On Thermal Instabilities in a Viscoelastic Fluid Subject to Internal Heat Generation

Authors: Donna M. G. Comissiong, Tyrone D. Dass, Harold Ramkissoon, Alana R. Sankar

Abstract:

The B'enard-Marangoni thermal instability problem for a viscoelastic Jeffreys- fluid layer with internal heat generation is investigated. The fluid layer is bounded above by a realistic free deformable surface and by a plane surface below. Our analysis shows that while the internal heat generation and the relaxation time both destabilize the fluid layer, its stability may be enhanced by an increased retardation time.

Keywords: Viscoelastic fluid, Jeffreys' model, Maxwell model, internal heat generation, retardation time, relaxation time.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1075264

References:

[1] H. Benard. Les tourbillons cellularies dans une nappe liquid. Revus Generale Des Sciences Pures Et Appliqus, 11:1261-1271, 1900.
[2] Lord Rayleigh. On the convection currents in a horizontal layer of fluid when the higher temperature is on the underside. Phil. Mag., 32:529- 546, 1916.
[3] J. R. A. Pearson. On convection cells induced by surface tension. J. Fluid Mech., 4:489-500, 1958.
[4] D. A. Nield. Surface tension and buoyancy effects in cellular convection. J. Fluid Mech., 19:341-352, 1964.
[5] R. D. Benguria and M. C. Depassier. On the linear stability theory of bnard-marangoni convection. Phys. Fluids A1, 7:1123-1127, 1989.
[6] C. Perez-Garcia and G. Carneiro. Linear stability analysis of bnardmarangoni convection in fluids with a deformable surface. Phys. Fluids A3, 2:292-298, 1991.
[7] H. Ramkissoon, G. Ramdath, D. M. G. Comissiong, and K. Rahaman. On thermal instabilities in a viscoelastic fluid. J. Non-Linear Mech., 41:18-25, 2006.
[8] E. M. R. Sparrow, R. J. Goldstein, and V. K. Johnson. Thermal instability on a horizontal fluid layer: Effect of boundary conditions and non-linear temperature profile. J. Fluid Mech., 18:513-529, 1964.
[9] P. H. Roberts. Convection in horizontal layers with internal heat generation: Theory. J. Fluid Mech., 30:33-49, 1967.
[10] P. D. Gasser and M. S. Kazimi. Onset of convection in a porous medium with internal heat generation. J. Heat Transfer, 98:49-54, 1976.
[11] M. Kaviany. Thermal convection instabilities in a porous medium. J. Heat Transfer, 106:137-142, 1984.
[12] M. Char and K. Chiang. Stability analysis of benard-marangoni convection in fluids with internal heat generation. J. of Physics D: Applied Physics, 27:748-755, 1994.
[13] M. Char, K. Chiang, and J. Jou. Oscillatory instability analysis of benard-marangoni convection in a rotating fluid with internal heat generation. Int. J. Heat Mass Transfer, 40:857-867, 1997.
[14] I. Hashim, H. Othman, and S. A. Kechil. Stabilization of thermocapillary instability in a fluid layer with internal heat source. Int. Comm. Heat Mass Transfer, 36(2):161-165, 2009.
[15] C. E. Nanjundappa, I. S. Shivakumara, J. Lee, and M. Ravisha. Effect of internal heat generation on the onset of brinkman-benard convection in a ferrofluid saturated porous layer. Int. J. of Thermal Sci., 50(2):160-168, 2011.
[16] K. Abdul, A. Mohammed, and S. Sharidan. Free convection boundary layer flow of a viscoelastic fluid in the presence of heat generation. World Academy of Sci. Engng. and Tech., 75:492-499, 2011.