Journal of Applied and Computational Mechanics

Analysis of Dual Solutions of Unsteady Micropolar Hybrid ‎Nanofluid Flow over a Stretching/Shrinking Sheet

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Dhaka, Dhaka, 1000, Bangladesh

2 Department of Mathematics, University of Dhaka, Dhaka, 1000, Bangladesh‎

3 Department of Applied Mathematics, Babeş-Bolyai University, Cluj-Napoca, Romania

Abstract

An unsteady boundary layer flow of a micropolar hybrid nanofluid over a stretching/shrinking sheet is analyzed. The nonlinear ordinary differential equations of the problem have been solved using the efficient implicit Runge–Kutta–Butcher method along with Nachtsheim–Swigert iteration technique. For a certain set of parameters, numerical results expose dual solutions with the change of the velocity ratio parameter. The dual solutions are presented in a wide range of the physical parameters. Using a lot of numerical data, the critical values of the velocity ratio parameter, local friction factor, local couple-stress and local Nusselt number for the existence of dual solutions are expressed as a function of the physical parameters. These expressions might be useful for the development of new technology or for the future experimental investigation.

Keywords

[1] Izadi, M., Mohammadi, S. A., Mehryan, S.A.M., Yang, T. F., Sheremet, M. A., Thermogravitational convection of magnetic micropolar nanofluid with coupling between energy and angular momentum equations, International Journal of Heat and Mass Transfer, 145, 2019, 118748.
[2] H. Hashemi, Z. Namazian, S.A.M. Mehryan, Cu-water micropolar nanofluid natural convection within a porous enclosure with heat generation, Journal of Molecular Liquids, 236, 2017, 48–60.
[3] Hashemi, H., Namazian, Z., Zadeh, S. M. H., Mehryan, S.A.M., MHD natural convection of a micropolar nanofluid flowing inside a radiative porous medium under LTNE condition with an elliptical heat source, Journal of Molecular Liquids, 271, 2018, 914-925..
[4] Bourantas, G. C., Loukopoulos, V. C., Modeling the natural convective flow of micropolar nanofluids, International Journal of Heat and Mass Transfer, 68, 2014, 35–41.
[5] Bourantas, G. C., Loukopoulos, V. C., MHD natural-convection flow in an inclined square enclosure filled with a micropolar-nanofluid, International Journal of Heat and Mass Transfer, 79, 2014, 930–944.
[6] Lok, Y.Y., Amin, N., Pop, I., Unsteady boundary layer flow of a micropolar fluid near the rear stagnation point of a plane surface, International Journal of Thermal Sciences, 42, 2003, 995–1001.
[7] Lok, Y.Y., Amin, N., Campean, D., Pop, I., Steady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface, International Journal of Numerical Methods for Heat & Fluid Flow, 15, 2005, 654–670.
[8] Hussain, S.T., Nadeem, S., Haq, R.U., Model-based analysis of micropolar nanofluid flow over a stretching surface, The European Physical Journal Plus, 129, 2014, 161.
[9] Patel, H. R., Mittal, A. S., Darji, R. R., MHD flow of micropolar nanofluid over a stretching/shrinking sheet considering radiation, International Communications in Heat and Mass Transfer, 108, 2019, 104322.
[10] Hussanan, A., Salleh, M. Z., Khan, I., Shafie, S., Convection heat transfer in micropolar nanofluids with oxide nanoparticles in water, kerosene and engine oil, Journal of Molecular Liquids, 229, 2016, 482–488.
[11] Ishak, A., Nazar, R., Pop, I., Boundary-layer flow of a micropolar fluid on a continuous moving or fixed surface, Canadian Journal of Physics, 84(5), 2006, 399–410.
[12] Bhattacharyya, K., Mukhopadhyay, S., Layek, G. C., Pop, I., Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet, International Journal of Heat and Mass Transfer, 55, 2012, 2945–2952.
[13] Hsiao, K. L., Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature, International Journal of Heat and Mass Transfer, 112, 2017, 983–990.
[14] Chamkha, A. J., MHD-free convection from a vertical plate embedded in a thermally stratified porous medium with Hall effects, Applied Mathematical Modelling, 21, 1997, 603-609.
[15] Krishna, M. V., Chamkha, A. J., Hall and ion slip effects on MHD rotating boundary layer flow of nanofluid past an infinite vertical plate embedded in a porous medium, Results in Physics, 15, 2019, 102652.
[16] Yasin, M. H. M., Anuar Ishak, A., Pop, I., MHD stagnation-point flow and heat transfer with effects of viscous dissipation, joule heating and partial velocity slip, Scientific Reports, 5, 2015, 17848
[17] Najib, N., Bachok, N., Arifin, N. M., Ishak, A., Stagnation point flow and mass transfer with chemical reaction past a stretching/shrinking cylinder, Scientific Reports, 4, 2014, 4178.
[18] Waini, I., Ishak, A., Pop, I., Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface, International Journal of Numerical Methods for Heat & Fluid Flow, 29(9), 2019, 3110–3127.
[19] Waini, I., Ishak, A., Pop, I., Hybrid nanofluid flow induced by an exponentially shrinking sheet, Chinese Journal of Physics, 2019. doi: https://doi.org/10.1016/j.cjph.2019.12.015
[20] Devi, S.S.U., Devi, S.P.A., Heat transfer enhancement of Cu-Al2O3/water hybrid nanofluid flow over a stretching sheet, Journal of Nigerian Mathematical Society, 36, 2017, 419–433.
[21] Lund, L. A., Omara, Z., Khan, I., Seikh, A. H., Sherif, E.-S. M., Nisar, K.S., Stability analysis and multiple solution of Cu–Al2O3/H2O nanofluid contains hybrid nanomaterials over a shrinking surface in the presence of viscous dissipation, Journal of Materials Research and Technology, 9(1), 2020, 421–432.
[22] M. Shamshuddin, T. Thirupathi, P.V. S. Narayana, Micropolar fluid flow induced due to a stretching sheet with heat source/sink and surface heat flux boundary condition effects, Journal of Applied and Computational Mechanics, 5(5), 2019, 816-826.
[23] Al-Hanaya, A. M., Sajid, F., Abbas, N., Nadeem, S., Effect of SWCNT and MWCNT on the flow of micropolar hybrid nanofluid over a curved stretching surface with induced magnetic field, Scientific Reports, 10, 2020, 8488.
[24] Sarkar, J., Ghosh, P., Adil, A., A review on hybrid nanofluids: recent research, development and applications, Renewable and Sustainable Energy Reviews, 43, 2015, 164-177.
[25] Sidik, N.A., Adamu, I.M., Jamil, M.M., Kefayati, G.H., Mamat, R., Najafi, G., Recent progress on hybrid nanofluids in heat transfer applications: a comprehensive review, International Journal of Heat and Mass Transfer, 78, 2016, 68-79.
[26] Sundar, L.S., Sharma, K.V., Singh, M.K., Sousa, A.C., Hybrid nanofluids preparation, thermal properties, heat transfer and friction factor–a review, Renewable and Sustainable Energy Reviews, 68, 2017, 185-198.
[27] Babu, J.R., Kumar, K.K., Rao, S.S., State-of-art review on hybrid nanofluids, Renewable and Sustainable Energy Reviews, 77, 2017, 551-65.
[28] Huminic, G., Huminic, A., Hybrid nanofluids for heat transfer applications – A state-of-the-art review, International Journal of Heat and Mass Transfer, 125, 2018, 82–103.
[29] Sajid, M.U., Ali, H.M., Thermal conductivity of hybrid nanofluids: a critical review, International Journal of Heat and Mass Transfer, 126, 2018, 211-234.
[30] Butcher, J. C., Implicit Runge-Kutta processes, Mathematics of Computation, 18, 1964, 50–64.
[31] Naschtsheim, P. R., Sweigert, P., Satisfaction of asymptotic boundary conditions in numerical solution of systems of non-linear equation of boundary layer type, NASA TN D-3004, 1965.
Journal of Applied and Computational Mechanics
Volume 7, Issue 1
January 2021
Pages 19-33