Thermosolutal Convection of Natural and Anti-Natural Solutions Through an Angled Cavity Under Cross Gradients in Temperature and Concentration

Authors

  • Abdelhakim Mebrouki Mechanical Department, Technology Faculty, University Batna 2, Batna, Algeria
  • Redha Rebhi Department of Mechanical Engineering, Faculty of Technology, University of Medea, Medea 26000, Algeria
  • Mokdad Hayawi Rahman Aeronautical Technical Engineering, Al-Farahidi University, Baghdad 10011, Iraq
  • Giulio Lorenzini Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze, 181/A, 43124 Parma, Italy
  • Younes Menni Department of Technology, University Center Salhi Ahmed Naama (Ctr. Univ. Naama), P.O. Box 66, Naama 45000, Algeria
  • Houari Ameur Department of Technology, University Center Salhi Ahmed Naama (Ctr. Univ. Naama), P.O. Box 66, Naama 45000, Algeria
  • Hijaz Ahmad Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy

DOI:

https://doi.org/10.37934/cfdl.15.5.97119

Keywords:

Natural and anti-natural solutions, thermosolutal convection, inclined cavity, concentration gradients, temperature gradients, numerical survey

Abstract

In the current study, cross-temperature and concentration gradients are used to model the     in a binary fluid contained in an angled square cavity. Using a  method, the , , and  conservation equations were numerically solved. The  inclined cavity under equal solutal buoyancy and thermal forces was the subject of the study . Since the horizontal components of the thermal and singular volume forces were equal but opposed to one another, an equilibrium solution for this situation that corresponds to the rest state of the immobile fluid is feasible. However, this equilibrium solution becomes unstable above a specific critical value of the , leading to vertical density stratification inside the enclosure. The results are shown using the  and  as well as the  and  for the flow intensity. The existence of the commencement of convection is demonstrated in this work, and both natural and anti-natural flow solutions are obtained. Subcritical convection has also been seen for the natural solution when the  is more or less than unity. For the start of supercritical and subcritical convection, the  number's critical values are identified. As the  climbed, so did the flow's intensity and the rates at which heat and mass were transferred. Reducing flow intensity and accelerating mass transfer are the results of raising the . Different flow patterns are shown for an aspect ratio of 4, and the existence interval of the oscillatory solutions is calculated.

Author Biography

Giulio Lorenzini, Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze, 181/A, 43124 Parma, Italy

giulio.lorenzini@unipr.it

References

Lapwood, E. R. "Convection of a fluid in a porous medium." In Mathematical Proceedings of the Cambridge Philosophical Society, vol. 44, no. 4, pp. 508-521. Cambridge University Press, 1948. https://doi.org/10.1017/S030500410002452X

Davis, G. de Vahl. "Natural convection of air in a square cavity: a bench mark numerical solution." International Journal for Numerical Methods in Fluids 3, no. 3 (1983): 249-264. https://doi.org/10.1002/fld.1650030305

Kimura, S., M. Vynnycky, and F. Alavyoon. "Unicellular natural circulation in a shallow horizontal porous layer heated from below by a constant flux." Journal of Fluid Mechanics 294 (1995): 231-257. https://doi.org/10.1017/S0022112095002874

Al-Azawy, Mohammed Ghalib, Saleem Khalefa Kadhim, and Azzam Sabah Hameed. "Newtonian and non-newtonian blood rheology inside a model of stenosis." CFD Letters 12, no. 11 (2020): 27-36. https://doi.org/10.37934/cfdl.12.11.2736

Mojtabi, Abdelkader, and Marie-Catherine Charrier-Mojtabi. "Double-diffusive convection in porous media." In Handbook of Porous Media, pp. 287-338. CRC Press, 2005. https://doi.org/10.1201/9780415876384-10

Nishimura, Tatsuo, Mikio Wakamatsu, and Alexandru M. Morega. "Oscillatory double-diffusive convection in a rectangular enclosure with combined horizontal temperature and concentration gradients." International Journal of Heat and Mass Transfer 41, no. 11 (1998): 1601-1611. https://doi.org/10.1016/S0017-9310(97)00271-8

Weaver, J. A., and Raymond Viskanta. "Natural convection in binary gases driven by combined horizontal thermal and vertical solutal gradients." Experimental Thermal and Fluid Science 5, no. 1 (1992): 57-68. https://doi.org/10.1016/0894-1777(92)90056-B

Chamkha, Ali J., and Hameed Al-Naser. "Double-diffusive convection in an inclined porous enclosure with opposing temperature and concentration gradients." International Journal of Thermal Sciences 40, no. 3 (2001): 227-244. https://doi.org/10.1016/S1290-0729(00)01213-8

Mohamad, Abdulmajeed A., and Rachid Bennacer. "Natural convection in a confined saturated porous medium with horizontal temperature and vertical solutal gradients." International Journal of Thermal Sciences 40, no. 1 (2001): 82-93. https://doi.org/10.1016/S1290-0729(00)01182-0

Mohamad, A. A., and R. Bennacer. "Double diffusion, natural convection in an enclosure filled with saturated porous medium subjected to cross gradients; stably stratified fluid." International Journal of Heat and Mass Transfer 45, no. 18 (2002): 3725-3740. https://doi.org/10.1016/S0017-9310(02)00093-5

Benhadji, K., and P. Vasseur. "Double diffusive convection in a shallow porous cavity filled with a non-Newtonian fluid." International Communications in Heat and Mass Transfer 28, no. 6 (2001): 763-772. https://doi.org/10.1016/S0735-1933(01)00280-9

Bahloul, A., N. Boutana, and P. Vasseur. "Double-diffusive and Soret-induced convection in a shallow horizontal porous layer." Journal of Fluid Mechanics 491 (2003): 325-352. https://doi.org/10.1017/S0022112003005524

Bahloul, A., P. Vasseur, and L. Robillard. "Convection of a binary fluid saturating a shallow porous cavity subjected to cross heat fluxes." Journal of Fluid Mechanics 574 (2007): 317-342. https://doi.org/10.1017/S0022112006004113

Rebhi, Redha, Mahmoud Mamou, Patrick Vasseur, and Mounir Alliche. "Form drag effect on the onset of non-linear convection and Hopf bifurcation in binary fluid saturating a tall porous cavity." International Journal of Heat and Mass Transfer 100 (2016): 178-190. https://doi.org/10.1016/j.ijheatmasstransfer.2016.04.060

Kumar, Gautam, Puranam Anantha Lakshmi Narayana, and Kirti Chandra Sahu. "Linear and nonlinear thermosolutal instabilities in an inclined porous layer." Proceedings of the Royal Society A 476, no. 2233 (2020): 20190705. https://doi.org/10.1098/rspa.2019.0705

Saxena, Ashish, Vimal Kishor, Suneet Singh, and Atul Srivastava. "Experimental and numerical study on the onset of natural convection in a cavity open at the top." Physics of Fluids 30, no. 5 (2018): 057102. https://doi.org/10.1063/1.5025092

Bihiche, K., M. Lamsaadi, and M. Hasnaoui. "Multiple steady state solutions for double-diffusive convection in a shallow horizontal rectangular cavity uniformly heated and salted from the side and filled with non-Newtonian power-law fluids." Journal of Non-Newtonian Fluid Mechanics 283 (2020): 104349. https://doi.org/10.1016/j.jnnfm.2020.104349

Bourich, M., M. Hasnaoui, and A. Amahmid. "A scale analysis of thermosolutal convection in a saturated porous enclosure submitted to vertical temperature and horizontal concentration gradients." Energy Conversion and Management 45, no. 18-19 (2004): 2795-2811. https://doi.org/10.1016/j.enconman.2004.01.010

Bahloul, A., L. Kalla, R. Bennacer, H. Beji, and P. Vasseur. "Natural convection in a vertical porous slot heated from below and with horizontal concentration gradients." International Journal of Thermal Sciences 43, no. 7 (2004): 653-663. https://doi.org/10.1016/j.ijthermalsci.2003.10.012

Bourich, M., M. Hasnaoui, and A. Amahmid. "Double-diffusive natural convection in a porous enclosure partially heated from below and differentially salted." International Journal of Heat and Fluid Flow 25, no. 6 (2004): 1034-1046. https://doi.org/10.1016/j.ijheatfluidflow.2004.01.003

Kramer, Janja, Renata Jecl, and L. Skerget. Natural convection in porous media under cross temperature and concentration gradients with Boundary Element Method. Vol. 47. WIT Press, 2008. https://doi.org/10.2495/BE080071

Chamkha, Ali J., Ali Al‐Mudhaf, and Eisa Al‐Meshaiei. "Thermo‐solutal convection in an inclined porous cavity with various aspect ratios under mixed thermal and species boundary conditions." Heat Transfer-Asian Research 40, no. 8 (2011): 693-720. https://doi.org/10.1002/htj.20369

Balla, Chandra Shekar, and Kishan Naikoti. "Soret and Dufour effects on free convective heat and solute transfer in fluid saturated inclined porous cavity." Engineering Science and Technology, an International Journal 18, no. 4 (2015): 543-554. https://doi.org/10.1016/j.jestch.2015.04.001

Ouzaouit, Meriem, Btissam Abourida, Lahoucine Belarche, Hicham Doghmi, and Mohamed Sannad. "Numerical study of the thermosolutal convection in a 3-D cavity submitted to cross gradients of temperature and concentration." Thermal Science 23, no. 3 Part B (2019): 1923-1933. https://doi.org/10.2298/TSCI170809070O

Balla, Chandra Shekar, Naikoti Kishan, Rama SR Gorla, and B. J. Gireesha. "MHD boundary layer flow and heat transfer in an inclined porous square cavity filled with nanofluids." Ain Shams Engineering Journal 8, no. 2 (2017): 237-254. https://doi.org/10.1016/j.asej.2016.02.010

Balla, Chandra Shekar, C. Haritha, and Naikoti Kishan. "Magnetohydrodynamic convection in a porous square cavity filled by a nanofluid with viscous dissipation effects." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 233, no. 3 (2019): 474-488. https://doi.org/10.1177/0954408918765314

Chakkingal, Manu, Roland Voigt, Chris R. Kleijn, and Saša Kenjereš. "Effect of double-diffusive convection with cross gradients on heat and mass transfer in a cubical enclosure with adiabatic cylindrical obstacles." International Journal of Heat and Fluid Flow 83 (2020): 108574. https://doi.org/10.1016/j.ijheatfluidflow.2020.108574

Rebhi, Redha, Noureddine Hadidi, and Rachid Bennacer. "Non-Darcian effect on double-diffusive natural convection inside aninclined square Dupuit-Darcy porous cavity under a magnetic field." Thermal Science 25, no. 1 Part A (2021): 121-132. https://doi.org/10.2298/TSCI190117271R

Ouazaa, Nabil, Smail Benisaad, and Mahmoud Mamou. "Double diffusion convection in a tilted square porous domain under cross temperature and concentration gradients." U.P.B. Scientific Bulletin, Series D 82, no. 2 (2020): 131-142.

Ghiasi, Emran Khoshrouye, and Reza Saleh. "Analytical and numerical solutions to the 2D Sakiadis flow of Casson fluid with cross diffusion, inclined magnetic force, viscous dissipation and thermal radiation based on Buongiorno's mathematical model." CFD Letters 11, no. 1 (2019): 40-54.

Khdher, Abdolbaqi Mohammed, Nor Azwadi Che Sidik, Siti Nurul Akmal Yusof, and M'hamed Beriache. "Heat Transfer Enhancement in Straight Channel with Nanofluid In Fully Developed Turbulent Flow." Journal of Advanced Research in Applied Mechanics 63, no. 1 (2019): 1-15.

Khan, Ansab Azam, Khairy Zaimi, Suliadi Firdaus Sufahani, and Mohammad Ferdows. "MHD flow and heat transfer of double stratified micropolar fluid over a vertical permeable shrinking/stretching sheet with chemical reaction and heat source." Journal of Advanced Research in Applied Sciences and Engineering Technology 21, no. 1 (2020): 1-14. https://doi.org/10.37934/araset.21.1.114

Yusof, Nur Syamila, Siti Khuzaimah Soid, Mohd Rijal Illias, Ahmad Sukri Abd Aziz, and Nor Ain Azeany Mohd Nasir. "Radiative Boundary Layer Flow of Casson Fluid Over an Exponentially Permeable Slippery Riga Plate with Viscous Dissipation." Journal of Advanced Research in Applied Sciences and Engineering Technology 21, no. 1 (2020): 41-51. https://doi.org/10.37934/araset.21.1.4151

Wahid, Nur Syahirah, Mohd Ezad Hafidz Hafidzuddin, Norihan Md Arifin, Mustafa Turkyilmazoglu, and Nor Aliza Abd Rahmin. "Magnetohydrodynamic (MHD) slip darcy flow of viscoelastic fluid over a stretching sheet and heat transfer with thermal radiation and viscous dissipation." CFD Letters 12, no. 1 (2020): 1-12.

Mahrous, Samar A., Nor Azwadi Che Sidik, and Khalid M. Saqr. "Newtonian and non-Newtonian CFD models of intracranial aneurysm: a review." CFD Letters 12, no. 1 (2020): 62-86.

Parvin, Shahanaz, Siti Suzilliana Putri Mohamed Isa, Norihan Md Arifin, and Fadzilah Md Ali. "The Magnetohydrodynamics Casson Fluid Flow, Heat and Mass Transfer Due to the Presence of Assisting Flow and Buoyancy Ratio Parameters." CFD Letters 12, no. 8 (2020): 64-75. https://doi.org/10.37934/cfdl.12.8.6475

Sikdar, Prabir, and Sunil Manohar Dash. "A Numerical Study on the Lid-Driven Cavity with Power-Law Fluids at Different Moving Lengths of the Top Lid." CFD Letters 12, no. 6 (2020): 107-117. https://doi.org/10.37934/cfdl.12.6.107117

Paliwal, R. C., and C. F. Chen. "Double-diffusive instability in an inclined fluid layer. Part 1. Experimental investigation." Journal of Fluid Mechanics 98, no. 4 (1980): 755-768. https://doi.org/10.1017/S0022112080000377

Paliwal, R. C., and C. F. Chen. "Double-diffusive instability in an inclined fluid layer Part 2. Stability analysis." Journal of Fluid Mechanics 98, no. 4 (1980): 769-785. https://doi.org/10.1017/S0022112080000389

Bodduna, Jamuna, M. P. Mallesh, Chandra Shekar Balla, and Sabir Ali Shehzad. "Activation energy process in bioconvection nanofluid flow through porous cavity." Journal of Porous Media 25, no. 4 (2022): 37-51. https://doi.org/10.1615/JPorMedia.2022040230

Akram, Safia, Maria Athar, Khalid Saeed, and Mir Yasir Umair. "Nanomaterials effects on induced magnetic field and double-diffusivity convection on peristaltic transport of Prandtl nanofluids in inclined asymmetric channel." Nanomaterials and Nanotechnology 12 (2022): 18479804211048630. https://doi.org/10.1177/18479804211048630

Saeed, Khalid, Safia Akram, Adeel Ahmad, Maria Athar, Muhammad Imran, and Taseer Muhammad. "Impact of partial slip on double diffusion convection and inclined magnetic field on peristaltic wave of six-constant Jeffreys nanofluid along asymmetric channel." The European Physical Journal Plus 137, no. 3 (2022): 364. https://doi.org/10.1140/epjp/s13360-022-02553-6

Akram, Safia, Alia Razia, Mir Yasir Umair, Tuqa Abdulrazzaq, and Raad Z. Homod. "Double‐diffusive convection on peristaltic flow of hyperbolic tangent nanofluid in non‐uniform channel with induced magnetic field." Mathematical Methods in the Applied Sciences (2022). https://doi.org/10.1002/mma.8188

Phu, Nguyen Minh, and Pham Ba Thao. "Thermohydraulic performance of a fin and inclined flat tube heat exchanger: A numerical analysis." CFD Letters 13, no. 7 (2021): 1-12. https://doi.org/10.37934/cfdl.13.7.112

Lounis, Selma, Redha Rebhi, Noureddine Hadidi, Giulio Lorenzini, Younes Menni, Houari Ameur, and Nor Azwadi Che Sidik. "Thermo-Solutal Convection of Carreau-Yasuda Non-Newtonian Fluids in Inclined Square Cavities Under Dufour and Soret Impacts." CFD Letters 14, no. 3 (2022): 96-118. https://doi.org/10.37934/cfdl.14.3.96118

Mebrouki, A., Mahmoud Mamou, and Rachid Saim. "Thermosolutal convection in a tilted square fluid enclosure subject to cross fluxes of heat and solute." 16èmes Journées Internationales de Thermique (JITH 2013) (2013).

Mamou, M., P. Vasseur, and E. Bilgen. "Analytical and numerical study of double diffusive convection in a vertical enclosure." Heat and Mass Transfer 32, no. 1 (1996): 115-125. https://doi.org/10.1007/s002310050100

Lee, Jin Wook, and Jae Min Hyun. "Double diffusive convection in a cavity under a vertical solutal gradient and a horizontal temperature gradient." International Journal of Heat and Mass Transfer 34, no. 9 (1991): 2423-2427. https://doi.org/10.1016/0017-9310(91)90066-N

Downloads

Published

2023-03-16

How to Cite

Abdelhakim Mebrouki, Redha Rebhi, Mokdad Hayawi Rahman, Lorenzini, G., Younes Menni, Houari Ameur, & Hijaz Ahmad. (2023). Thermosolutal Convection of Natural and Anti-Natural Solutions Through an Angled Cavity Under Cross Gradients in Temperature and Concentration. CFD Letters, 15(5), 97–119. https://doi.org/10.37934/cfdl.15.5.97119

Issue

Section

Articles