Dual solutions of time-dependent magnetohydrodynamic stagnation point boundary layer micropolar nanofluid flow over shrinking/stretching surface

doi:10.1007/s10483-021-2749-7

Abstract

Abstract: Time-dependent, two-dimensional (2D) magnetohydrodynamic (MHD) micropolar nanomaterial flow over a shrinking/stretching surface near the stagnant point is considered. Mass and heat transfer characteristics are incorporated in the problem. A model of the partial differential expressions is altered into the forms of the ordinary differential equations via similarity transformations. The obtained equations are numerically solved by a shooting scheme in the MAPLE software. Dual solutions are observed at different values of the specified physical parameters. The stability of first and second solutions is examined through the stability analysis process. This analysis interprets that the first solution is stabilized and physically feasible while the second one is un-stable and not feasible. Furthermore, the natures of various physical factors on the drag force, skin-friction factor, and rate of mass and heat transfer are determined and interpreted. The micropolar nanofluid velocity declines with a rise in the suction and magnetic parameters, whereas it increases by increasing the unsteadiness parameter. The temperature of the micropolar nanofluid rises with increase in the Brownian motion, radiation, thermophoresis, unsteady and magnetic parameters, but it decreases against an increment in the thermal slip constraint and Prandtl number. The concentration of nanoparticles reduces against the augmented Schmidt number and Brownian movement values but rises for incremented thermophoresis parameter values.

Key words: dual solution, stability analysis, micropolar nanofluid, magnetic field, stretching/shrinking surface

2010 MSC Number:

76Sxx
76Bxx

H. B. LANJWANI, M. S. CHANDIO, M. I. ANWAR, S. A. SHEHZAD, M. IZADI. Dual solutions of time-dependent magnetohydrodynamic stagnation point boundary layer micropolar nanofluid flow over shrinking/stretching surface. Applied Mathematics and Mechanics (English Edition), 2021, 42(7): 1013-1028.

TrendMD

References

[1] ERINGEN, A. C. Theory of micropolar fluids. Journal of Mathematics and Mechanics, 16, 1–18(1966)
[2] LUKASZEWICZ, G. Micropolar Fluids: Theory and Applications, Springer Science & Business Media, 237–250(1999)
[3] CHIAM, T. C. Micropolar fluid flow over a stretching sheet. Zeitschrift für Angewandte Mathematik und Mechanik, 62, 565–568(1982)
[4] SANDEEP, N. and SULOCHANA, C. Dual solutions for unsteady mixed convection flow of MHD micropolar fluid over a stretching/shrinking sheet with non-uniform heat source/sink. Engineering Science and Technology, an International Journal, 18, 738–745(2015)
[5] TURKYILMAZOGLU, M. Magnetic field and slip effects on the flow and heat transfer of stagnation point Jeffrey fluid over deformable surfaces. Zeitschrift für Naturforschung A, 71, 549–556(2016)
[6] TURKYILMAZOGLU, M. Magnetohydrodynamic two-phase dusty fluid flow and heat model over deforming isothermal surfaces. Physics of Fluids, 29, 013302(2017)
[7] HSIAO, K. Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet. Applied Thermal Engineering, 98, 850–861(2016)
[8] HSIAO, K. Micropolar nanofluid flow with MHD and viscous dissipation effects towards a stretching sheet with multimedia feature. International Journal of Heat and Mass Transfer, 112, 983–990(2017)
[9] RAUF, A., ABBAS, Z., and SHEHZAD, S. A. Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium. Applied Mathematics and Mechanics (English Edition), 40(6), 837–850(2019) https://doi.org/10.1007/s10483-019-2488-9
[10] SHEIKHOLELSAMI, M., ARABKOOHSAR, A., and BABAZADEH, H. Modeling of nanomaterial treatment through a porous space including magnetic forces. Journal of Thermal Analysis and Calorimetry, 140, 825–834(2020)
[11] SHEHZAD, S. A., KHAN, S. U., ABBAS, Z., and RAUF, A. A revised Cattaneo-Christov micropolar viscoelastic nanofluid model with combined porosity and magnetic effects. Applied Mathematics and Mechanics (English Edition), 41(3), 521–532(2020) https://doi.org/10.1007/s10483-020-2581-5
[12] IZADI, M., SHEREMET, M. A., MEHRYAN, S. A. M., POP, I., OZTOP, H. F., and ABU-HAMDEH, N. MHD thermogravitational convection and thermal radiation of a micropolar nanoliquid in a porous chamber. International Communications in Heat and Mass Transfer, 110, 104409(2020)
[13] CHOI, S. U. S. and EASTMAN, J. A. Enhancing thermal conductivity of fluids with nanoparticles. ASME International Mechanical Engineering Congress and Exposition, San Franciscos, U.S.A., 99–105(1995)
[14] BUONGIORNO, J. Convective transport in nanofluids. Journal of Heat Transfer, 128, 240–250(2006)
[15] KEBLINSKI, P., PRASHER, R., and EAPEN, J. Thermal conductance of nanofluids: is the controversy over? Journal of Nanoparticle Research, 10, 1089–1097(2008)
[16] PRASHER, R., SONG, D., WANG, J., and PHELAN, P. Measurements of nanofluid viscosity and its implications for thermal applications. Applied Physics Letters, 89, 133108(2006)
[17] BACHOK, N., ISHAK, A., and POP, I. Flow and heat transfer characteristics on a moving plate in a nanofluid. International Journal of Heat and Mass Transfer, 55, 642–648(2012)
[18] ROHNI, A. M., AHMAD, S., ISMAIL, A. I. M., and 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, 75–80(2013)
[19] SHEREMET, M. A., POP, I., and MAHIAN, O. J. I. J. O. H. Natural convection in an inclined cavity with time-periodic temperature boundary conditions using nanofluids: application in solar collectors. International Journal of Heat and Mass Transfer, 116, 751–761(2018)
[20] DERO, S., UDDIN, M. J., and ROHNI, A. M. Stefan blowing and slip effects on unsteady nanofluid transport past a shrinking sheet: multiple solutions. Heat Transfer—Asian Research, 48, 2047–2066(2019)
[21] LUND, L. A., OMAR, Z., RAZA, J., KHAN, I., and SHERIF, E. S. M. Effects of Stefan blowing and slip conditions on unsteady MHD Casson nanofluid flow over an unsteady shrinking sheet: dual solutions. Symmetry, 12, 487(2020)
[22] KUMAR, K. A., SUGUNAMMA, V., and SANDEEP, N. Physical aspects on unsteady MHD-free convective stagnation point flow of micropolar fluid over a stretching surface. Heat Transfer—Asian Research, 48, 3968–3985(2019)
[23] ISHAK, A., NAZAR, R., and POP, I. Heat transfer over a stretching surface with variable heat flux in micropolar fluids. Physics Letters A, 372, 559–561(2008)
[24] HARRIS, S. D., INGHAM, D. B., and 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, 267–285(2009)
[25] MEADE, D. B., HARAN, B. S., and WHITE, R. E. The shooting technique for the solution of two-point boundary value problems. Maple Technical Newsletter, 3, 1–8(1996)