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Rayleigh-Bѐnard Convection in a Second-Order Fluid with Maxwell-Cattaneo Law

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Abstract:

The objective of the paper is to study the Rayleigh-Bѐnard convection in second order fluid by replacing the classical Fourier heat law by non-classical Maxwell-Cattaneo law using Galerkin technique. The eigen value of the problem is obtained using the general boundary conditions on velocity and third type of boundary conditions on temperature. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. The classical Fourier flux law over predicts the critical Rayleigh number compared to that predicted by the non-classical law. The present non-classical Maxwell-Cattaneo heat flux law involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigen values are less than the classical ones. Over stability is the preferred mode of convection.

Info:

Periodical:
The Bulletin of Society for Mathematical Services and Standards (Volume 2)
Pages:
24-32
Citation:
S. S. Nagouda and S. Pranesh, "Rayleigh-Bѐnard Convection in a Second-Order Fluid with Maxwell-Cattaneo Law", The Bulletin of Society for Mathematical Services and Standards, Vol. 2, pp. 24-32, 2012
Online since:
June 2012
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References:

[1] Coleman B. D, Noll W., 1960, An Approximation Theorem For Functionals With Applications In Continuum Mechanics, Arch. Rational Mech. Anal., Vol. 6, p.355.

DOI: https://doi.org/10.1007/bf00276168

[2] Kaloni P. N., 1989, Some Remarks On Useful Theorems For Second-Order Fluids, J. Non-Newt. Fluid Mech., Vol. 31, p.115.

[3] Siddheshwar. P. G. and Srikrishna, C. V. (2002) Unsteady non-linear convection in a second order fluid, Int. J. Non-linear Mech., Vol. 37, p.321.

DOI: https://doi.org/10.1016/s0020-7462(00)00119-0

[4] Siddeshwar. P. G, Sekhar G. N, Jayalatha G. (2010) , Effect of time period vertical oscillations of the Rayleigh- Bѐnard system on non-linear convection in viscoelastic liquids, J. Non Newtonian fluid Mech., Vol. 165, p.1412.

DOI: https://doi.org/10.1016/j.jnnfm.2010.07.008

[5] Sekhar G. N , Jayalatha G. (2010), Elastic effect on Rayleigh Bѐnardin liquid in temperature dependent viscocity, Int. Journal of thermal sciences, Vol. 49, p.67.

[6] Lindsay K. A. and Straughan, B. (1978) Acceleration waves and second sound in a perfect fluid, Arch. Rational Mech. Anal. Vol. 68, 53.

DOI: https://doi.org/10.1007/bf00276179

[7] Straughan B. and Franchi F. (1984) Benard convection and the Cattaneo law of heat conduction, Proc. of Roy. Soc. Of Edi. Vol. 96A, 175.

[8] Lebon G. and Cloot A. (1984) Benard-Marangoni instability in a Maxwell-Cattaneo fluid, Phy. Let. Vol 105 A, 361.

DOI: https://doi.org/10.1016/0375-9601(84)90281-0

[9] Siddheshwar P. G. (1999) Rayleigh Benard convection in a second order Ferromagnetic fluid with second sound,. Proc. VIII Asian Cong., Fluid Mech. China, Dec. 6-10, 631.

[10] Siddheshwar P. G. and Pranesh S. (1998) Effects of a Non-Uniform Basic Temperature Gradient on Rayleigh-Bénard Convection in a Micropolar Fluid, International Journal of Engineering Science, Vol. 36, No. 11, September, p.1183.

DOI: https://doi.org/10.1016/s0020-7225(98)00015-9

[11] Pranesh S. and Kiran R. V. (2010), Study of Rayleigh-Bѐnard Magneto convection in a micropolar fluid with Maxwell Cattaneo law, Applied Mathematics, Vol. 1, p.470.

DOI: https://doi.org/10.4236/am.2010.16062
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