Marangoni Convection in a Fluid Layer with Internal Heat Generation
In this paper we use classical linear stability theory
to investigate the effects of uniform internal heat generation on the
onset of Marangoni convection in a horizontal layer of fluid heated
from below. We use a analytical technique to obtain the close form
analytical expression for the onset of Marangoni convection when
the lower boundary is conducting with free-slip condition. We show
that the effect of increasing the internal heat generation is always to
destabilize the layer.
[1] J. R. A.Pearson, "On convection cells induce by surface tension," J. Fluid
Mech., vol. 4, pp 489-500, 1958.
[2] E. M. Sparrow, R .J Goldstein and V. K. Jonsson, "Thermal stability
in a horizontal fluid layer: effect of boundary conditions and non-linear
temperature," J. Fluid Mech., vol. 18, pp 513-529,1964.
[3] P. H. Roberts, "Convection in horizontal layers with internal heat generation:
Theory," J. Fluid Mech., vol. 30, pp 33 -49, 1967.
[4] M. I. Char and K. T. Chiang, "Stability analysis of B'enard-Marangoni
convection in fluids with internal heat generation," J. Phys. D:Appl.
Phys., vol. 27, pp 748 -755, 1994.
[5] S. K. Wilson, "The effect of uniform internal heat generation on the onset
of steady Marangoni convection in a horizontal layer of fluid," Acta
Mechanica, vol. 124, pp 63 -78, 1997.
[6] N. M. Arifin and N. Bachok, "Boundary effect on the Onset of Marangoni
Convection with Internal Heat Generation," International Journal of
Mathematical, Physical and Engineering Sciences, vol. 2, pp 131-134,
2008.
[7] N. M. Arifin and N. Bachok, "Effects of Control on the Onset of
Marangoni-Bnard convection with Uniform Internal Heat Generation,"
Matematika, vol. 24, pp 23-29. 2008.
[8] Boeck, T., & Thess, A., Inertial B'enard-Marangoni convection, Journal
of Fluid Mechanics, vol. 350, pp 149-175, 1997.
[1] J. R. A.Pearson, "On convection cells induce by surface tension," J. Fluid
Mech., vol. 4, pp 489-500, 1958.
[2] E. M. Sparrow, R .J Goldstein and V. K. Jonsson, "Thermal stability
in a horizontal fluid layer: effect of boundary conditions and non-linear
temperature," J. Fluid Mech., vol. 18, pp 513-529,1964.
[3] P. H. Roberts, "Convection in horizontal layers with internal heat generation:
Theory," J. Fluid Mech., vol. 30, pp 33 -49, 1967.
[4] M. I. Char and K. T. Chiang, "Stability analysis of B'enard-Marangoni
convection in fluids with internal heat generation," J. Phys. D:Appl.
Phys., vol. 27, pp 748 -755, 1994.
[5] S. K. Wilson, "The effect of uniform internal heat generation on the onset
of steady Marangoni convection in a horizontal layer of fluid," Acta
Mechanica, vol. 124, pp 63 -78, 1997.
[6] N. M. Arifin and N. Bachok, "Boundary effect on the Onset of Marangoni
Convection with Internal Heat Generation," International Journal of
Mathematical, Physical and Engineering Sciences, vol. 2, pp 131-134,
2008.
[7] N. M. Arifin and N. Bachok, "Effects of Control on the Onset of
Marangoni-Bnard convection with Uniform Internal Heat Generation,"
Matematika, vol. 24, pp 23-29. 2008.
[8] Boeck, T., & Thess, A., Inertial B'enard-Marangoni convection, Journal
of Fluid Mechanics, vol. 350, pp 149-175, 1997.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:58673", author = "Norfifah Bachok and Norihan Md. Arifin", title = "Marangoni Convection in a Fluid Layer with Internal Heat Generation", abstract = "In this paper we use classical linear stability theory
to investigate the effects of uniform internal heat generation on the
onset of Marangoni convection in a horizontal layer of fluid heated
from below. We use a analytical technique to obtain the close form
analytical expression for the onset of Marangoni convection when
the lower boundary is conducting with free-slip condition. We show
that the effect of increasing the internal heat generation is always to
destabilize the layer.", keywords = "Marangoni convection, heat generation, free-slip", volume = "2", number = "10", pages = "731-3", }