Linear and Non-Linear Analysis of Rayleigh-Bénard Convection in a Micropolar Fluid Occupying Enclosures With Realistic Boundaries

Authors

DOI:

https://doi.org/10.26713/cma.v14i4.2578

Keywords:

Micropolar fluid, Rayleigh-Bénard convection, Enclosure, Realistic boundaries

Abstract

The linear and non-linear analysis of Rayleigh-Bénard convection (RBC) in a micropolar fluid (MPF) occupying enclosures are analyzed for realistic boundaries. The different enclosures considered are shallow enclosure \((h<b)\), square enclosure \((h=b)\) and tall enclosure \((h>b)\). Linear analysis is conducted to study the on-set-of-convection, using the Fourier series representation. The different boundaries taken into consideration are Free-Free (F-F), Rigid-Free (R-F) and Rigid-Rigid (R-R). Using the Fourier-series representation, the fourth order Lorenz model is derived to quantify the heat transport. The effect of various MPF parameters has been analyzed. The rate of heat transfer is calculated from average Nusselt number, \((\overline{\mathcal{N}u(t)})\).

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References

G. Ahmadi, Stability of a micropolar fluid layer heated from below, International Journal of Engineering Science 14(1) (1976), 81 – 89, DOI: 10.1016/0020-7225(76)90058-6.

S. P. Bhattacharyya and S. K. Jena, On the stability of a hot layer of micropolar fluid, International Journal of Engineering Science 21(9) (1983), 1019 – 1024, DOI: 10.1016/0020-7225(83)90043-5.

M. Corcione, Effects of the thermal boundary conditions at the sidewalls upon natural convection in rectangular enclosures heated from below and cooled from above, International Journal of Thermal Sciences 42(2) (2003), 199 – 208, DOI: 10.1016/S1290-0729(02)00019-4.

A. B. Datta and V. U. K. Sastry, Thermal instability of a horizontal layer of micropolar fluid heated from below, International Journal of Engineering Science 14(7) (1976), 631 – 637, DOI: 10.1016/0020-7225(76)90005-7.

M. C. D’Orazio, C. Cianfrini and M. Corcione, Rayleigh–Bénard convection in tall rectangular enclosures, International Journal of Thermal Sciences 43(2) (2004), 135 – 144, DOI: 10.1016/j.ijthermalsci.2003.05.002.

A. C. Eringen, Simple microfluids, International Journal of Engineering Science 2(2) (1964), 205 – 217, DOI: 10.1016/0020-7225(64)90005-9.

A. C. Eringen, Theory of micropolar fluids, Indiana University Mathematics Journal 16(1) (1966), 1 – 18, DOI: 10.1512/iumj.1967.16.16001.

A. Y. Gelfgat, Different modes of Rayleigh–Bénard instability in two- and three-dimensional rectangular enclosures, Journal of Computational Physics 156(2) (1999), 300 – 324, DOI: 10.1006/jcph.1999.6363.

A. E. Gill, The boundary-layer regime for convection in a rectangular cavity, Journal of Fluid Mechanics 26(3) (1966), 515 – 536, DOI: 10.1017/S0022112066001368.

C. Kanchana, O. P. Suthar and P. G. Siddheshwar, A study of Rayleigh-Bénard-Taylor convection in very-shallow, shallow, square and tall enclosures, International Journal of Applied and Computational Mathematics 6 (2020), Article number: 78, DOI: 10.1007/s40819-020-00833-2.

S. Kimura and A. Bejan, The boundary layer natural convection regime in a rectangular cavity with uniform heat flux from the side, ASME Journal of Heat and Mass Transfer 106(1) (1984), 98 – 103, DOI: 10.1115/1.3246666

S. A. Mikhailenko, I. V. Miroshnichenko and M. A. Sheremet, Thermal radiation and natural convection in a large-scale enclosure heated from below: Building application, Building Simulation 14 (2020), 681 – 691, DOI: 10.1007/s12273-020-0668-4.

S. Ostrach, Natural convection in enclosures, Advances in Heat Transfer 8 (1972), 161 – 227, DOI: 10.1016/S0065-2717(08)70039-X.

O. A. Olayemi, A.-F. Khaled, O. J. Temitope, O. O. Victor, C. B. Odetunde and I. K. Adegun, Parametric study of natural convection heat transfer from an inclined rectangular cylinder embedded in a square enclosuree, Australian Journal of Mechanical Engineering 21 (2) (2023), 668 – 681, DOI: 10.1080/14484846.2021.1913853.

L. E. Payne and B. Straughan, Order of convergence estimates on the interaction term for a micropolar fluid, International Journal of Engineering Science 27(7) (1989), 837 – 846, DOI: 10.1016/0020-7225(89)90049-9.

Y. Qin and P. N. Kaloni, A thermal instability problem in a rotating micropolar fluid, International Journal of Engineering Science 30(9) (1992), 1117 – 1126, DOI: 10.1016/0020-7225(92)90061-K.

K. V. R. Rao, Thermal instability in a micropolar fluid layer subject to a magnetic field, International Journal of Engineering Science 18(5) (1980), 741 – 750, DOI: 10.1016/0020-7225(80)90107-X.

P. R. M. Santos, A. Lugarini, S. L. M. Junqueira and A. T. Franco, Natural convection of a viscoplastic fluid in an enclosure filled with solid obstacles, International Journal of Thermal Sciences 166 (2021), 106991, DOI: 10.1016/j.ijthermalsci.2021.106991.

D. R. V. S. R. K. Sastry, N. N. Kumar, P. K. Kameswaran and S. Shaw, Unsteady 3D micropolar nanofluid flow through a squeezing channel: Application to cardiovascular disorders, Indian Journal of Physics 96 (2022), 57 – 70, DOI: 10.1007/s12648-020-01951-9.

P. G. Siddheshwar and C. Kanchana, Unicellular unsteady Rayleigh-Bénard convection in Newtonian liquids and Newtonian nanoliquids occupying enclosures: New findings, International Journal of Mechanical Sciences 131–132 (2017), 1061 – 1072, DOI: 10.1016/j.ijmecsci.2017.07.050.

P. G. Siddheshwar and S. Pranesh, Effect of temperature/gravity modulation on the onset of magneto-convection in weak electrically conducting fluids with internal angular momentum, Journal of Magnetism and Magnetic Materials 192(1) (1999), 159 – 176, DOI: 10.1016/S0304-8853(98)00384-9.

P. G. Siddheshwar and S. Pranesh, Magnetoconvection in a micropolar fluid, International Journal of Engineering Science 36(10) (1998), 1173 – 1181, DOI: 10.1016/S0020-7225(98)00013-5.

P. G. Siddheshwar and C. Siddabasappa, Unsteady natural convection in a liquid-saturated porous enclosure with local thermal non-equilibrium effect, Meccanica 55 (2020), 1763 – 1780, DOI: 10.1007/s11012-020-01198-y.

P. G. Siddheshwar and T. S. Sushma, Reduction of a tri-modal Lorenz model of ferrofluid convection to a cubic-quintic Ginzburg-Landau equation using the center manifold theorem, Differential Equations and Dynamical Systems 2021 (2021), 1 – 19, DOI: 10.1007/s12591-021-00565-9.

O. V. Trevisan and A. Bejan, Combined heat and mass transfer by natural convection in a vertical enclosure, ASME Journal of Heat and Mass Transfer 109(1) (1987), 104 – 112, DOI: 10.1115/1.3248027.

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Published

25-12-2023
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How to Cite

Jestine, S., & Pranesh, S. (2023). Linear and Non-Linear Analysis of Rayleigh-Bénard Convection in a Micropolar Fluid Occupying Enclosures With Realistic Boundaries. Communications in Mathematics and Applications, 14(4), 1405–1419. https://doi.org/10.26713/cma.v14i4.2578

Issue

Vol. 14 No. 4 (2023)

Section

Research Article

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