Numerical investigation on MHD Jeffery-Hamel nanofluid flow with different nanoparticles using fuzzy extension of generalized dual parametric homotopy algorithm

Abstract

This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper, Al₂O₃ and SiO₂ between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual parametric homotopy algorithm. The nanofluids have been formulated to enhance the thermophysical characteristics of fluids, including thermal diffusivity, conductivity, convective heat transfer coefficients and viscosity. Due to the presence of distinct nanofluids, a change in the value of volume fraction occurs that influences the velocity profiles of the flow. The short value of nanoparticles volume fraction is considered an uncertain parameter and represented in a triangular fuzzy number range among [0.0, 0.1, 0.2]. A novel generalized dual parametric homotopy algorithm with fuzzy extension is used here to study the fuzzy velocities at various channel positions. Finally, the effectiveness of the proposed approach has been demonstrated through a comparison with the available results in the crisp case.

Keywords

fuzzy number / Jeffery-Hamel(J-H) flow / nanofluid / homotopy analysis method

References

[[1]] Jeffery G B L. The two-dimensional steady motion of a viscous fluid. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1915, 29(172): 455-465, J]

[[2]] Hamel G. Spiral motions of viscous fluids. Jahresbericht der deutschen mathematiker-vereinigung, 1917, 25: 34-60 [J]

[[3]] Alfvén H. Existence of electromagnetic-hydrodynamic waves. Nature, 1942, 150(3805): 405-406, J]

[[4]] Al-Rashed A A A A, Shahsavar A, Akbari M, et al.. Finite volume simulation of mixed convection in an inclined lid-driven cavity filled with nanofluids: Effects of a hot elliptical centric cylinder, cavity angle and volume fraction of nanoparticles. Physica A: Statistical Mechanics and Its Applications, 2019, 527: 121122, J]

[[5]] Hafeez M, Hashim, Khan M. Jeffery-Hamel flow of hybrid nanofluids in convergent and divergent channels with heat transfer characteristics. Applied Nanoscience, 2020, 10(12): 5459-5468, J]

[[6]] Chamkha A J, Abu-Nada E. Mixed convection flow in single- and double-lid driven square cavities filled with water-Al₂O₃ nanofluid: Effect of viscosity models. European Journal of Mechanics - B/Fluids, 2012, 36: 82-96, J]

[[7]] Moradi A, Alsaedi A, Hayat T. Investigation of nanoparticles effect on the Jeffery-Hamel flow. Arabian Journal for Science and Engineering, 2013, 38(10): 2845-2853, J]

[[8]] Esmaili Q, Ramiar A, Alizadeh E, et al.. An approximation of the analytical solution of the Jeffery-Hamel flow by decomposition method. Physics Letters A, 2008, 372(19): 3434-3439, J]

[[9]] Singh J, Shishodia Y S. A modified analytical technique for Jeffery-Hamel flow using sumudu transform. Journal of the Association of Arab Universities for Basic and Applied Sciences, 2014, 16: 11-15 [J]

[[10]] Marinca V, Ene R D. Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem. Open Physics, 2017, 15(1): 42-57, J]

[[11]] Patel H S, Meher R. Analytical investigation of jeffery-hamel flow by modified adomian decomposition method. Ain Shams Engineering Journal, 2018, 9(4): 599-606, J]

[[12]] Patel N D, Meher R. Analytical investigation of Jeffery-Hemal flow with magnetic field by differential transform method. Int J Adv Appl Math Mech, 2018, 6: 1-9 [J]

[[13]] Patel N D, Meher R. Investigation of a Jeffery-Hamel flow between two rectangular inclined smooth walls using the Differential Transform Method. Journal of Applied Mathematics and Computational Mechanics, 2018, 17(4): 47-57, J]

[[14]] Meher R, Patel N D. A study on magneto hydrodynamics Jeffery-Hamel flow with heat transfer problem in Eyring-Powell fluid using Differential Transform Method. Journal of Applied Mathematics and Computational Mechanics, 2019, 18(3): 57-68, J]

[[15]] Meher R, Patel N D. Numerical study of magnetohydrodynamics Jeffery - Hamel flow with Cu-water nanofluid between two rectangular smooth walls with transverse magnetic field. International Journal of Computational Materials Science and Engineering, 2020, 9(2): 2050010, J]

[[16]] Makinde O D, Mhone P Y. Hermite-Padé approximation approach to MHD Jeffery-Hamel flows. Applied Mathematics and Computation, 2006, 181(2): 966-972, J]

[[17]] Makinde O D, Mhone P Y. Temporal stability of small disturbances in MHD Jeffery-Hamel flows. Computers & Mathematics with Applications, 2007, 53(1): 128-136, J]

[[18]] Makinde O D. Effect of arbitrary magnetic Reynolds number on MHD flows in convergent-divergent channels. International Journal of Numerical Methods for Heat and Fluid Flow, 2008, 18(6): 697-707, J]

[[19]] Alam M S, Khan M A H, Makinde O D. Magnetonanofluid dynamics in convergent-divergent channel and its inherent irreversibility. Defect and Diffusion Forum, 2017, 377: 95-110, J]

[[20]] Sheikholeslami M, Ganji D D, Ashorynejad H R, et al.. Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method. Applied Mathematics and Mechanics, 2012, 33(1): 25-36, J]

[[21]] Dib A, Haiahem A, Bou-Said B. An analytical solution of the MHD Jeffery-Hamel flow by the modified Adomian decomposition method. Computers & Fluids, 2014, 102: 111-115, J]

[[22]] Hatami M, Ganji D D. MHD nanofluid flow analysis in divergent and convergent channels using WRMs and numerical method. International Journal of Numerical Methods for Heat & Fluid Flow, 2014, 24(5): 1191-1203, J]

[[23]] Domairry D G, Mohsenzadeh A, Famouri M. The application of homotopy analysis method to solve nonlinear differential equation governing Jeffery-Hamel flow. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(1): 85-95, J]

[[24]] Biswal U, Chakraverty S, Ojha B K, et al.. Study of Jeffery-Hamel flow problem for nanofluid with fuzzy volume fraction using double parametric based Adomian decomposition method. International Communications in Heat and Mass Transfer, 2021, 126: 105435, J]

[[25]] Choi S U, Eastman J A. . Enhancing thermal conductivity of fluids with nanoparticles, 1995 Argonne, IL (United States) Argonne National Lab. (ANL) [R]

[[26]] Das S K, Choi S U S, Yu W-h, et al.. . Nanofluids, 2007 Hoboken, New Jersey Wiley, M]

[[27]] Chu Y-m, Khan M I, Waqas H, et al.. Numerical simulation of squeezing flow Jeffrey nanofluid confined by two parallel disks with the help of chemical reaction: Effects of activation energy and microorganisms. International Journal of Chemical Reactor Engineering, 2021, 19(7): 717-725, J]

[[28]] Ghulam R, Anum S, Chu Y-m, et al.. Optimal homotopic exploration of features of Cattaneo-Christov model in second grade nanofluid flow via Darcy-Forchheimer medium subject to viscous dissipation and thermal radiation. Combinatorial Chemistry & High Throughput Screening, 2021, 25(14): 2485-2497 [J]

[[29]] Ibrahim M, Algehyne E A, Saeed T, et al.. Study of capabilities of the ANN and RSM models to predict the thermal conductivity of nanofluids containing SiO₂ nanoparticles. Journal of Thermal Analysis and Calorimetry, 2021, 145(4): 1993-2003, J]

[[30]] Adnan, Ali Zaidi S Z, Khan U, et al.. Impacts of freezing temperature based thermal conductivity on the heat transfer gradient in nanofluids: Applications for a curved Riga surface. Molecules, 2020, 25(9): 2152, J]

[[31]] Khan U, Adnan, Ahmed N, et al.. γ-nanofluid thermal transport between parallel plates suspended by microcantilever sensor by incorporating the effective Prandtl model: Applications to biological and medical sciences. Molecules, 2020, 25(8): 1777, J]

[[32]] Ashraf M, Abbas A, Zia S, et al.. Computational analysis of the effect of nano particle material motion on mixed convection flow in the presence of heat generation and absorption. Computers, Materials & Continua, 2020, 65(2): 1809-1823, J]

[[33]] Chung J D, Ramzan M, Gul H, et al.. Partially ionized hybrid nanofluid flow with thermal stratification. Journal of Materials Research and Technology, 2021, 11: 1457-1468, J]

[[34]] Madhukesh J K, Naveen Kumar R, Punith Gowda R J, et al.. Numerical simulation of AA7072-AA7075/water-based hybrid nanofluid flow over a curved stretching sheet with Newtonian heating: A non-Fourier heat flux model approach. Journal of Molecular Liquids, 2021, 335: 116103, J]

[[35]] Ibrahim M, Saeed T, Bani F R, et al.. Two-phase analysis of heat transfer and entropy generation of water-based magnetite nanofluid flow in a circular microtube with twisted porous blocks under a uniform magnetic field. Powder Technology, 2021, 384: 522-541, J]

[[36]] Heydari M R, Hemmat Esfe M, Hajmohammad M H, et al.. Mixed convection heat transfer in a double lid-driven inclined square enclosure subjected to cu-water nanofluid with particle diameter of 90 nm. Heat Transfer Research, 2014, 45(1): 75-95, J]

[[37]] Rostami A K, Akbari M R, Ganji D D, et al.. Investigating Jeffery-Hamel flow with high magnetic field and nanoparticle by HPM and AGM. Central European Journal of Engineering, 2014, 4(4): 357-370 [J]

[[38]] Umavathi J C, Shekar M. Effect of MHD on Jeffery-Hamel flow in nanofluids by differential transform method. International Journal of Engineering Research and Applications, 2013, 3(5): 953-962 [J]

[[39]] Hemmat Esfe M, Akbari M, Karimipour A. Mixed convection in a lid-driven cavity with an inside hot obstacle filled by an Al₂O₃-water nanofluid. Journal of Applied Mechanics and Technical Physics, 2015, 56(3): 443-453, J]

[[40]] Verma L, Meher R. Effect of heat transfer on Jeffery-Hamel Cu/Ag-water nanofluid flow with uncertain volume fraction using the double parametric fuzzy homotopy analysis method. The European Physical Journal Plus, 2022, 137(3): 372, J]

[[41]] Meher R, Verma L, Avazzadeh Z, et al.. Study of MHD nanofluid flow with fuzzy volume fraction in thermal field-flow fractionation. AIP Advances, 2023, 13(1): 015204, J]

[[42]] VERMA L, MEHER R, AVAZZADEH Z, et al. Solution for generalized fuzzy fractional Kortewege-de Varies equation using a robust fuzzy double parametric approach [J]. Journal of Ocean Engineering and Science, 2022. DOI: https://doi.org/10.1016/j.joes.2022.04.026.

[[43]] Bede B, Gal S G. Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets and Systems, 2005, 151(3): 581-599, J]

[[44]] Sartanpara P P, Meher R. A robust fuzzy-fractional approach for the atmospheric internal wave model. Journal of Ocean Engineering and Science, 2023, 8(3): 308-322, J]

[[45]] Allahviranloo T, Ahmady N, Ahmady E. Numerical solution of fuzzy differential equations by predictor-corrector method. Information Sciences, 2007, 177(7): 1633-1647, J]

[[46]] Verma L, Meher R. Fuzzy computational study on the generalized fractional smoking model with caputo gH-type derivatives. International Journal of Biomathematics, 2024, 17(4): 2350037, J]

[[47]] VERMA L, MEHER R. Solution for generalized fuzzy time-fractional Fisher’s equation using a robust fuzzy analytical approach [J]. Journal of Ocean Engineering and Science, 2022 DOI: https://doi.org/10.1016/j.joes.2022.03.019.