Rayleigh-Benard Convection in Nanofluids Layer saturated in a Rotating Anisotropic Porous Medium with Feedback Control and Internal Heat Source

Authors

  • Izzati Khalidah Khalid Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia
  • Nor Fadzillah Mohd Mokhtar Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
  • Zarina Bibi Ibrahim Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

DOI:

https://doi.org/10.37934/cfdl.13.11.120

Keywords:

Feedback Control, Rotation, Nanofluids, Internal Heat Source, Porous Medium

Abstract

Control strategy on Rayleigh-Benard convection in rotating nanofluids saturated in anisotropic porous layer heated from below is studied in the presence of uniformly internal heat source for rigid-rigid, free-free, and lower-rigid and upper-free boundaries. Feedback control strategy with an array of sensors situated at the top plate and actuators located at the bottom plate of the nanofluids layer are considered in this study. Linear stability analysis based on normal mode technique has been performed, the eigenvalue problem is obtained numerically by implementing the Galerkin method and computed by using Maple software. Model employed for the nanofluids includes the mechanisms of Brownian motion and thermophoresis. The problem of the onset of convective rolls instabilities in a horizontal porous layer with isothermal boundaries at unequal temperatures known as Horton-Roger-Lapwood model based on the Darcy model for the fluids flow is used. The influences of internal heat source’s strength, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection, meanwhile the mechanical anisotropy parameter, thermal anisotropy parameter, porosity, rotation, and controller effects are to slow down the process of convective instability. No visible observation on the modified particle density increment and rigid-rigid boundaries are the most stable system compared to free-free and rigid-free boundaries.

Author Biographies

Izzati Khalidah Khalid, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia

izzatikk@uitm.edu.my

Nor Fadzillah Mohd Mokhtar, Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

norfadzillah.mokhtar@gmail.com

Zarina Bibi Ibrahim, Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

zarinabb@upm.edu.my

References

Choi, S. US, and Jeffrey A. Eastman. Enhancing thermal conductivity of fluids with nanoparticles. No. ANL/MSD/CP-84938; CONF-951135-29. Argonne National Lab., IL (United States), 1995.

Menni, Younes, Ali J. Chamkha, Giulio Lorenzini, Noureddine Kaid, Houari Ameur, and Mohammed Bensafi. "Advances of nanofluids in solar collectors—a review of numerical studies." Math Model Eng Probl 6, no. 3 (2019): 415-27. https://doi.org/10.18280/mmep.060313

Barber, Jacqueline, David Brutin, and Lounes Tadrist. "A review on boiling heat transfer enhancement with nanofluids." Nanoscale research letters 6, no. 1 (2011): 1-16. https://doi.org/10.1186/1556-276X-6-280

Yu, Wei, and Huaqing Xie. "A review on nanofluids: preparation, stability mechanisms, and applications." Journal of nanomaterials 2012 (2012). https://doi.org/10.1155/2012/435873

Goharshadi, E. K., Hossein Ahmadzadeh, Sara Samiee, and Mahboobeh Hadadian. "Nanofluids for heat transfer enhancement-a review." (2013): 1-33. https://doi.org/10.22036/pcr.2013.27911

Mahbubul, I. M., Rahman Saidur, and M. A. Amalina. "Latest developments on the viscosity of nanofluids." International Journal of Heat and Mass Transfer 55, no. 4 (2012): 874-885. https://doi.org/10.1016/j.ijheatmasstransfer.2011.10.021

Hussein, Adnan M., K. V. Sharma, R. A. Bakar, and K. Kadirgama. "A review of forced convection heat transfer enhancement and hydrodynamic characteristics of a nanofluid." Renewable and Sustainable Energy Reviews 29 (2014): 734-743. https://doi.org/10.1016/j.rser.2013.08.014

Tzou, Da Yu. "Instability of nanofluids in natural convection." Journal of Heat Transfer 130, no. 7 (2008). https://doi.org/10.1115/1.2908427

Tzou, Da Yu. "Thermal instability of nanofluids in natural convection." International Journal of Heat and Mass Transfer 51, no. 11-12 (2008): 2967-2979. https://doi.org/10.1016/j.ijheatmasstransfer.2007.09.014

Buongiorno, Jacopo. "Convective transport in nanofluids." (2006): 240-250. https://doi.org/10.1115/1.2150834

Kim, Jake, Yong Tae Kang, and Chang Kyun Choi. "Analysis of convective instability and heat transfer characteristics of nanofluids." Physics of fluids 16, no. 7 (2004): 2395-2401. https://doi.org/10.1063/1.1739247

Nield, D. A., and Andrey V. Kuznetsov. "The onset of convection in a horizontal nanofluid layer of finite depth." European Journal of Mechanics-B/Fluids 29, no. 3 (2010): 217-223. https://doi.org/10.1016/j.euromechflu.2010.02.003

Yadav, Dhananjaya, G. S. Agrawal, and Rama Bhargava. “Rayleigh-Benard convection in nanofluids.” International Journal of Applied Mathematics and Mechanics 7, no. 2 (2011): 61-76.

Haddad, Zoubida, Eiyad Abu-Nada, Hakan F. Oztop, and Amina Mataoui. "Natural convection in nanofluids: are the thermophoresis and Brownian motion effects significant in nanofluid heat transfer enhancement?." International Journal of Thermal Sciences 57 (2012): 152-162. https://doi.org/10.1016/j.ijthermalsci.2012.01.016

Sharma, Jyoti, Urvashi Gupta, and Veena Sharma. "Modified model for binary nanofluid convection with initial constant nanoparticle volume fraction." Journal of Applied Fluid Mechanics (JAFM) 10, no. 5 (2017): 1387-1395. https://doi.org/10.18869/acadpub.jafm.73.242.27754

Menni, Younes, Ali J. Chamkha, and Houari Ameur. "Advances of nanofluids in heat exchangers—A review." Heat Transfer 49, no. 8 (2020): 4321-4349. https://doi.org/10.1002/htj.21829

Gupta, Urvashi, Jyoti Sharma, and Mamta Devi. "Casson nanofluid convection in an internally heated layer." Materials Today: Proceedings 28 (2020): 1748-1752. https://doi.org/10.1016/j.matpr.2020.05.156

Gupta, Urvashi, Jyoti Sharma, and Mamta Devi. "Double-diffusive instability of Casson nanofluids with numerical investigations for blood-based fluid." The European Physical Journal Special Topics (2021): 1-11. https://doi.org/10.1140/epjs/s11734-021-00053-9

Aliouane, Imane, Noureddine Kaid, Houari Ameur, and Houssem Laidoudi. "Investigation of the flow and thermal fields in square enclosures: Rayleigh-Bénard’s instabilities of nanofluids." Thermal Science and Engineering Progress 25 (2021): 100959. https://doi.org/10.1016/j.tsep.2021.100959

Mahammedi, Abdelkader, Houari Ameur, Younes Menni, and Driss Meddah Medjahed. "Numerical study of turbulent flows and convective heat transfer of Al2O3-water nanofluids in a circular tube." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 77, no. 2 (2021): 1-12. https://doi.org/10.37934/arfmts.77.2.112

Douha, Mohammed, Draoui Belkacem, Kaid Noureddine, Ameur Houari, Belkacem Abdellah, Mohamed Elmir, Merabti Abdelhak, and Aissani Houcine. "Study of Laminar Naturel Convection in Partially Porous Cavity in the Presence of Nanofluids." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 79, no. 1 (2021): 91-110. https://doi.org/10.37934/arfmts.79.1.91110

Abdelkader, Mahammedi, Houari Ameur, and Younes Menni. "Investigation of the convective heat transfer and friction factor of magnetic Ni nanofluids within cylindrical pipes." transfer 2 (2021): 4. https://doi.org/10.36963/IJTST.2021080101

Sparrow, Ephraim M., Richard J. Goldstein, and V. K. Jonsson. "Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile." Journal of Fluid Mechanics 18, no. 4 (1964): 513-528. https://doi.org/10.1017/S0022112064000386

Char, Ming-I., and Ko-Ta Chiang. "Stability analysis of Benard-Marangoni convection in fluids with internal heat generation." Journal of Physics D: Applied Physics 27, no. 4 (1994): 748. https://doi.org/10.1088/0022-3727/27/4/012

Nield, D. A., and Andrey V. Kuznetsov. "Thermal instability in a porous medium layer saturated by a nanofluid." International Journal of Heat and Mass Transfer 52, no. 25-26 (2009): 5796-5801. https://doi.org/10.1016/j.ijheatmasstransfer.2009.07.023

Nanjundappa, C. E., I. S. Shivakumara, Jinho Lee, and M. Ravisha. "Effect of internal heat generation on the onset of Brinkman–Bénard convection in a ferrofluid saturated porous layer." International journal of thermal sciences 50, no. 2 (2011): 160-168. https://doi.org/10.1016/j.ijthermalsci.2010.10.003

Yadav, Dhananjay, R. Bhargava, and G. S. Agrawal. "Boundary and internal heat source effects on the onset of Darcy–Brinkman convection in a porous layer saturated by nanofluid." International Journal of Thermal Sciences 60 (2012): 244-254. https://doi.org/10.1016/j.ijthermalsci.2012.05.011

Shivakumara, I. S., and M. Dhananjaya. "Penetrative Brinkman convection in an anisotropic porous layer saturated by a nanofluid." Ain Shams engineering journal 6, no. 2 (2015): 703-713. https://doi.org/10.1016/j.asej.2014.12.005

Chand, R., G. C. Rana, and S. Kumar. "Variable gravity effects on thermal instability of nanofluid in anisotropic porous medium." International Journal of Applied Mechanics and Engineering 18, no. 3 (2013). https://doi.org/10.2478/ijame-2013-0038

Hamid, Nur Zarifah Abdul, Nor Fadzillah Mohd Mokhtar, Norihan Md Arifin, and Mohammad Hasan Abdul Sathar. "Effect of Nonlinear Temperature Profile on Thermal Convection in a Binary Fluid Saturated an Anisotropic Porous Medium." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 56, no. 1 (2019): 43-58.

Rusdi, Nadia Diana Mohd, Nor Fadzillah Mohd Mokhtar, Norazak Senu, and Siti Suzilliana Putri Mohamed Isa. "Effect of Coriolis force and magnetic field on thermal convection in an anisotropic porous medium." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 56, no. 1 (2019): 20-30.

Rusdi, Nadia Diana Mohd, Nor Fadzillah Mohd Mokhtar, Norazak Senu, and Siti Suzilliana Putri Mohamed Isa. "Stability Convection in a Couple Stress Fluid Saturated in an Anisotropic Porous Medium with Internal Heating Effect." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 76, no. 2 (2020): 75-84. https://doi.org/10.37934/arfmts.76.2.7584

Senin, Nor Halawati, Nor Fadzillah Mohd Mokhtar, and Mohamad Hasan Abdul Sathar. "Ferroconvection in an Anisotropic Porous Medium with Variable Gravity." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 71, no. 2 (2020): 56-68. https://doi.org/10.37934/arfmts.71.2.5668

Wang, Yuzhou, Jonathan Singer, and Haim H. Bau. "Controlling chaos in a thermal convection loop." Journal of Fluid Mechanics 237 (1992): 479-498. https://doi.org/10.1017/S0022112092003501

Tang, Jie, and Haim H. Bau. "Feedback control stabilization of the no-motion state of a fluid confined in a horizontal porous layer heated from below." Journal of Fluid Mechanics 257 (1993): 485-505. https://doi.org/10.1017/S0022112093003179

Bau, Haim H. "Control of Marangoni–Bénard convection." International Journal of Heat and Mass Transfer 42, no. 7 (1999): 1327-1341. https://doi.org/10.1016/S0017-9310(98)00234-8

Hashim, I., and Z. Siri. "Stabilization of steady and oscillatory Marangoni instability in rotating fluid layer by feedback control strategy." Numerical Heat Transfer, Part A: Applications 54, no. 6 (2008): 647-663. https://doi.org/10.1080/10407780802289384

Roslan, R., M. N. Mahmud, and I. Hashim. "Effects of feedback control on chaotic convection in fluid-saturated porous media." International journal of heat and mass transfer 54, no. 1-3 (2011): 404-412. https://doi.org/10.1016/j.ijheatmasstransfer.2010.09.031

Mahmud, M. N., and I. Hashim. "Small and moderate Vadasz number chaotic convection in porous media in the presence of non-Boussinesq effects and feedback control." Physics Letters A 375, no. 24 (2011): 2382-2393. https://doi.org/10.1016/j.physleta.2011.05.024

Vadasz, Peter. "Coriolis effect on gravity-driven convection in a rotating porous layer heated from below." Journal of Fluid Mechanics 376 (1998): 351-375. https://doi.org/10.1017/S0022112098002961

Govender, Saneshan. "Coriolis effect on the stability of centrifugally driven convection in a rotating anisotropic porous layer subjected to gravity." Transport in porous media 67, no. 2 (2007): 219-227. https://doi.org/10.1007/s11242-006-9003-5

Khalid, Izzati Khalidah, Nor Fadzillah Mohd Mokhtar, Zarina Bibi Ibrahim, and Zailan Siri. "Rayleigh–Bénard convection in Maxwell nanofluids layer saturated in a rotating porous medium with feedback control subjected to viscosity and thermal conductivity variations." Applied Nanoscience 10, no. 8 (2020): 3085-3095. https://doi.org/10.1007/s13204-020-01302-4

Sharma, Jyoti, and Urvashi Gupta. "Double-diffusive nanofluid convection in porous medium with rotation: Darcy-Brinkman model." Procedia Engineering 127 (2015): 783-790. https://doi.org/10.1016/j.proeng.2015.11.413

Sharma, Jyoti, Urvashi Gupta, and R. K. Wanchoo. "Numerical study on binary nanofluid convection in a rotating porous layer." Differential Equations and Dynamical Systems 25, no. 2 (2017): 239-249. https://doi.org/10.1007/s12591-015-0268-4

Downloads

Published

2021-11-11

How to Cite

Izzati Khalidah Khalid, Nor Fadzillah Mohd Mokhtar, & Zarina Bibi Ibrahim. (2021). Rayleigh-Benard Convection in Nanofluids Layer saturated in a Rotating Anisotropic Porous Medium with Feedback Control and Internal Heat Source. CFD Letters, 13(11), 1–20. https://doi.org/10.37934/cfdl.13.11.120

Issue

Section

Articles

Most read articles by the same author(s)