., Fadzillah Mohd Mokhtar, N., Zarifah Abdul Hamid, N., & Abdul Majid, Z. (2018). Surface deformation on thermocapillary convection in a binary fluid with internal heat generation and temperature dependent viscosity. International Journal of Engineering & Technology, 7(2.15), 86-89. https://doi.org/10.14419/ijet.v7i2.15.11220

    Received date: 2018-04-06

    Accepted date: 2018-04-06

    Published date: 2018-04-06