### Multiple Solutions for Slip Effects on Dissipative Magneto-Nanofluid Transport Phenomena in Porous Media: Stability Analysis

Document Type: Research Paper

Authors

1 Department of Mathematics, Jaypee Institute of Information Technology, A-10, Sector-62, Noida-201307, Uttar Pradesh, India

2 Aeronautical and Mechanical Engineering, School of Computing, Science & Engineering, University of Salford, Newton Building, M54WT, UK

3 Petroleum and Gas Engineering, School of Computing, Science & Engineering, University of Salford, Newton Building, M54WT, UK

Abstract

In the present paper, a numerical investigation of transport phenomena is considered in electrically-conducting nanofluid flow within a porous bed utilizing Buongiorno’s transport model and Runge-Kutta-Fehlberg fourth-fifth order method. Induced flow by non-isothermal stretching/shrinking sheet along with magnetic field impact, dissipation effect, and slip conditions at the surface are also included. The numerical results show the existence of two branches of the solution for a selected range of the governing parameters. The physical significance of both branches of solutions is ensured by performing a stability analysis in which a linearized eigenvalue problem is solved. The multiple regression analysis with the help of MATLAB LinearModel.fit package has also been conducted to estimate the dependence of the parameters on Nusselt number.

Keywords

Main Subjects

[1] Crane L.J., Flow past a stretching plate, Applied Mathematics and Physics, 21, 1970, 645-647.
[2] Miklavcic M., Wang C.Y., Viscous flow due to a shrinking sheet, Quarterly of Applied Mathematics, 64, 2006, 283-290.
[3] Fang T, Boundary layer flow over a shrinking sheet with power-law velocity, International Journal of Heat and Mass Transfer, 51, 2008, 5838-5843.
[4] Fang T., Zhang J., Closed-form exact solution of MHD viscous flow over a shrinking sheet, Communications in Nonlinear Science and Numerical Simulation, 14, 2009, 2853-2857.
[5] Javed T., Abbas Z., Sajid M., Ali N., Heat transfer analysis for a hydromagnetic viscous fluid over a non-linear shrinking sheet, International Journal of Heat and Mass Transfer, 54, 2011, 2034-2042.
[6] Buongiorno J., Convective transport in nanofluids, ASME Journal of Heat Transfer, 128, 2006, 240–250.
[7] Rohni A.M., Ahmad S., A., Ismail A. I. Md., Pop I., Flow and heat transfer over an unsteady shrinking sheet with suction in a nanofluid using Buongiorno’s model, International Communications in Heat and Mass Transfer, 43, 2013, 75-80.
[8] Zaimi K., Ishak A., Pop I., Flow past a permeable stretching/shrinking sheet in a nanofluid using two-phase model, Plos One, 9, 2014, 111743 (1-6).
[9] Naramgari S., Sulochana C., MHD flow over a permeable stretching/shrinking sheet of a nanofluid with suction/injection, Alexandria Engineering Journal, 55, 2016, 819–827.
[10] Uddin Md.J., Bég O.Anwar and Ismail A.I., Radiative convective nanofluid flow past a stretching/shrinking sheet with slip effects, AIAA Journal of Thermophysics and Heat Transfer, 29, 2015, 513-523.
[11] Singh G., Chamkha A.J., Dual solutions for second-order slip flow and heat transfer on a vertical permeable shrinking sheet, Ain Shams Engineering Journal, 4, 2013, 911-917.
[12] Hsiao, K. L., To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau-Nanofluid with parameters control method, Energy, 130, 2017, 486-499.
[13] Hsiao, K. L., Combined electrical MHD heat transfer thermal extrusion system using Maxwell fluid with radiative and viscous dissipation effects, Applied Thermal Engineering, 112, 2017, 1281-1288.
[14] 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.
[15] Hsiao, K. L., Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet, Applied Thermal Engineering, 98, 2016, 850-861.
[16] Waqas, M., Shehzad, S. A., Hayat, T., Khan, M. I., Alsaedi, A., Simulation of magnetohydrodynamics and radiative heat transport in convectively heated stratified flow of Jeffrey nanofluid, Journal of Physics and Chemistry of Solids, 133, 2019, 45-51.
[17] Waqas, M., Jabeen, S., Hayat, T., Khan, M. I., Alsaedi, A., Modeling and analysis for magnetic dipole impact in nonlinear thermally radiating Carreau nanofluid flow subject to heat generation, Journal of Magnetism and Magnetic Materials, 485, 2019, 197-204.
[18] Dhanai R., Rana P., Kumar L., MHD mixed convection nanofluid flow and heat transfer over an inclined cylinder due to velocity and thermal slip effects: Buongiorno’s model, Powder Technology, 288, 2016, 140–150.
[19] Subba Rao, A., V.R.Prasad, K. Harshavalli and O. Anwar Bég, Thermal radiation effects on non-Newtonian fluid in a variable porosity regime with partial slip, Journal of Porous Media, 19 (4), 2016, 1–17.
[20] Siavashi, M., Karimi, K., Xiong, Q., Doranehgard, M. H., Numerical analysis of mixed convection of two-phase non-Newtonian nanofluid flow inside a partially porous square enclosure with a rotating cylinder, Journal of Thermal Analysis and Calorimetry, 137(1), 2019, 267-287.
[21] Dhanai R., Rana P., Kumar L., Multiple solutions of MHD boundary layer flow and heat transfer behavior of nanofluids induced by a power-law stretching/shrinking permeable sheet with viscous dissipation, Powder Technology, 273, 2015, 62-70.
[22] Izadi, A., Siavashi, M., Xiong, Q., Impingement jet hydrogen, air and CuH2O nanofluid cooling of a hot surface covered by porous media with non-uniform input jet velocity, International Journal of Hydrogen Energy, 44(30), 2019, 15933-15948.
[23] Bég, O. Anwar, M. F. M. Basir, M.J. Uddin and A. I. Md. Ismail, Numerical study of slip effects on asymmetric bioconvective nanofluid flow in a porous microchannel with an expanding/contracting upper wall using Buongiorno’s model, Journal of Mechanics in Medicine and Biology, 17, 2017, 1750059.
[24] Rashid, M., Khan, M. I., Hayat, T., Khan, M. I., Alsaedi, A., Entropy generation in flow of ferromagnetic liquid with nonlinear radiation and slip condition, Journal of Molecular Liquids, 276, 2019, 441-452.
[25] Khan, M. W. A., Khan, M. I., Hayat, T., Alsaedi, A, Entropy generation minimization (EGM) of nanofluid flow by a thin moving needle with nonlinear thermal radiation, Physica B: Condensed Matter, 534, 2018, 113-119.
[26] Shukla, N., Rana, P., Bég, O.A., Singh, B. and Kadir, A., Homotopy study of magnetohydrodynamic mixed convection nanofluid multiple slip flow and heat transfer from a vertical cylinder with entropy generation, Propulsion and Power Research, 8, 2019, 147-162.
[27] Rana, P., Shukla, N., Bég, O.A. and Bhardwaj, A., Lie group analysis of nanofluid slip flow with Stefan Blowing effect via modified Buongiorno’s Model: entropy generation analysis, Differential Equations and Dynamical Systems, 2019, 1-18.
[28] Rana, P. and Shukla, N., Entropy generation analysis for non-similar analytical study of nanofluid flow and heat transfer under the influence of aligned magnetic field, Alexandria Engineering Journal, 57(4), 2018, 3299-3310.
[29] Hayat, T., Khan, M. I., Farooq, M., Alsaedi, A., Waqas, M., Yasmeen, T., Impact of Cattaneo–Christov heat flux model in flow of variable thermal conductivity fluid over a variable thicked surface, International Journal of Heat and Mass Transfer, 99, 2016, 702-710.
[30] Hayat, T., Khan, M. I., Farooq, M., Yasmeen, T., Alsaedi, A., Stagnation point flow with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions, Journal of Molecular Liquids, 220, 2016, 49-55.
[31] Khan, M. I., Waqas, M., Hayat, T., Alsaedi, A, A comparative study of Casson fluid with homogeneous-heterogeneous reactions, Journal of Colloid and Interface Science, 498, 2017, 85-90.
[32] Hayat, T., Aslam, N., Khan, M. I., Khan, M. I., Alsaedi, A., Physical significance of heat generation/absorption and Soret effects on peristalsis flow of pseudoplastic fluid in an inclined channel, Journal of Molecular Liquids, 275, 2019, 599-615.
[33] Hayat, T., Javed, S., Khan, M. I., Khan, M. I., Alsaedi, A., Physical aspects of irreversibility in radiative flow of viscous material with cubic autocatalysis chemical reaction, The European Physical Journal Plus, 134(4), 2019, 172.
[34] Ghosh S., Mukhopadhyay S., Vajravelu K., Dual solutions of slip flow past a nonlinearly shrinking permeable sheet, Alexandria Engineering Journal, 55, 2016, 1835–1840.
[35] Rana P., Dhanai R., Kumar L., Radiative nanofluid flow and heat transfer over a non-linear permeable sheet with slip conditions and variable magnetic field: Dual solutions, Ain Shams Engineering Journal, 8, 2017, 341-352.
[36] Merkin J.H, On dual solution occurring in mixed convection in a porous medium, Journal of Engineering Mathematics, 20, 1985, 171-179.
[37] Harris S.D., Ingham D.B., Pop I., Mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip, Transport in Porous Media, 77, 2009, 267-285.
[38] Awaludin, I.S., Ishak, A. and Pop, I., 2018. On the stability of MHD boundary layer flow over a stretching/shrinking wedge, Scientific Reports, 8(1), 2018, 13622.
[39] Yasin, M.H.M., Ishak, A. and Pop, I., Boundary layer flow and heat transfer past a permeable shrinking surface embedded in a porous medium with a second-order slip: A stability analysis, Applied Thermal Engineering, 115, 2017, 1407-1411.
[40] Rana, P., Dhanai, R. and Kumar, L., 2017. MHD slip flow and heat transfer of Al2O3-water nanofluid over a horizontal shrinking cylinder using Buongiorno’s model: Effect of nanolayer and nanoparticle diameter, Advanced Powder Technology, 28(7), 2017, 1727-1738.
[41] Rana, P., Uddin, M.J., Gupta, Y. and Ismail, A.M., Slip effects on MHD Hiemenz stagnation point nanofluid flow and heat transfer along a nonlinearly shrinking sheet with induced magnetic field: multiple solutions, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(9), 2017, 3363-3374.
[42] Rana, P., Shukla, N., Gupta, Y. and Pop, I., 2019. Homotopy analysis method for predicting multiple solutions in the channel flow with stability analysis, Communications in Nonlinear Science and Numerical Simulation, 66, 2019, 183-193.
[43] Rana, P., Shukla, N., Gupta, Y. and Pop, I. Analytical prediction of multiple solutions for MHD Jeffery–Hamel flow and heat transfer utilizing KKL nanofluid model, Physics Letters A, 383(2-3), 2019, 176-185.
[44] Chen, C.H., Laminar mixed convection adjacent to vertical, continuously stretching sheets, Heat and Mass Transfer, 33, 1998, 471–476.
[45] Khader, M. M., Megahed, A. M., Effect of viscous dissipation on the boundary layer flow and heat transfer past a permeable stretching surface embedded in a porous medium with a second-order slip using Chebyshev finite difference method, Transport in Porous Media, 105(3), 2014, 487-501.