Boundary Effect on the Onset of Marangoni Convection with Internal Heat Generation
The onset of Marangoni convection in a horizontal
fluid layer with internal heat generation overlying a solid layer
heated from below is studied. The upper free surface of a fluid is
nondeformable and the bottom boundary are rigid and no-slip. The
resulting eigenvalue problem is solved exactly. The critical values of
the Marangoni numbers for the onset of Marangoni convection are
calculated and the latter is found to be critically dependent on the
internal heating, depth ratio and conductivity ratio. The effects of the
thermal conductivity and the thickness of the solid plate on the onset
of convective instability with internal heating are studied in detail.
[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, 1977.
[6] H. Q. Yang, "Boundary effects on the B'enard-Marangoni instability," Int.
J. Heat Mass Transfer, vol. 35, pp 2413-2420, 1992.
[7] M. I. Char and C. C. Chen, "Influence of viscosity variation on the
stationary B'enard-Marangoni instability with a boundary slab of finite
conductivity," Acta Mechanica, vol. 135, pp 181-198, 1999.
[8] N. M. Arifin and I. Pop, "Stability of Marangoni Convection in a
composite Porous- Fluid with a boundary slab of finite conductivity,
(Accepted for publication)," Fluid Dynamics & Material Processing, to
be published.
[9] N. Z. Abidin, N. M. Arifin and M. S. M. Noorani, "Boundary effect on
Marangoni convection in a variable viscosity fluid layer, (Accepted for
publication)," J. Mathematics and Statistics, to be published.
[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, 1977.
[6] H. Q. Yang, "Boundary effects on the B'enard-Marangoni instability," Int.
J. Heat Mass Transfer, vol. 35, pp 2413-2420, 1992.
[7] M. I. Char and C. C. Chen, "Influence of viscosity variation on the
stationary B'enard-Marangoni instability with a boundary slab of finite
conductivity," Acta Mechanica, vol. 135, pp 181-198, 1999.
[8] N. M. Arifin and I. Pop, "Stability of Marangoni Convection in a
composite Porous- Fluid with a boundary slab of finite conductivity,
(Accepted for publication)," Fluid Dynamics & Material Processing, to
be published.
[9] N. Z. Abidin, N. M. Arifin and M. S. M. Noorani, "Boundary effect on
Marangoni convection in a variable viscosity fluid layer, (Accepted for
publication)," J. Mathematics and Statistics, to be published.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59322", author = "Norihan Md Arifin and Norfifah Bachok", title = "Boundary Effect on the Onset of Marangoni Convection with Internal Heat Generation", abstract = "The onset of Marangoni convection in a horizontal
fluid layer with internal heat generation overlying a solid layer
heated from below is studied. The upper free surface of a fluid is
nondeformable and the bottom boundary are rigid and no-slip. The
resulting eigenvalue problem is solved exactly. The critical values of
the Marangoni numbers for the onset of Marangoni convection are
calculated and the latter is found to be critically dependent on the
internal heating, depth ratio and conductivity ratio. The effects of the
thermal conductivity and the thickness of the solid plate on the onset
of convective instability with internal heating are studied in detail.", keywords = "Linear stability, Marangoni convection, Internal Heatgeneration.", volume = "2", number = "2", pages = "129-4", }