On Thermal Instabilities in a Viscoelastic Fluid Subject to Internal Heat Generation
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59508", author = "Donna M. G. Comissiong and Tyrone D. Dass and Harold Ramkissoon and Alana R. Sankar", title = "On Thermal Instabilities in a Viscoelastic Fluid Subject to Internal Heat Generation", 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.", volume = "5", number = "8", pages = "1361-8", }