Engineering Transactions, Online first

Natural Convection Flow in Semi-Trapezoidal Porous Enclosure Filled with Alumina-Water Nanofluid Using Tiwari and Das’ Nanofluid Model

Koneru Lakshmaiah Education Foundation

Indian Institute of Information Technology

Sreenivasa Institute of Technology and Management Studies; JNTUA College of Engineering

G. Sankara Sekhar RAJU
JNTUA College of Engineering

Nowadays, optimal parameters are necessary for heat transfer enhancement in different practical applications. A numerical simulation of natural convection in a semi-trapezoidal enclosure
embedded with porous medium is presented. Stream function and temperature using the Darcy–Boussinesq approximation and Tiwari and Das’ nanofluid model with new more realistic empirical correlations for the physical properties of the nanofluids are formulated. The developed partial differential equations are employed with the help of the stream function approach. The in-house developed computational MATLAB code is validated with the
previously published work. The impact of a wide range of governing parameters on fluid flow patterns and temperature gradient variations is presented. The thermal Rayleigh number (Ra)
can be a control key parameter for heat and convective flow. Thermal dispersion effects are also examined in this study. An increase in the Rayleigh number leads to an increase in heat
transfer, where one can find a reduction of convective heat transfer with Φ.
Keywords: natural convection; laminar flow; porous medium; nanofluid; semi-trapezoidal enclosure
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).


Singh S., Experimental and numerical investigations of a single and double pass porous serpentine wavy wire mesh packed bed solar air heater, Renewable Energy, 145: 1361–1387, 2020, doi: 10.1016/j.renene.2019.06.137.

Dukhan N., Analysis of Brinkman-extended Darcy flow in porous media and experimental verification using metal foam, ASME. Journal of Fluids Engineering, 134(7): 071201, 2012, doi: 10.1115/1.4005678.

Bég O.A., Motsa S.S., Kadir A., Bég T.A., Islam M.N., Spectral quasilinear numerical simulation of micropolar convective wall plumes in high permeability porous media, Journal of Engineering Thermophysics, 25: 576–599, 2016, doi: 10.1134/S1810232816040147.

Choi W., Ooka R., Effect of natural convection on thermal response test conducted in saturated porous formation: Comparison of gravel-backfilled and cementgrouted borehole heat exchangers, Renewable Energy, 96(Part A): 891–903, 2016, doi: 10.1016/j.renene.2016.05.040.

Bég O.A., Motsa S.S., Bég T.A., Abbas A.J., Kadir A., Sohail A., Numerical study of nonlinear heat transfer from a wavy surface to a high permeability medium with pseudospectral and smoothed particle methods, International Journal of Applied and Computational Mathematics, 3: 3593–3613, 2017, doi: 10.1007/s40819-017-0318-4.

Belabid J., Impact of wall waviness on the convection patterns inside a horizontal porous annulus, ASME. Journal of Fluids Engineering, 142(7): 071304, 2020, doi: 10.1115/ 1.4046481.

Vafai K. [Ed], Porous Media: Applications in Biological Systems and Biotechnology, CRC Press, 1st ed., Boca Raton, Florida, 2010.

Tripathi D., Bég O.A., A numerical study of oscillating peristaltic flow of generalized Maxwell viscoelastic fluids through a porous medium, Transport in Porous Media, 95: 337–348, 2012, doi: 10.1007/s11242-012-0046-5.

Bég O.A., Prasad V.R., Vasu B., Numerical study of mixed bioconvection in porous media saturated with nanofluid and containing oxytactic micro-organisms, Journal of Mechanics Medicine and Biology, 13(4): 1350067, 2013, doi: 10.1142/S021951941350067X.

Caltagirone J.P., Thermoconvective instabilities in a porous medium bounded by two concentric horizontal cylinders, Journal of Fluid Mechanics, 76(2): 337–362, 1976, doi: 10.1017/S0022112076000669.

Kuznetsov A.V., Nield D.A., The onset of double-diffusive nanofluid convection in a layer of a saturated porous medium, Transport in Porous Media, 85: 941–951, 2010, doi: 10.1007/s11242-010-9600-1.

Kuznetsov A.V., Nield D.A., The Cheng–Minkowycz problem for natural convective boundary layer flow in a porous medium saturated by a nanofluid: a revised model, International Journal of Heat and Mass Transfer, 65: 682–685, 2013, doi: 10.1016/j.ijheatmasstransfer.2013.06.054.

Nield D.A., Kuznetsov A.V., The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid, International Journal of Heat and Mass Transfer, 52(25–26): 5792–5795, 2009, doi: 10.1016/j.ijheatmasstransfer.2009.07.024.

Nield D.A., Kuznetsov A.V., Thermal instability in a porous medium layer saturated by a nanofluid: a revised model, International Journal of Heat and Mass Transfer, 68: 211–214, 2014, doi: 10.1016/j.ijheatmasstransfer.2013.09.026.

Dogonchi A.S., Seyyedi S.M., Hashemi-Tilehnoee M., Chamkha A.J., Ganji D.D., Investigation of natural convection of magnetic nanofluid in an enclosure with a porous medium considering Brownian motion, Case Studies in Thermal Engineering, 14: 100502, 2019, doi: 10.1016/j.csite.2019.100502.

Sivasankaran S., Bhuvaneswari M., Alzahrani A.K., Numerical simulation on convection of non-Newtonian fluid in a porous enclosure with non-uniform heating and thermal radiation, Alexandria Engineering Journal, 59: 3315–3323, 2020, doi: 10.1016/j.aej.2020.04.045.

Seyyedi S.M., Hashemi-Tilehnoee M., Sharifpur M., Impact of fusion temperature on hydrothermal features of flow within an annulus loaded with nanoencapsulated phase change materials (NEPCMs) during natural convection process, Mathematical Problems in Engineering, 2021: Article ID 4276894, 2021, doi: 10.1155/2021/4276894.

Hashemi-Tilehnoee M., Dogonchi, A.S., Seyyedi S.M., Chamkha A.J., Ganji D.D., Magnetohydrodynamic natural convection and entropy generation analyses inside a nanofluid-filled incinerator-shaped porous cavity with wavy heater block, Journal of Thermal Analysis and Calorimetry, 141(5): 2033–2045, 2020, doi: 10.1007/s10973-019-09220-6.

Raizah Z.A.S., Ahmed S.E., Aly A.M., ISPH simulations of natural convection flow in E-enclosure filled with a nanofluid including homogeneous/heterogeneous porous media and solid particles, International Journal of Heat and Mass Transfer, 160: 120153, 2020, doi: 10.1016/j.ijheatmasstransfer.2020.120153.

Seyyedi S.M., Hashemi-Tilehnoee M., Sharifpur M., Effect of inclined magnetic field on the entropy generation in an annulus filled with NEPCM suspension, Mathematical Problems in Engineering, 2021: Article ID 8103300, 2021, doi: 10.1155/2021/8103300.

Hashemi-Tilehnoee M., Dogonchi A.S., Seyyedi S.M., Sharifpur M., Magneto-fluid dynamic and second law analysis in a hot porous cavity filled by nanofluid and nanoencapsulated phase change material suspension with different layout of cooling channels, Journal of Energy Storage, 31: 101720, 2020, doi: 10.1016/j.est.2020.101720.

Seyyedi S.M,. On the entropy generation for a porous enclosure subject to a magnetic field: different orientations of cardioid geometry, International Communications in Heat and Mass Transfer, 116: 104712, 2020, doi: 10.1016/j.icheatmasstransfer.2020.104712.

Sun Q., Pop I., Free convection in a triangle cavity filled with a porous medium saturated with nanofluids with flush mounted heater on the wall, International Journal of Thermal Sciences, 50(11): 2141–2153, 2011, doi: 10.1016/j.ijthermalsci.2011.06.005.

Liu W., Shahsavar A., Barzinjy A.A., Al-Rashed A.A.A.A., Afrand M., Natural convection and entropy generation of a nanofluid in two connected inclined triangular enclosures under magnetic field effects, International Communications in Heat and Mass Transfer, 108: 104309, 2019, doi: 10.1016/j.icheatmasstransfer.2019.104309.

Brinkman H.C., The viscosity of concentrated suspensions and solutions, The Journal of Chemical Physics, 20(4): 571–581, 1952, doi: 10.1063/1.1700493.

Khanafer K., Vafai K., Lightstone M., Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, International Journal of Heat and Mass Transfer, 46(19): 3639–3653, 2003, doi: 10.1016/S0017-9310(03)00156-X.

Oztop H.F., Abu-Nada E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, International Journal of Heat and Fluid Flow, 29(5): 1326–1336, 2008, doi: 10.1016/j.ijheatfluidflow.2008.04.009.

Abu-Nada E., Oztop H.F., Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid, International Journal of Heat and Fluid Flow, 30(4): 669–678, 2009, doi: 10.1016/j.ijheatfluidflow.2009.02.001.

Muthtamilselvan M., Kandaswamy P., Lee J., Heat transfer enhancement of copper-water nanofluids in a lid-driven enclosure, Communications in Nonlinear Science and Numerical Simulation, 15: 1501–1510, 2010, doi: 10.1016/j.cnsns.2009.06.015.

Nield D.A., Bejan A., Convection in Porous Media, 4th ed., Springer, New York, 2013.

Yu W., France D.M., Routbort J.L., Choi S.U.S., Review and comparison of nanofluid thermal conductivity and heat transfer enhancements, Heat Transfer Engineering, 29(5): 432–460, 2008, doi: 10.1080/01457630701850851.

Venkatadri K., B´eg O.A., Rajarajeswari P., Ramachandra Prasad V., Subbarao A., Hidayathulla Khan B.Md., Numerical simulation and energy flux vector visualization of radiative-convection heat transfer in a porous triangular enclosure, Journal of Porous Media, 23(12): 1187–1199, 2020, doi: 10.1615/JPorMedia.2020033653.

Bég O.A., Venkatadri K., Prasad V.R., B´eg T.A., Kadir A., Leonard H.J., Numerical simulation of hydromagnetic Marangoni convection flow in a Darcian porous semiconductor melt enclosure with buoyancy and heat generation effects, Materials Science and Engineering: B, 261: 114722, 2020, doi: 10.1016/j.mseb.2020.114722.

Venkatadri K., Bég O.A., Rajarajeswari P., Ramachandra Prasad V., Numerical simulation of thermal radiation influence on natural convection in a trapezoidal enclosure: Heat flow visualization through energy flux vectors, International Journal of Mechanical Sciences, 171: 105391, 2020, doi: 10.1016/j.ijmecsci.2019.105391.

Venkatadri K., Abdul Gaffar S., Rajarajeswari P., Ramachandra Prasad V., Bég O.A., Hidayathulla Khan B.Md., Melting heat transfer analysis of electrically conducting nanofluid flow over an exponentially shrinking/stretching porous sheet with radiative heat flux under a magnetic field, Heat Transfer, 49(8): 4281–4303, 2020, doi: 10.1002/htj.21827.

Venkatadri K., Abdul Gaffar S., Suryanarayana Reddy M., Ramachandra Prasad V., Hidayathulla Khan B.Md., Beg O.A., Melting heat transfer on magnetohydrodynamics buoyancy convection in an enclosure: A numerical study, Journal of Applied and Computational Mechanics, 6(1): 52–62, 2020, doi: 10.22055/JACM.2019.28761.1504.

Chamkha A.J., Ismael M.A., Conjugate heat transfer in a porous cavity filled with nanofluids and heated by a triangular thick wall, International Journal of Thermal Sciences, 67: 135–151 2013, doi: 10.1016/j.ijthermalsci.2012.12.002.

Tiwari R.K., Das M.K., Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, International Journal of Heat and Mass Transfer, 50(9–10): 2002–2018, 2007, doi: 10.1016/j.ijheatmasstransfer.2006.09.034.

DOI: 10.24423/EngTrans.1285.20221004