Entropy Production Due to Conjugate Natural Convection in a Nanofluid-Filled Enclosure With a Stepped Wall
Abstract
The main aim of this paper is to improve the heat transfer in a square cavity with a body at the left wall filled with a Al2O3/water nanofluid for different geometries. Numerous simulation experiments are conducted. A relative temperature is maintained at the vertical and top horizontal walls while the bottom wall is warm. The finite volume approach is considered to resolve the equations governing the thermal transfer flow in the physical domain based on the SIMPLER algorithm. In this study, different values of the following parameters are considered: Rayleigh number (104 ≤ Ra ≤ 105) and solid volume fraction (0 ≤ ϕ ≤ 0.1) of nanoparticles (NPs). Parameters, such as the Rayleigh (Ra) and Bejan (Be) numbers, thermal conductivity, body’s dimensions, and NPs volume fraction, which directly affect the entropy generation and heat transfer rate, are studied in a particular way. The obtained results show that entropy generation goes ahead with the Ra increase and inverse to the solid volume fraction increase. One can notice that the heat transfer has a proportional relation with ϕ and Ra.
Keywords:
entropy generation, natural convection, nanofluids, cavity, wallReferences
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31. Aminossadati S.M., Ghasemi B., Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure, European Journal of Mechanics – B/Fluids, 28(5): 630–640, 2009, https://doi.org/10.1016/j.euromechflu.2009.05.006 https://doi.org/10.1016/j.euromechflu.2009.05.006
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33. Shafiq A., Mebarek-Oudina F., Sindhu T.N., Rassol G., Sensitivity analysis for Walters-B nanoliquid flow over a radiative Riga surface by RSM, Scientia Iranica, 29(3): 1236–1249, 2022, https://doi.org/10.24200/sci.2021.58293.5662
34. Reddy Y.D., Mebarek-Oudina F., Goud B.S., Ismail A.I., Radiation velocity and thermal slips effect toward MHD boundary layer flow through heat and mass transport of Williamson nanofluid with porous medium, Arabian Journal for Science and Engineering, 47(12): 16355–16369, 2022, https://doi.org/10.1007/s13369-022-06825-2
35. Dhif K., Mebarek-Oudina F., Chouf S., Vaidya H., Chamkha A.J., Thermal analysis of the solar collector cum storage system using a hybrid-nanofluids, Journal of Nanofluids, 10(4): 616–626, 2021, https://doi.org/10.1166/jon.2021.1807
36. Mebarek-Oudina F., Numerical modeling of the hydrodynamic stability in vertical annulus with heat source of different lengths, Engineering Science and Technology, an International Journal, 20(4): 1324–1333, 2017, https://doi.org/10.1016/j.jestch.2017.08.003
37. Mebarek-Oudina F., Convective heat transfer of Titania nanofluids of different base fluids in cylindrical annulus with discrete heat source, Heat Transfer – Asian Research, 48(1): 135–147, 2019, https://doi.org/10.1002/htj.21375
38. Chabani I., Mebarek-Oudina F., Vaidya H., Ismail A.I., Numerical analysis of magnetic hybrid nano-fluid natural convective flow in an adjusted porous trapezoidal enclosure, Journal of Magnetism and Magnetic Materials, 564(2): 170142, 2022, https://doi.org/10.1016/j.jmmm.2022.170142
39. Marzougui S., Mebarek-Oudina F., Magherbi M., Mchirgui A., Entropy generation and heat transport of Cu-water nanoliquid in porous lid-driven cavity through magnetic field, International Journal of Numerical Methods for Heat & Fluid Flow, 32(6): 2047–2069, 2022, doi: /10.1108/HFF-04-2021-0288.
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2. Zhang Y., Li L., Ma H.B., Yang M., Effect of Brownian and thermophoretic diffusions of nanoparticles on nonequilibrium heat conduction in a nanofluid layer with periodic heat flux, Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology, 56(4): 325–341, 2009, https://doi.org/10.1080/10407780903163876
3. Jou R.-Y., Tzeng S.-C., Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures, International Communications in Heat and Mass Transfer, 33(6): 727–736, 2006, https://doi.org/10.1016/j.Icheatmasstransfer.2006.02.016
4. Heris Z.S., Esfahany M.N., Etemad G., Numerical investigation of nanofluid laminar convection heat transfer through a circular tube, Numerical Heat Transfer, Part A:Applications: An International Journal of Computation and Methodology, 52(11): 1043–1058, 2007, https://doi.org/10.1080/10407780701364411
5. Abu-Nada E., Investigation of entropy generation over a backward facing step under bleeding conditions, Energy Conversion and Management, 49(11): 3237–3242, 2008, https://doi.org/10.1016/j.enconman.2007.10.031
6. Kim S.S., Baek S.W., Radiation affected compressible turbulent flow over a backward facing step, International Journal of Heat and Mass Transfer, 39(16): 3325–3332, 1996, https://doi.org/10.1016/0017-9310%2896%2900046-4
7. Guerrero J.S.P., Cotta R.M., Benchmark integral transform results for flow over a backward-facing step, Computers & Fluids, 25(5): 527–540, 1996, https://doi.org/10.1016/0045-7930%2896%2900005-9
8. Benard N., Garrido P.S., Bonnet J.P., Moreau E., Control of the coherent structure dynamics downstream of a backward facing step by DBD plasma actuator, International Journal of Heat and Fluid Flow, 61(Part A): 158–173, 2016, https://doi.org/10.1016/j.ijheatfluidflow.2016.04.009
9. Chang T.S., Tsay Y.L., Natural convection heat transfer in an enclosure with a heated backward step, International Journal of Heat and Mass Transfer, 44(20): 3963–3971, 2001, https://doi.org/10.1016/S0017-9310%2801%2900035-7
10. Ramšak M., Conjugate heat transfer of backward-facing step flow: A benchmark problem revisited, International Journal of Heat and Mass Transfer, 84: 791–799, 2015, https://doi.org/10.1016/j.ijheatmasstransfer.2015.01.067
11. Niemann M., Fröhlich J., Buoyancy-affected backward-facing step flow with heat transfer at low Prandtl number, International Journal of Heat and Mass Transfer, 101: 1237–1250, 2016, https://doi.org/10.1016/j.ijheatmasstransfer.2016.05.137 https://doi.org/10.1016/j.ijheatmasstransfer.2016.05.137
12. Xu F., Gao Z., Ming X., Xia L., Wang Y., Sun W., Ma R., The optimization for the backward-facing step flow control with synthetic jet based on experiment, Experimental Thermal and Fluid Science, 64: 94–107, 2015, https://doi.org/10.1016/j.expthermflusci.2015.02.014
13. Kherbeet A.S., Mohammed H.A., Salman B.H., Ahmed H.E., Alawi O.A., Rashidi M.M., Experimental study of nanofluid flow and heat transfer over microscale backward- and forward-facing steps, Experimental Thermal and Fluid Science, 65: 13–21, 2015, https://doi.org/10.1016/j.expthermflusci.2015.02.023
14. Mramor K., Vertnik R., Šarler B., Simulation of laminar backward facing step flow under magnetic field with explicit local radial basis function collocation method, Engineering Analysis with Boundary Elements, 49: 37–47, 2014, https://doi.org/10.1016/j.enganabound.2014.04.013
15. Statnikov V., Bolgar I., Scharnowski S., Meinke M., Kähler C.J., Schrӧder W., Analysis of characteristic wake flow modes on a generic transonic backward-facing step configuration, European Journal of Mechanics – B/Fluids, 59: 124–134, 2016, https://doi.org/10.1016/j.euromechflu.2016.05.008
16. Aghakhani S., Pordanjani A.H., Afrand M., Sharifpur M., Meyer J.P., Natural convective heat transfer and entropy generation of alumina/water nanofluid in a tilted enclosure with an elliptic constant temperature: applying magnetic field and radiation effects, International Journal of Mechanical Sciences, 174: 105470, 2020, https://doi.org/10.1016/j.ijmecsci.2020.105470
17. Alnaqi A.A., Aghakhani S., Pordanjani A.H., Bakhtiari R., Asadi A., Tran M.-D., Effects of magnetic field on the convective heat transfer rate and entropy generation of a nanofluid in an inclined square cavity equipped with a conductor fin: Considering the radiation effect, International Journal of Heat and Mass Transfer, 133: 256–267, 2019, https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.110
18. Baghsaz S., Rezanejad S., Moghimi M., Numerical investigation of transient natural convection and entropy generation analysis in a porous cavity filled with nanofluid considering nanoparticles sedimentation, Journal of Molecular Liquids, 279: 327–341, 2019, https://doi.org/10.1016/j.molliq.2019.01.117
19. Bezi S., Souayeh B., Cheikh N.B., Beya B.B., Numerical simulation of entropy generation due to unsteady natural convection in a semi-annular enclosure filled with nanofluid, International Journal of Heat and Mass Transfer, 124: 841–859, 2018, https://doi.org/10.1016/j.ijheatmasstransfer.2018.03.109
20. Bondareva N.S., Sheremet M.A., Oztop H.F., Hamdeh N.A., Entropy generation due to natural convection of a nanofluid in a partially open triangular cavity, Advanced Powder Technology, 28(1): 244–255, 2017, https://doi.org/10.1016/j.apt.2016.09.030
21. Cho C.-C., Heat transfer and entropy generation of mixed convection flow in Cu-water nanofluid-filled lid-driven cavity with wavy surface, International Journal of Heat and Mass Transfer, 119: 163–174, 2018, https://doi.org/10.1016/j.ijheatmasstransfer.2017.11.090
22. Dogonchia A.S., Seyyedib S.M., Tilehnoeea M.H., Chamkha A.J., Ganji D.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, https://doi.org/10.1016/j.csite.2019.100502
23. Dormohammadi R., Farzaneh-Gord M., Ebrahimi-Moghadam A., Ahmadi M.H., Heat transfer and entropy generation of the nanofluid flow inside sinusoidal wavy channels, Journal of Molecular Liquids, 269: 229–240, 2018, https://doi.org/10.1016/j.molliq.2018.07.119
24. Hashim I., Alsabery A.I., Sheremet M.A., Chamkha A.J, Numerical investigation of natural convection of Al2O3-water nanofluid in a wavy cavity with conductive inner block using Buongiorno’s two-phase model, Advanced Powder Technology, 30(2): 399–414, 2019, https://doi.org/10.1016/j.apt.2018.11.017
25. Khakrah H., Hooshmand P., Jamalabadi M.Y.A., Azar S., Thermal lattice Boltzmann simulation of natural convection in a multi-pipe sinusoidal-wall cavity filled with Al2O3-EG nanofluid, Powder Technology, 356: 240–252, 2019, https://doi.org/10.1016/j.powtec.2019.08.013
26. Rahimi A., Sepehr M., Lariche M.J., Kasaeipoor A., Malekshah E.H., Kolsi L., Entropy generation analysis and heatline visualization of free convection in nanofluid (KKL model-based)-filled cavity including internal active fins using lattice Boltzmann method, Computers & Mathematics with Applications, 75(5): 1814–1830, 2018, https://doi.org/10.1016/j.camwa.2017.12.008
27. Rahimi A., Sepehr M., Lariche M.J., Mesbah M., Kasaeipoor A., Malekshah E.H., Analysis of natural convection in nanofluid-filled H-shaped cavity by entropy generation and heatline visualization using lattice Boltzmann method, Physica E: Low-dimensional Systems and Nanostructures, 97: 347–362, 2018, https://doi.org/10.1016/j.physe.2017.12.003
28. Selimefendigil F., Öztop H.F., Effects of conductive curved partition and magnetic field on natural convection and entropy generation in an inclined cavity filled with nanofluid, Physica A: Statistical Mechanics and its apllications, 540: 123004, 2020, https://doi.org/10.1016/j.physa.2019.123004
29. Sheikholeslami M., Öztop H.F., MHD, free convection of nanofluid in a cavity with sinusoidal walls by using CVFEM, Chinese Journal of Physics, 55(6): 2291–2304, 2017, https://doi.org/10.1016/j.cjph.2017.09.006
30. Sheremet M.A., Pop I., Öztop H.F., Hamdeh N.A., Natural convective heat transfer and nanofluid flow in a cavity with top wavy wall and corner heater, Journal of Hydrodynamics, 28(5):873–885, 2016, https://doi.org/10.1016/S1001-6058%2816%2960688-1
31. Aminossadati S.M., Ghasemi B., Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure, European Journal of Mechanics – B/Fluids, 28(5): 630–640, 2009, https://doi.org/10.1016/j.euromechflu.2009.05.006 https://doi.org/10.1016/j.euromechflu.2009.05.006
32. Hassan M., Mebarek-Oudina F., Faisal A., Ghafar A., Ismail A.I., Thermal energy and mass transport of shear thinning fluid under effects of low to high shear rate viscosity, International Journal of Thermofluids, 15: 100176, 2022, https://doi.org/10.1016/j.ijft.2022.100176
33. Shafiq A., Mebarek-Oudina F., Sindhu T.N., Rassol G., Sensitivity analysis for Walters-B nanoliquid flow over a radiative Riga surface by RSM, Scientia Iranica, 29(3): 1236–1249, 2022, https://doi.org/10.24200/sci.2021.58293.5662
34. Reddy Y.D., Mebarek-Oudina F., Goud B.S., Ismail A.I., Radiation velocity and thermal slips effect toward MHD boundary layer flow through heat and mass transport of Williamson nanofluid with porous medium, Arabian Journal for Science and Engineering, 47(12): 16355–16369, 2022, https://doi.org/10.1007/s13369-022-06825-2
35. Dhif K., Mebarek-Oudina F., Chouf S., Vaidya H., Chamkha A.J., Thermal analysis of the solar collector cum storage system using a hybrid-nanofluids, Journal of Nanofluids, 10(4): 616–626, 2021, https://doi.org/10.1166/jon.2021.1807
36. Mebarek-Oudina F., Numerical modeling of the hydrodynamic stability in vertical annulus with heat source of different lengths, Engineering Science and Technology, an International Journal, 20(4): 1324–1333, 2017, https://doi.org/10.1016/j.jestch.2017.08.003
37. Mebarek-Oudina F., Convective heat transfer of Titania nanofluids of different base fluids in cylindrical annulus with discrete heat source, Heat Transfer – Asian Research, 48(1): 135–147, 2019, https://doi.org/10.1002/htj.21375
38. Chabani I., Mebarek-Oudina F., Vaidya H., Ismail A.I., Numerical analysis of magnetic hybrid nano-fluid natural convective flow in an adjusted porous trapezoidal enclosure, Journal of Magnetism and Magnetic Materials, 564(2): 170142, 2022, https://doi.org/10.1016/j.jmmm.2022.170142
39. Marzougui S., Mebarek-Oudina F., Magherbi M., Mchirgui A., Entropy generation and heat transport of Cu-water nanoliquid in porous lid-driven cavity through magnetic field, International Journal of Numerical Methods for Heat & Fluid Flow, 32(6): 2047–2069, 2022, doi: /10.1108/HFF-04-2021-0288.
40. Brinkman H.C., The viscosity of concentrated suspensions and solution, The Journal of Chemical Physics, 20(4): 571–581, 1952, https://doi.org/10.1063/1.1700493
41. Maxwell J., A Treatise on Electricity and Magnetism, 2nd ed., Oxford University Press, Cambridge, UK, 1904.
42. Patankar S.V., Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.
