Volume 9, Issue 2 (February 2022), Pages: 167-172
----------------------------------------------
Original Research Paper
Title: Rayleigh-Benard convection in a binary fluid-saturated anisotropic porous layer with variable viscosity effect
Author(s): Nurul Hafizah Zainal Abidin 1, *, Norfadzillah Mohd Mokhtar 2, Izzati Khalidah Khalid 1, Norazam Arbin 1, Roslah Arsad 1
Affiliation(s):
1Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Shah Alam, Malaysia
2Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, Seri Kembangan, Malaysia
Full Text - PDF XML
* Corresponding Author.
Corresponding author's ORCID profile: https://orcid.org/0000-0003-4965-7444
Digital Object Identifier:
https://doi.org/10.21833/ijaas.2022.02.019
Abstract:
Rayleigh-Benard convection due to buoyancy that occurred in a horizontal binary fluid layer saturated anisotropic porous media is investigated numerically. The system is heated from below and cooled from above. The temperature-dependent viscosity effect was applied to the double-diffusive binary fluid and the critical Rayleigh number for free-free, rigid-free, and rigid-rigid representing the lower-upper boundary were obtained by using the single-term Galerkin expansion procedure. Both boundaries are conducted to temperature. The effect of temperature-dependent viscosity, mechanical anisotropy, thermal anisotropy, Soret, and Dufour parameters on the onset of stationary convection are discussed and shown graphically.
© 2022 The Authors. Published by IASE.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Binary fluid, Double diffusive, Galerkin technique, Stationary mode, Temperature-dependent viscosity
Article History: Received 10 September 2021, Received in revised form 25 November 2021, Accepted 26 December 2021
Acknowledgment
No Acknowledgment.
Compliance with ethical standards
Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Citation:
Abidin NHZ, Mokhtar NM, and Khalid IK et al. (2022). Rayleigh-Benard convection in a binary fluid-saturated anisotropic porous layer with variable viscosity effect. International Journal of Advanced and Applied Sciences, 9(2): 167-172
Permanent Link to this page
Figures
Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5
Tables
Table 1 Table 2
----------------------------------------------
References (27)
- Abidin NHZ, Mokhtar NFM, Suardi MSZ, Majid ZA, and Abd Ghani SS (2017). Magnetoconvection in a Soret driven binary fluid mixture induced by temperature dependent viscosity. Journal of Engineering and Applied Sciences, 12(3): 494-500. [Google Scholar]
- Arifin NM and Abidin NHZ (2009). Marangoni convection in a variable viscosity fluid layer with feedback control. Journal of Applied Computer Science and Mathematics, 3: 373-382. [Google Scholar]
- Bergeon A, Henry D, Benhadid H, and Tuckerman LS (1998). Marangoni convection in binary mixtures with Soret effect. Journal of Fluid Mechanics, 375: 143-177. https://doi.org/10.1017/S0022112098002614 [Google Scholar]
- Griffiths RW (1986). Thermals in extremely viscous fluids, including the effects of temperature-dependent viscosity. Journal of Fluid Mechanics, 166: 115-138. https://doi.org/10.1017/S002211208600006X [Google Scholar]
- Hirata SC, Goyeau B, and Gobin D (2012). Onset of convective instabilities in under-ice melt ponds. Physical Review E, 85(6): 066306. https://doi.org/10.1103/PhysRevE.85.066306 [Google Scholar] PMid:23005205
- Horton CW and Rogers FT (1945). Convection currents in a porous medium. Journal of Applied Physics, 16(6): 367-370. https://doi.org/10.1063/1.1707601 [Google Scholar]
- Hurle DTJ and Jakeman E (1971). Soret-driven thermosolutal convection. Journal of Fluid Mechanics, 47(4): 667-687. https://doi.org/10.1017/S0022112071001319 [Google Scholar]
- Kozhoukharova Z and Rozé C (1999). Influence of the surface deformability and variable viscosity on buoyant-thermocapillary instability in a liquid layer. The European Physical Journal B-Condensed Matter and Complex Systems, 8(1): 125-135. https://doi.org/10.1007/s100510050674 [Google Scholar]
- Lam TT and Bayazitoglu Y (1987). Effects of internal heat generation and variable viscosity on Marangoni convection. Numerical Heat Transfer, Part A Applications, 11(2): 165-182. https://doi.org/10.1080/10407788708913548 [Google Scholar]
- Lapwood E (1948). Convection of a fluid in a porous medium. In the Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, Cambridge, UK, 44: 508-521. https://doi.org/10.1017/S030500410002452X [Google Scholar]
- Malashetty MS and Swamy M (2010). The onset of convection in a binary fluid saturated anisotropic porous layer. International Journal of Thermal Sciences, 49(6): 867-878. https://doi.org/10.1016/j.ijthermalsci.2009.12.008 [Google Scholar]
- Morrison HL, Rogers FT, and Horton CW (1949). Convection currents in porous media: II. Observation of conditions at onset of convection. Journal of Applied Physics, 20(11): 1027-1029. https://doi.org/10.1063/1.1698267 [Google Scholar]
- Nanjundappa CE, Shivakumara IS, and Arunkumar R (2013). Onset of Marangoni-Bénard ferroconvection with temperature dependent viscosity. Microgravity Science and Technology, 25(2): 103-112. https://doi.org/10.1007/s12217-012-9330-9 [Google Scholar]
- Nield DA (1968). Onset of thermohaline convection in a porous medium. Water Resources Research, 4(3): 553-560. https://doi.org/10.1029/WR004i003p00553 [Google Scholar]
- Nield DA and Bejan A (2006). Convection in porous media. Volume 3, Springer, New York, USA. [Google Scholar]
- Nield DA and Kuznetsov AV (2011). The onset of double-diffusive convection in a nanofluid layer. International Journal of Heat and Fluid Flow, 32(4): 771-776. https://doi.org/10.1016/j.ijheatfluidflow.2011.03.010 [Google Scholar]
- Prats M (1966). The effect of horizontal fluid flow on thermally induced convection currents in porous mediums. Journal of Geophysical Research, 71(20): 4835-4838. https://doi.org/10.1029/JZ071i020p04835 [Google Scholar]
- Ramirez NE and Saez AE (1990). The effect of variable viscosity on boundary-layer heat transfer in a porous medium. International Communications in Heat and Mass Transfer, 17(4): 477-488. https://doi.org/10.1016/0735-1933(90)90066-S [Google Scholar]
- Saravanan S and Sivakumar T (2009). Exact solution of Marangoni convection in a binary fluid with throughflow and Soret effect. Applied Mathematical Modelling, 33(9): 3674-3681. https://doi.org/10.1016/j.apm.2008.12.017 [Google Scholar]
- Shivakumara IS, Lee J, Ravisha M, and Reddy RG (2011). Effects of MFD viscosity and LTNE on the onset of ferromagnetic convection in a porous medium. International Journal of Heat and Mass Transfer, 54(11-12): 2630-2641. https://doi.org/10.1016/j.ijheatmasstransfer.2011.01.022 [Google Scholar]
- Slavtchev S, Simeonov G, Van Vaerenbergh S, and Legros JC (1999). Technical note Marangoni instability of a layer of binary liquid in the presence of nonlinear Soret effect. International Journal of Heat and Mass Transfer, 42(15): 3007-3011. https://doi.org/10.1016/S0017-9310(98)00353-6 [Google Scholar]
- Stengel KC, Oliver DS, and Booker JR (1982). Onset of convection in a variable-viscosity fluid. Journal of Fluid Mechanics, 120: 411-431. https://doi.org/10.1017/S0022112082002821 [Google Scholar]
- Storesletten L (1993). Natural convection in a horizontal porous layer with anisotropic thermal diffusivity. Transport in Porous Media, 12(1): 19-29. https://doi.org/10.1007/BF00616359 [Google Scholar]
- Torrance KE and Turcotte DL (1971). Thermal convection with large viscosity variations. Journal of Fluid Mechanics, 47(1): 113-125. https://doi.org/10.1017/S002211207100096X [Google Scholar]
- Tyvand PA and Storesletten L (1991). Onset of convection in an anisotropic porous medium with oblique principal axes. Journal of Fluid Mechanics, 226: 371-382. https://doi.org/10.1017/S0022112091002422 [Google Scholar]
- Yadav D, Agrawal GS, and Bhargava R (2013). Onset of double-diffusive nanofluid convection in a layer of saturated porous medium with thermal conductivity and viscosity variation. Journal of Porous Media, 16(2): 105-121. https://doi.org/10.1615/JPorMedia.v16.i2.30 [Google Scholar]
- Yadav R, Balaji C, and Venkateshan SP (2017). Implementation of SLW model in the radiative heat transfer problems with particles and high temperature gradients. International Journal of Numerical Methods for Heat and Fluid Flow, 27(5): 1128-1141. https://doi.org/10.1108/HFF-03-2016-0095 [Google Scholar]
|