Abstract
The entropy generation from convective hybrid nanofluid flow within the odd-shaped geometries using the finite element method is examined is examined. The flow domain is filled by variable porosity and permeability porous media. Also, the thermal conductivity is assumed to be heterogeneous, and the Brinkman extended non-Darcy model is applied to simulate the porous medium. The geometry is considered partially/fully filled by the porous medium and four cases are assumed, namely, only the horizontal channel is a porous (case 1), only the vertical channel is a porous (case 2), the entire domain is a porous (case 3) and the entire domain is a non-porous (case 4). Different designs of the odd-geometry are taken into account based on the aspect ratio. The characteristic-based split (CBS) based on semi-implicit (SI) scheme is used to treat the governing equations. Simulations are carried out for various values of the maximum Darcy parameter \({\text{Da}}_{\hbox{max} }\), alumina-copper volume fraction \(\phi_{Al} , \phi_{Cu}\) and different conditions of the porous domain. It is noted that the case of the heterogeneous thermal conductivity maximizes the irreversibility from heat transfer and total entropy generation. Also, a weakness in values of the average Bejan number is obtained as the Rayleigh number is grown, regardless the porous conditions.
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References
Ahmed, S.E.: FEM-CBS algorithm for convective transport of nanofluids in inclined enclosures filled with anisotropic non-Darcy porous media using LTNEM. Int. J. Numer. Meth. Heat Fluid Flow (2020). https://doi.org/10.1108/HFF-01-2020-0042
Rashed, Z.Z.; Ahmed, Sameh E.; Raizah, Z.A.S.: Thermal dispersion and buongiorno’s nanofluid model effects on natural convection in an inclined rectangular enclosure partially filled with heat generating porous medium. J. Porous Media 23(4), 341–361 (2020)
Ahmed, S. E.: Non-Darcian natural convection of a nanofluid due to triangular fins within trapezoidal enclosures partially filled with a thermal non-equilibrium porous layer. J. Thermal Anal. Calorim. (2020)
Ahmed, S.E.; Mahdy, A.: Laminar MHD natural convection of nanofluid containing gyrotactic microorganisms over vertical wavy surface saturated non-Darcian porous media. Appl. Math. Mech. 37, 471–484 (2016)
Raizah, Z.A.S.; Aly, A.M.; Ahmed, S.E.: Natural convection flow of a power-law non-Newtonian nanofluid in inclined open shallow cavities filled with porous media. Int. J. Mech. Sci. 140, 376–393 (2018)
Ahmed, S.E.; Aly, A.M.: Mixed convection in a nanofluid-filled sloshing porous cavity including inner heated rose. J. Thermal Anal. Calorim. (2020)
Al-Weheibi, S.M.; Rahman, M.M.; Saghir, M.Z.: Impacts of variable porosity and variable permeability on the thermal augmentation of Cu–H2O nanofluid-drenched porous trapezoidal enclosure considering thermal nonequilibrium model. Arabian J. Sci. Eng. 45(2), 1237–1251 (2020)
Abelman, S.; Parsa, A.B.; Sayehvand, H.-O.: Nanofluid flow and heat transfer in a Brinkman porous channel with variable porosity. Quaestiones Mathe. 41(4), 449–467 (2018)
Saif, R.S.; Muhammad, T.; Sadia, H.: Significance of inclined magnetic field in Darcy-Forchheimer flow with variable porosity and thermal conductivity. Phys. A 551, 124067 (2020)
Nithiarasu, P.; Seetharamu, K.N.; Sundararajan, T.: Natural convective heat transfer in a fluid saturated variable porosity medium. Int. J. Heat Mass Transf. 40(16), 3955–3967 (1997)
S.M.M. El-Kabeir, M.A. El-Hakiem, A.M. Rashad, Natural convection from a permeable sphere embedded in a variable porosity porous medium due to thermal dispersion. Nonlinear Anal. Model. Control, vol 12, no 3, (2007).
Amiri, A.; Vafai, K.: Analysis of dispersion effects and non-thermal equilibrium, non-Darcian, variable porosity incompressible flow through porous media. Int. J. Heat Mass Transf. 37(6), 939–954 (1994)
Raizah, Z.: Mixed convection in a lid-driven cavity filled by a nanofluid with an inside circular cylinder. J. Nanofluids 6, 927–939 (2017)
Ahmed, S.E.: Natural convection of dusty hybrid nanofluids in diverging-converging cavities including volumetric heat sources. J. Therm. Sci. Eng. Appl. pp. 1–17, (2020)
Ahmed, S.E.: Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature. Appl. Math. Mech. 38(8), 1171–1180 (2017)
Alqarni, M.; Tabassum, R.; Malik, M.; Mehmood, R.: Shape effects of molybdenum disulfide (nm) micro-rotating particles in crosswise transport of hydrogen oxide:(mos2–h2o) nano polymer gel. Phys. Scr. 95(3), 035002 (2020)
Sundar, L.S.; Singh, M.K.; Sousa, A.C.M.: Enhanced heat transfer and friction factor of MWCNT–Fe3O4/water hybrid nanofluids. Int. Commun. Heat Mass Transf. 52, 73–83 (2014)
Sarkar, J.; Ghosh, P.; Adil, A.: A review on hybrid nanofluids: recent research, development and applications. Renew. Sustain. Energy Rev. 43, 164–177 (2015)
Kalidasan, K.; RajeshKanna, P.: Natural convection on an open square cavity containing diagonally placed heaters and adiabatic square block and filled with hybrid nanofluid of nanodiamond—cobalt oxide/water. Int. Commun. Heat Mass Transf. 81, 64–71 (2017)
Ashorynejad, H.R.; Shahriari, A.: MHD natural convection of hybrid nanofluid in an open wavy cavity. Results Phys. 9, 440–455 (2018)
Mansour, M.; Siddiqa, S.; Gorla, R.S.R.; Rashad, A.: Effects of heat source and sink on entropy generation and MHD natural convection of Al2O3-Cu/water hybrid nanofluid filled with square porous cavity. Thermal Sci. Eng. Progress 6, 57–71 (2018)
Raizah, Z.A.: Natural convection of dusty hybrid nanofluids in an enclosure including two oriented heated fins. Appl. Sci. 9, 2673 (2019)
Kadhim, H.T.; Jabbar, F.A.; Rona, A.: Cu-Al2O3 hybrid nanofluid natural convection in an inclined enclosure with wavy walls partially layered by porous medium. Int. J. Mech. Sci. 186, 105889 (2020)
Wang, B.; Shih, T.-M.; Huang, J.: Enhancing and attenuating heat transfer characteristics for circulating flows of nanofluids within rectangular enclosures. Int. Commun. Heat Mass Transfer 117, 104800 (2020)
Saha, S.K.: Magnetohydrodynamic buoyancy driven al2o3-water nanofluid flow in a differentially heated trapezoidal enclosure with a cylindrical barrier. Int. Commun. Heat Mass Transf. 114, 104593 (2020)
Keramat, F.; Dehghan, P.; Mofarahi, M.; Lee, C.-H.: Numerical analysis of natural convection of alumina–water nanofluid in h-shaped enclosure with a v-shaped baffle. J. Taiwan Institute Chem. Eng. 111, 63–72 (2020)
Yan, S.-R.; Hajatzadeh Pordanjani, A.; Aghakhani, S.; Shahsavar Goldanlou, A.; Afrand, M.: Managment of natural convection of nanofluids inside a square enclosure by different nano powder shapes in presence of fins with different shapes and magnetic field effect. Adv. Powder Technol. 31(7), 2759–2777 (2020)
Kefayati, G.: Heat transfer and entropy generation of natural convection on non-Newtonian nanofluids in a porous cavity. Powder Technol. 299, 127–149 (2016)
Kefayati, G.: Simulation of natural convection and entropy generation of non-Newtonian nanofluid in a porous cavity using Buongiorno’s mathematical model. Int. J. Heat Mass Transf. 112, 709–744 (2017)
Siavashi, M.; Yousofvand, R.; Rezanejad, S.: Nanofluid and porous fins effect on natural convection and entropy generation of flow inside a cavity. Adv. Powder Technol. 29, 142–156 (2018)
Goqo, S.P.; Mondal, H.; Sibanda, P.; Motsa, S.S.: A multivariate spectral quasilinearisation method for entropy generation in a square cavity filled with porous medium saturated by nanofluid. Case Stud. Thermal Eng. 14, 100415 (2019)
Rahimi, A.; Kasaeipoor, A.; Malekshah, E.H.; Amiri, A.: Natural convection analysis employing entropy generation and heatline visualization in a hollow L-shaped cavity filled with nanofluid using lattice Boltzmann method- experimental thermo-physical properties. Phys. E 97, 82–97 (2018)
Wang, S.; Nan, C.; Qiao, J.; Huang, D.; Nabipour, N.; Ross, D.: Free convection and entropy generation in a nanofluid-filled star-ellipse annulus using lattice Boltzmann method supported by immersed boundary method. Int. J. Mech. Sci. 176, 105526 (2020)
Parvin, S.; Chamkha, A.J.: An analysis on free convection flow, heat transfer and entropy generation in an odd-shaped cavity filled with nanofluid. Int. Commun. Heat Mass Transf. 54, 8–17 (2014)
Amiri, A.; Vafai, K.: Analysis of dispersion effects and non-thermal equilibrium, non-Darcian, variable porosity incompressible flow through porous media. Int. J. Heat Mass Transf. 37, 939–954 (1994)
Al-Weheibi, S.M.; Rahman, M.M.; Saghir, M.Z.: Impacts of variable porosity and variable permeability on the thermal augmentation of Cu–H2O nanofluid-drenched porous trapezoidal enclosure considering thermal nonequilibrium model. Arab. J. Sci. Eng. 45, 1237–1251 (2020)
Ergun, S.: Fluid flow through packed columns. Chem. Eng. Progress 48(2), 89–94 (1952)
Cheng, P.; Hsu, C.T.: Fully developed, forced convective flow through an annular packed-sphere bed with wall effects. Int. J. Heat Mass Transfer 29, 1843–1853 (1986)
Ahmed, S.E.: Caputo fractional convective flow in an inclined wavy vented cavity filled with a porous medium using Al2O3-Cu hybrid nanofluids. Int. Commun. Heat Mass Transfer 116, 104690 (2020)
Lewis, R.W.; Nithiarasu, P.; Seetharamu, K.N.: Fundamentals of the Finite Element Method for Heat and Fluid Flow, 1st edn. Wiley, Hoboken (2004)
Ilis, G.G.; Mobedi, M.; Sunden, B.: Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls. Int. Commun. Heat Mass Transf. 35, 696–703 (2008)
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The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through General Research Project under grant number (G.R.P/4/42).
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Ahmed, S.E., Raizah, Z.A.S. & Aly, A.M. Impacts of the Variable Properties of a Porous Medium on the Entropy Analysis Within Odd-Shaped Enclosures Filled by Hybrid Nanofluids. Arab J Sci Eng 46, 7379–7398 (2021). https://doi.org/10.1007/s13369-020-05218-7
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DOI: https://doi.org/10.1007/s13369-020-05218-7