Influence of Anisotropic Permeability and Soret Effect on the Convective Heat and Mass Transfer through a Porous Cavity Saturated by a Non-Newtonian Fluid — Oak Academic Publishing
Research ArticleOpen AccessGoogle Scholar indexed
Influence of Anisotropic Permeability and Soret Effect on the Convective Heat and Mass Transfer through a Porous Cavity Saturated by a Non-Newtonian Fluid
Laboratoire d’Energétique et de Mécanique Appliquées, LEMA-EPAC, Université d’Abomey Calavi, Cotonou, Bénin
,
Laboratoire d’Energétique et de Mécanique Appliquées, LEMA-EPAC, Université d’Abomey Calavi, Cotonou, Bénin
,
Université Nationale des Sciences Technologies, Ingénierie et Mathématiques, Abomey, Bénin
1 Laboratoire d’Energétique et de Mécanique Appliquées, LEMA-EPAC, Université d’Abomey Calavi, Cotonou, Bénin
2 Laboratoire d’Energétique et de Mécanique Appliquées, LEMA-EPAC, Université d’Abomey Calavi, Cotonou, Bénin
3 Université Nationale des Sciences Technologies, Ingénierie et Mathématiques, Abomey, Bénin
In this work, an analytical study is carried out on double-diffusive natural convection through a horizontal anisotropic porous layer saturated with a non-Newtonian fluid by using the Darcy model with the Boussinesq approximations. The horizontal walls of the system are subject to vertical uniform fluxes of heat and mass, whereas the vertical walls are assumed to be adiabatic and impermeable. The Soret effect is taken into consideration. Based on parallel flow approximation theory, the problem is solved in the limit of a thin layer and documented the effects of the physical parameters describing this investigation.
KeywordsSoret NumberHeat and Mass TransferNon-Newtonian FluidIsotropyAni-sotropySupercritical Rayleigh Number
Nield, D.A. and Bejan, A. (1999) Convection in Porous Media. Springer-Verlag, Berlin. https://doi.org/10.1007/978-1-4757-3033-3
Chen, H.T. and Chen, C.K. (1987) Natural Convection of Non Newtonian Fluids about a Horizontal Surface in Porous Medium. Journal of Energy Resources Technology, 109, 119-123. https://doi.org/10.1115/1.3231336
Christopher, R.V. and Middleman (1965) Power-Law Flow through a Packed Tube. Industrial & Engineering Chemistry Fundamentals, 4, 422-426. https://doi.org/10.1021/i160016a011
Dharmadhikari, R.V. and Kale, D.D. (1985) Flow of Non Newtonian Fluids through Porous Media. Chemical Engineering Science, 40, 527-529. https://doi.org/10.1016/0009-2509(85)85113-7
Pascal, H. (1983) Rheological Behaviour Effect of Non Newtonian Fluids on Steady and Unsteady Flow through a Porous Media. International Journal for Numerical and Analytical Methods in Geo Mechanics, 7, 289-303. https://doi.org/10.1002/nag.1610070303
Pascal, H. (1986) Rheological Effects of Non Newtonian Behaviour of Displacing Fluids on Stability of a Moving Interface in Radial Oil Displacement Mechanism in Porous Media. International Journal Engineering Science, 24, 1465-1476. https://doi.org/10.1016/0020-7225(86)90157-6
Chen, H.T. and Chen, C.K. (1988) Free Convection Flow of Non Newtonian Fluids along a Vertical Plate Embedded in a Porous Medium. Journal of Heat Transfer, 110, 257-260. https://doi.org/10.1115/1.3250462
Pascal, H. and Pascal, J.P. (1989) Non Linear Effects of Non Newtonian Fluids on Natural Convection in a Porous Medium. Physica D, 40, 393-402. https://doi.org/10.1016/0167-2789(89)90051-1
Amari, B., Vasseur, P. and Bilgen, E. (1994) Natural Convection of Non Newtonian Fluids in a Horizontal Porous Layer. Warme- und Stoffübertragung, 29, 185-193. https://doi.org/10.1007/BF01548603
Getachew, D., Minkowycz, W.J. and Poulikakos, D. (1996) Natural Convection in a Porous Cavity Saturated with a Non Newtonian Fluid. Journal of Thermo Physics and Heat Transfer, 10, 640-651. https://doi.org/10.2514/3.841
Cheng, C.-Y. (2012) Free Convection of Non-Newtonian Nano Fluids about a Vertical Truncated Cone in a Porous Medium. International Communications in Heat and Mass Transfer, 39, 1348-1353. https://doi.org/10.1016/j.icheatmasstransfer.2012.08.004
Bejan, A. (1984) Convection Heat Transfer. John Wiley Sons, Hoboken.
Platten, J.K. and Legros, J.C. (1984) Convection in Liquids. Springer-Verlag, Berlin. https://doi.org/10.1007/978-3-642-82095-3
Oztop, H.F., Al-Salem, K., Varol, Y. and Pop, I. (2011) Natural Convection Heat Transfer in a Partially Opened Cavity Filled with Porous Media. International Journal of Heat and Mass Transfer, 54, 2253-2261. https://doi.org/10.1016/j.ijheatmasstransfer.2011.02.040
Maatki, C., Kolsi, L., Oztop, H.F., Chamkha, A., Borjini, M.N., Ben Aissia, H. and Al-Salem, K. (2013) Effects of Magnetic Field on 3D Double Diffusive Convection in a Cubic Cavity Filled with a Binary Mixture. The International Communications in Heat and Mass Transfer, 49, 86-95. https://doi.org/10.1016/j.icheatmasstransfer.2013.08.019
Chourasia, M. and Goswami, T. (2007) Three Dimensional Modeling on Air Flow, Heat and Mass Transfer in Partially Impermeable Enclosure Containing Agricultural Produce during Natural Convective Cooling. Energy Conversion and Management, 48, 2136-2149. https://doi.org/10.1016/j.enconman.2006.12.018
Demir, M.M. and Ulku, S. (2009) Effects of Porosity on Heat and Mass Transfer in a Granular Adsorbent Bed. International Communications in Heat and Mass Transfer, 36, 372-377. https://doi.org/10.1016/j.icheatmasstransfer.2009.01.008
Han, S. and Goldstein, R.J. (2008) The Heat/Mass Transfer Analogy for a Simulated Turbine Blade. International Journal of Heat and Mass Transfer, 51, 5209-5225. https://doi.org/10.1016/j.ijheatmasstransfer.2008.04.002
Han, S. and Goldstein, R.J. (2008) The Heat/Mass Transfer Analogy for a Simulated Turbine End Wall. International Journal of Heat and Mass Transfer, 51, 3227-3244. https://doi.org/10.1016/j.ijheatmasstransfer.2008.01.011
Juncu, G. (2010) Unsteady Conjugate Forced Convection Heat/Mass Transfer in Ensembles of Newtonian Fluid Spheres. International Journal of Heat and Mass Transfer, 53, 2780-2789. https://doi.org/10.1016/j.ijheatmasstransfer.2010.02.020
Leu, J.-S., Jang, J.-Y. and Chou, Y. (2006) Heat and Mass Transfer for Liquid Film Evaporation a Long a Vertical Plate Covered with a Thin Porous Layer. International Journal of Heat and Mass Transfer, 49, 1937-1945. https://doi.org/10.1016/j.ijheatmasstransfer.2005.11.004
Pirompugd, W., Wang, C.-C. and Wongwises, S. (2007) Finite Circular Fin Method for Heat and Mass Transfer Characteristics for Plain Fin-and-Tube Heat Exchangers Underfully and Partiallywet Surface Conditions. International Journal of Heat and Mass Transfer, 50, 552-565. https://doi.org/10.1016/j.ijheatmasstransfer.2006.07.017
Pirompugd, W., Wongwises, S. and Wang, C.-C. (2006) Simultaneous Heat and Mass Transfer Characteristics for Wavy Fin-and-Tube Heat Exchangers under Dehumidifying Conditions. International Journal of Heat and Mass Transfer, 49, 132-143. https://doi.org/10.1016/j.ijheatmasstransfer.2005.05.043
Suresh, M. and Mani, A. (2010) Heat and Mass Transfer Studies on R134a Bubble Absorber in R134a/DMF Solution Based on Phenomenological Theory. International Journal of Heat and Mass Transfer, 53, 2813-2825. https://doi.org/10.1016/j.ijheatmasstransfer.2010.02.016
Talukdar, P., Iskra, C.R. and Simonson, C.J. (2008) Combined Heat and Mass Transfer for Laminar Flow of Moist Air in a 3D Rectangular Duct: CFD Simulation and Validation with Experimental Data. International Journal of Heat and Mass Transfer, 51, 3091-3102. https://doi.org/10.1016/j.ijheatmasstransfer.2007.08.034
Zhang, L.-Z. (2008) Heat and Mass Transfer in Plate-Fin Sinusoidal Passages with Vapor Permeable Wall Materials. International Journal of Heat and Mass Transfer, 51, 618-629. https://doi.org/10.1016/j.ijheatmasstransfer.2007.04.050
Zhang, L.-Z. (2012) Coupled Heat and Mass Transfer in an Application Scale Cross Flow Hollow Fiber Membrane Module for Air Humidification. International Journal of Heat and Mass Transfer, 55, 5861-5869. https://doi.org/10.1016/j.ijheatmasstransfer.2012.05.083
Zhao, F.-Y., Liu, D. and Tang, G.-F. (2007) Application Issues of the Streamline, Heat Line and Mass Line for Conjugate Heat and Mass Transfer. International Journal of Heat and Mass Transfer, 50, 320-334. https://doi.org/10.1016/j.ijheatmasstransfer.2006.06.026
Rastogi, S.K. and Poulikakos, D. (1995) Double Diffusion from a Vertical Surface in a Porous Region Saturated with a Non Newtonian Fluid. International Journal of Heat and Mass Transfer, 38, 935-946. https://doi.org/10.1016/0017-9310(94)00198-5
Getachew, D., Minkowycz, W.J. and Poulikakos, D. (1998) Double Diffusion in a Porous Cavity Saturated with Non Newtonian Fluid. Journal of Thermo Physics and Heat Transfer, 12, 437-446. https://doi.org/10.2514/2.6357
Jumah, R.Y. and Mujumdar, A.S. (2000) Free Convection Heat and Mass Transfer of Non-Newtonian Power Law Fluids with Yield Stress from a Vertical Flat Plate in Saturated Porous Media. International Communications in Heat Mass Transfer, 27, 485-494. https://doi.org/10.1016/S0735-1933(00)00131-7
Benhadji, K. and Vasseur, P. (2001) Double Diffusive Convection in a Shallow Porous Cavity Filled with a Non-Newtonian Fluid. International Communications in Heat and Mass Transfer, 28, 763-772. https://doi.org/10.1016/S0735-1933(01)00280-9
Rebhi, R., Mamou, M. and Hadidi, N. (2021) Onset of Linear and Nonlinear Thermosolutal Convection with Soret and Dufour Effects in a Porous Collector under a Uniform Magnetic Field. Fluids, 6, Article No. 243. https://doi.org/10.3390/fluids6070243
Changhao, L. and Payne, L.E. (2008) Continuous Dependence on the Soret Coefficient for Double Diffusive Convection in Darcy Flow. Journal of Mathematical Analysis and Applications, 342, 311-320. https://doi.org/10.1016/j.jmaa.2007.11.036
Mutschler, D. and Mojtabi, A. (2020) Theoretical and Numerical Analysis of Soret-Driven Convection in a Horizontal Porous Layer Saturated by an n-Component Mixture: Application to Ternary Hydrocarbon Mixture Tetralin, Isobutyl Benzene, n-Dodecane with Mass Fractions 0.8-0.1-0.1. International Journal of Heat and Mass Transfer, 162, Article ID: 120339. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120339
Benano-Melly, L., Caltagirone, J.-P., Faissat, B., Montel, F. and Costeseque, P. (2001) Modeling Soret Coefficient Measurement Experiments in Porous Media Considering Thermal and Solutal Convection. International Journal of Heat and Mass Transfer, 44, 1285-1297. https://doi.org/10.1016/S0017-9310(00)00183-6
Mansour, A., Amahmid, A. and Hasnaoui, M. (2008) Soret Effect on Thermosolutal Convection Developed in a Horizontal Shallow Porous Layer Salted from below and Subject to Cross Fluxes of Heat. International Journal of Heat and Fluid Flow, 29, 306-314. https://doi.org/10.1016/j.ijheatfluidflow.2007.07.002
Joly, F., Vasseur, P. and Labrosse, G. (2001) Soret Instability in a Vertical Brinkman Porous Enclosure. Numerical Heat Transfer, Part A: Applications, 39, 339-359. https://doi.org/10.1080/10407780151063133
Gaikwad, S., Malashetty, M. and Prasad, K.R. (2009) An Analytical Study of linear and Nonlinear Double Diffusive Convection in a Fluid Saturated Anisotropic Porous Layer with Soret Effect. Applied Mathematical Modelling, 33, 3617-3635. https://doi.org/10.1016/j.apm.2008.12.013
Malashetty, M., Pop, I., Kollur, P. and Sidram, W. (2012) Soret Effect on Double Diffusive Convection in a Darcy Porous Medium Saturated with a Couple Stress Fluid. International Journal of Thermal Sciences, 53, 130-140. https://doi.org/10.1016/j.ijthermalsci.2011.11.001
Patil, P.R. and Parvathy, C.P. (1989) Thermohaline Convection with Cross-Diffusion in an Anisotropic Porous Medium. Proceedings of the Indian Academy of Sciences, 99, 93-101. https://doi.org/10.1007/BF02874650
Malashetty, M.S., Tan, W.C. and Swamy, M. (2009) The Onset of Double Diffusive Convection in a Binary Viscoelastic Fluid Saturated Anisotropic Porous Layer. Physics of Fluids, 21, Article ID: 084101. https://doi.org/10.1063/1.3194288
Malashetty, M.S., Swamy, M.S. and Sidram, W. (2011) Double Diffusive Convection in a Rotating Anisotropic Porous Layer Saturated with Viscoelastic Fluid. International Journal of Thermal Sciences, 50, 1757-1769. https://doi.org/10.1016/j.ijthermalsci.2011.04.006
Aly, A.M. and Asai, M. (2015) Double-Diffusive Natural Convection with Cross- Diffusion Effects Using ISPH Method. In: Solecki, M., Ed., Mass Transfer— Advancement in Process Modelling, IntechOpen, London, 65-97.
Singh, A. and Shakya, K. (2018) Double Diffusive Convection in a Couple Stress Fluid Saturated Rotating Anisotropic Porous Layer with Internal Heating and Soret Effect. S-JPSET, 10, 121-136. https://doi.org/10.18090/samriddhi.v10i02.7
Ali, S.A., Rudziva, M., Sibanda, P., Noreldin, O.A.I., Goqo, S.P., Goqo, S.P. and Mthethwa, H.S. (2022) A Numerical Study of Double-Diffusive Convection in the Anisotropic Porous Layer under Rotational Modulation with Internal Heat Generation. International Communications in Heat and Mass Transfer.
Yeliyur Honnappa, G., Narayanappa, M., Udhayakumar, R., Almarri, B., Elshenhab, A.M. and Honnappa, N. (2023) Darcy-Brinkman Double Diffusive Convection in an Anisotropic Porous Layer with Gravity Fluctuation and Throughflow. Mathematics, 11, Article No. 1287. https://doi.org/10.3390/math11061287
Julien, Y., Latif, F., Marius, K.B.S., Dieudonné, K. and Gérard, D. (2020) Effect of Anisotropic Permeability on Thermosolutal Convection in a Porous Cavity Saturated by a Non-Newtonian Fluid. International Journal of Fluid Mechanics Thermal Sciences, 6, 124-131. https://doi.org/10.11648/j.ijfmts.20200604.13
Makayssi, T., Lamsaadi, M., Nami, M., Hasnaoui, M., Raji, A. and Bahlaoui, A. (2008) Natural Double-Diffusive Convection in a Shallow Horizontal Rectangular Cavity Uniformly Heated and Salted from the Side and Filled with Non-Newtonian Power-Law Fluids: The Cooperating Case. Energy Conversion and Management, 49, 2016-2025. https://doi.org/10.1016/j.enconman.2008.02.008
Mamou, M., Vasseur, P., Bilgen, E. and Gobin, D. (1995) Double Diffusive Convection in an Inclined Slot Filled with Porous Medium. European Journal of Mechanics, B/Fluids, 14, 629-652. https://doi.org/10.1615/IHTC10.4350
Kalla, L., Mamou, M., Vasseur, P. and Robillard, L. (1999) Multiple Steady States for Natural Convection in a Shallow Porous Cavity Subject to Uniform Heat Fluxes. International Communications in Heat Mass Transfer, 26, 761-770. https://doi.org/10.1016/S0735-1933(99)00064-0
Mamou, M. (2003) Stability Analysis of the Perturbed Rest State and of the Finite Amplitude Steady Double-Diffusive Convection in a Shallow Porous Enclosure. International Journal of Heat and Mass Transfer, 46, 2263-2277. https://doi.org/10.1016/S0017-9310(02)00523-9
Alloui, Z. and Vasseur, P. (2010) Convection in Superposed Fluid and Porous Layers. Acta Mechanica, 214, 245-260. https://doi.org/10.1007/s00707-010-0284-y
Degan, G., Yovogan, J., Fagbémi, L. and Alloui, Z. (2019) Stability of Geothermal Convection in Anisotropic River Beds. Engineering, 11, 343-365. https://doi.org/10.4236/eng.2019.117026
Attia, A., Mamou, M., Benissaad, S. and Ouazaa, N. (2018) Linear and Nonlinear Stability of Soret-Dufour Lapwood Convection near Double Codimension-2 Points. Heat Transfer—Asian Research, 48, 763-792. https://doi.org/10.1002/htj.21405
Nield, D.A. (1968) Onset of Thermohaline Convection in a Porous Medium. Water Resources Research, 4, 553-560. https://doi.org/10.1029/WR004i003p00553
Vasseur, P., Wang, C.H. and Sen, M. (1989) The Brinkman Model for Natural Convection in Shallow Porous Cavity with Uniform Heat Flux. Numerical Heat Transfer, 15, 221-242. https://doi.org/10.1080/10407788908944686