Optimization of Heat Transfer in MHD Mixed Convection Hybrid Nanofluid Flow Over a Shrinking Plate Using Response Surface Methodology.
DOI:
https://doi.org/10.66901/4bjhz792Keywords:
Hybrid nanofluid; mixed convection; nanoparticle shape; Response Surface MethodologyAbstract
This study focuses on optimizing the heat transfer performance of magnetohydrodynamic (MHD) mixed convection flow of a hybrid nanofluid (MgO–Ag/H₂O) over a shrinking plate, with a focus on nanoparticle shape effects. The governing equations, which are based on boundary layer theory, are reduced to a system of nonlinear ordinary differential equations through similarity transformations and are computed numerically for this purpose. The governing partial differential equations are first reduced to ordinary differential equations using similarity transformations. The resulting ODEs are then solved numerically using the bvp4c built-in solver in MATLAB software. The findings of this study reveal significant insights into the influence of nanoparticle shapes, MgO concentration, and magnetic parameters on various flow and heat transfer characteristics. It is observed that cylindrical nanoparticles exhibit higher skin friction and Nusselt numbers compared to brick and spherical nanoparticles. Moreover, an increase in MgO concentration leads to higher skin friction but lower Nusselt numbers. For opposing flow, a decrease in the magnetic parameter correlates with reduced skin friction and Nusselt numbers, while an increase in the magnetic parameter during assisting flow results in higher skin friction and Nusselt numbers. Additionally, spherical-shaped nanoparticles demonstrate the highest velocity and temperature profiles, whereas an increase in MgO concentration causes a reduction in velocity and temperature profiles. Using Response Surface Methodology (RSM), the optimized combination of Ag and MgO concentrations and magnetic parameters is determined to achieve the highest skin friction and Nusselt numbers. The desirability of 99.95% and 99.98% is achieved for skin friction and Nusselt numbers, respectively, highlighting the effectiveness of the proposed approach in optimizing flow and heat transfer characteristics under different flow conditions.
References
[1] Mahmood, Z., Rafique, K., Khan, U., Adnan, El-Rahman, M.A, & Alharbi, R. (2024). Analysis of mixed convective stagnation point flow of hybrid nanofluid over sheet with variable thermal conductivity and slip conditions: A model-based study, International Journal of Heat and Fluid Flow, 106 (2024), 109296. https://doi.org/10.1016/j.ijheatfluidflow.2024.109296
[2] Jamrus, F.N., Waini, I., Khan, U., & Ishak, A. (2024). Effects of magnetohydrodynamics and velocity slip on mixed convective flow of thermally stratified ternary hybrid nanofluid over a stretching/shrinking sheet, Case Studies in Thermal Engineering, 55, 104161. Case Studies in Thermal Engineering, 55, 104161. https://doi.org/10.1016/j.csite.2024.104161
[3] Ummeda P., & Ontela, S. (2023). Irreversibility analysis of magnetohydrodynamic (MHD) mixed convection flow of viscoelastic hybrid nanofluid flow in a channel, Chemical Engineering Journal Advances, 16, 100566. https://doi.org/10.1016/j.ceja.2023.100566
[4] Paul, A., Sarma, N., & Patgiri, B.(2023). Mixed convection of shear-thinning hybrid nanofluid flow across a radiative unsteady cone with suction and slip effect, Materials Today Communications, 37, 107522. https://doi.org/10.1016/j.mtcomm.2023.107522
[5] Yadav, S., Yadav, S., & Yadav, P.K. (2024). The mixed convection thermally radiated hybrid nanofluid flow through an inclined permeable shrinking plate with slip condition and inclined magnetic effect, Chinese Journal of Physics, Doi: 10.1016/j.cjph.2023.12.039. https://doi.org/10.1016/j.cjph.2023.12.039
[6] Rajarathinam, M., Akermi, M., Khan, M.I., & Nithyadevi, N. (2024). MHD mixed convection heat transfer of copper water nanofluid in an inclined porous cavity having isothermal solid block, Journal of Magnetism and Magnetic Materials, 593, 171845. https://doi.org/10.1016/j.jmmm.2024.171845
[7] Abood, F.A., Yaseen, S. J., Mohammed, I. G., Homad, R. Z., & Mohammed, H. I. (2024) Enhancing thermal performance in a magnetized square cavity: Novel insights from mixed convection of Ag-MgO nanofluid around a rotating cylinder, International Journal of Thermofluids, 22, 100630. https://doi.org/10.1016/j.ijft.2024.100630
[8] Zhang, R., Zaydan, M., Alshehri, M., Raju, C. S. K., Wakif, A., & Shah, N. A. (2024). Further insights into mixed convective boundary layer flows of internally heated Jeffery nanofluids: Stefan’s blowing case study with convective heating and thermal radiation impressions, Case Studies in Thermal Engineering, 55, 104121. https://doi.org/10.1016/j.csite.2024.104121
[9] Hameed, R. H., Al-Srayyih, B. M., Al-Amir, Q. R., Hamzah, H. K., Ali, F. H, & Alahmer, A. (2024). Magnetic field effect on mixed convection flow inside an oval-shaped annulus enclosure filled by a non-Newtonian nanofluid, International Journal of Thermofluids, 21, 100571. https://doi.org/10.1016/j.ijft.2024.100571
[10] Mustafa, J., Alqaed, S., Husain, S., & Sharifpur, M. (2024). Impact of five obstacles with constant temperatures on the mixed convection flow of water/copper nanofluid in a rectangular cavity with a magnetic field, Results in Physics, 57, 107424. https://doi.org/10.1016/j.rinp.2024.107424
[11] Hussain, A., Riaz, S., Hassan, A., Malik, M.Y., Alqahtani, A.S., Karamti, H., Saeed, A.M., & Eldin, S.M. (2023). Magneto-bio-convection enhanced heat transfer in Prandtl hybrid nanofluid with inclined magnetization and microorganism migration, Journal of Magnetism and Magnetic Materials, 588 (Part A), 171403. https://doi.org/10.1016/j.jmmm.2023.171403
[12] Dinarvand, S., Berehal, H., Tamim, H., Sowmya, G., Noeiaghdam, S., & Abdollahzadeh, M. (2023) Squeezing flow of aqueous CNTs-Fe3O4 hybrid nanofluid through mass-based approach: Effect of heat source/sink, nanoparticle shape, and an oblique magnetic field, Results in Engineering, 17, 100976.. https://doi.org/10.1016/j.rineng.2022.100976
[13] Sundar, L.S., & Ramana, E.V. (2023), Influence of magnetic field location on the heat transfer and friction factor of CoFe2O4-BaTiO3/EG hybrid nanofluids in laminar flow: An experimental study, Journal of Magnetism and Magnetic Materials, 579 (2023), 170837. https://doi.org/10.1016/j.jmmm.2023.170837
[14] Giwa, S.O., Sharifpur, M., Meyer, J.P., Taziwa, R.T., & Shah, N.A. (2024) Synergetic effect of magnetic field location, strength and orientation on heat transfer characteristics of brine-based hybrid nanofluid in rectangular confinement, Journal of Magnetism and Magnetic Materials, 590, 171642. https://doi.org/10.1016/j.jmmm.2024.171642
[15] Mahabaleshwar, U.S., Sachhin, S.M., Perez, L.M., & Oztop, H.F. (2024) An impact of inclined MHD on biviscosity Bingham hybrid nanofluid flow over porous stretching/shrinking sheet with heat transfer, Journal of Molecular Liquids, 398, 124244. https://doi.org/10.1016/j.molliq.2024.124244
[16] Sundar, L.S., Alklaibi, A.M., Sambasivam, S., & Mouli, K.V.V.C. (2024). Experimentally determining the thermophysical properties, heat transfer and friction factor Fe3O4-TiO2 magnetic hybrid nanofluids in a mini-heat sink under magnetic field: Proposing new correlations, Journal of Magnetism and Magnetic Materials, 594, 171889. https://doi.org/10.1016/j.jmmm.2024.171889
[17] Rajesh, V., & Oztop, H.F. (2024). Conjugate free convection in a non-uniform heating walled enclosure filled by ternary hybrid nanofluid under magnetic field, Chinese Journal of Physics, 89, 210-226. https://doi.org/10.1016/j.cjph.2024.03.021
[18] Khan, M.A., Ul-Haq, S., & Ali, F. (2024). Analysis of Newtonian heating in fractional hybrid nanofluid with the influence of transverse magnetic field, International Journal of Heat and Fluid Flow, 106, 109293. https://doi.org/10.1016/j.ijheatfluidflow.2024.109293
[19] Dero, S., Fadhel, M.A., Shah, Z., Lund, L.A., Vrinceanu, N., Dewidar, A.Z., & Elansary, H.O. (2023). Multiple solutions of Hiemenz flow of CNTs hybrid base C2H6O2+H2O nanofluid and heat transfer over stretching/shrinking surface: Stability analysis, Case Studies in Thermal Engineering, 49, 103190. https://doi.org/10.1016/j.csite.2023.103190
[20] Yahaya, R.I., Mustafa, M.S., Arifin, N.M., Pop, I., Ali, F.M., & Isa, S.S.P.M.(2023). Hybrid nanofluid flow past a biaxial stretching/shrinking permeable surface with radiation effect: Stability analysis and heat transfer optimization, Chinese Journal of Physics, 85, 402-420. https://doi.org/10.1016/j.cjph.2023.06.018
[21] Hafeez, A., Aldosari, F.M., Helmi, M.M., Ghazwani, H.A., Hussien, M., & Hassan, A.M. (2023). Heat transfer performance in a Hybrid nanofluid (Cu-Al2O3 /kerosene oil) flow over a shrinking cylinder, Case Studies in Thermal Engineering, 52, 103539. https://doi.org/10.1016/j.csite.2023.103539
[22] Jaafar, A., Jamaludin, A., Nasir, N.A. A. M., Nazar, R. & Pop, I. (2023). MHD opposing flow of Cu-TiO2 hybrid nanofluid under an exponentially stretching/shrinking surface embedded in porous media with heat source and slip impacts, Results in Engineering, 17, 101005. https://doi.org/10.1016/j.rineng.2022.101005
[23] Yasir, M., Khan, M., Alqahtani, A. S. & Malik, M. Y. (2023). Mass transpiration effect on rotating flow of radiative hybrid nanofluid due to shrinking surface with irregular heat source/sink, Case Studies in Thermal Engineering, 44, 102870. https://doi.org/10.1016/j.csite.2023.102870
[24] Waini, I., Alabdulhady, S., Ishak, A. & Pop, I. (2023). Viscous dissipation effects on hybrid nanofluid flow over a non-linearly shrinking sheet with power-law velocity, Heliyon, 9(10), e20910. https://doi.org/10.1016/j.heliyon.2023.e20910
[25] Roy, N.C. & Akter, A. (2023). Dual solutions of mixed convective hybrid nanofluid flow over a shrinking cylinder placed in a porous medium, Heliyon, 9(11), e22166. https://doi.org/10.1016/j.heliyon.2023.e22166
[26] Saleem, S., Ahmad, B., Naseem, A., Riaz, M. B. & Abbas, T. (2024). Mono and hybrid nanofluid analysis over shrinking surface with thermal radiation: A numerical approach, Case Studies in Thermal Engineering, 54, 104023. https://doi.org/10.1016/j.csite.2024.104023
[27] Shah, Z., Asghar, A., Ying, T. Y., Lund, L. A., Alshehri, A. & Vrinceanu, N. (2024). Numerical investigation of sodium alginate-alumina/copper radiative hybrid nanofluid flow over a power law stretching/shrinking sheet with suction effect: A study of dual solutions, Results in Engineering, 21, 101881. https://doi.org/10.1016/j.rineng.2024.101881
[28] Asifa, A. T., Kumam, P. & Muhammad, S. (2022). New fractional model to analyze impacts of Newtonian heating, shape factor and ramped flow function on MgO-SiO2-Kerosene oil hybrid nanofluid, Case Studies in Thermal Engineering, 38, 102361. https://doi.org/10.1016/j.csite.2022.102361
[29] Anwar, T., Asifa, & Kumam, P. (2022). A fractal fractional model for thermal analysis of GO − NaAlg − Gr hybrid nanofluid flow in a channel considering shape effects, Case Studies in Thermal Engineering, 31, 101828. https://doi.org/10.1016/j.csite.2022.101828
[30] Rafique, K., Mahmood, Z., Saleem, S., Eldin, S.M., and Khan, U. (2023). Impact of nanoparticle shape on entropy production of nanofluid over permeable MHD stretching sheet at quadratic velocity and viscous dissipation, Case Studies in Thermal Engineering, 45, 102992. https://doi.org/10.1016/j.csite.2023.102992
[31] Kezzar, M., Talbi, N., Sari, M. R., Nehal, A., Sharifpur, M., Kumar, R., Gharib, N., Salsoul, W. & Fatiha, H. (2023). Velocity-slip boundary conditions and shape factor effects on MHD hybrid nanofluid flow via converging/diverging channels, Journal of Magnetism and Magnetic Materials, 587, 171215. https://doi.org/10.1016/j.jmmm.2023.171215
[32] Rahman, M., Turkyilmazoglu, M. & Matloob, K. (2023). Impact of multiple shapes on Al2O3-Cu/H2O-C2H6O2 towards a permeable surface of cylinder, Journal of Magnetism and Magnetic Materials, 581, 170965. https://doi.org/10.1016/j.jmmm.2023.170965
[33] Jeevankumar & Sandeep, N. (2024). Computational analysis to examine the role of nanoparticle shape on operative usage of solar energy, International Journal of Hydrogen Energy, 56, 937-948. https://doi.org/10.1016/j.ijhydene.2023.11.256
[34] Ragupathi, E., Prakash, D., Muthtamilselvan, M. & Al-Mdallal, Q. M. (2024). A case study on heat transport of electrically conducting water based-CoFe2O4 ferrofluid flow over the disc with various nanoparticle shapes and highly oscillating magnetic field, Journal of Magnetism and Magnetic Materials, 589, 171624. https://doi.org/10.1016/j.jmmm.2024.171624
[35] Yahyaee, A. (2024). Influence of nanoparticle shapes in nanofluid film boiling on vertical cylinders: A numerical study, International Journal of Thermofluids, 22, 100631. https://doi.org/10.1016/j.ijft.2024.100631
[36] Wahid N. S., Arifin N. M., Pop I., Bachok N. & Hafidzuddin M. E. H. (2022). MHD stagnation-point flow of nanofluid due to a shrinking sheet with melting, viscous dissipation and Joule heating effects, Alexandria Engineering Journal 61(12), 12661–12672. https://doi.org/10.1016/j.aej.2022.05.050
[37] Khashi’ie, N. S., Arifin, N. M., Nazar, R., Hafidzuddin, E. H., Wahi, N. & Pop, I. (2019). Mixed Convective Flow and Heat Transfer of a Dual Stratified Micropolar Fluid Induced by a Permeable stretching/Shrinking Sheet, Entropy, 21, 1162. https://doi.org/10.3390/e21121162
[38] Sarfraz M., Yasir M., and Khan M. (2023). Multiple solutions for non-linear radiative mixed convective hybrid nanofluid flow over an exponentially shrinking surface,Scientific Reports 13, 3443. https://doi.org/10.1038/s41598-023-30548-5
[39] Redouane F., Jamshed W., Devi S. S.U., Prakash M., Nasir N. A. A. M, Hammouch Z., Eid M. R., Nisar K.S., Mohammed A, B., Abdel-Aty A., Yahia I. S. & Eed EM. (2022). Heat flow saturate of Ag/MgO-water hybrid nanofluid in heated trigonal enclosure with rotate cylindrical cavity by using Galerkin finite element, Scientific Reports 12, 2302. https://doi.org/10.1038/s41598-022-06385-3
[40] Alabdulhadi S., Bakar S.A., Ishak A., Waini I. & Ahmed SE. Effect of buoyancy force on an unsteady thin film flow of Al2O3/water nanofluid over an inclined stretching sheet, Mathematics 11(3) (2023) 739. https://doi.org/10.3390/math11030739
[41] Bachok N., Ishak A. & Pop I. (2010) Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet, Physics Letters A, 374(40), 4075–4079. https://doi.org/10.1016/j.physleta.2010.08.032
