A Paired Quasi-linearization on Magnetohydrodynamic Flow and Heat Transfer of Casson Nanofluid with Hall Effects

Document Type : Research Paper


1 Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, Gandhinagar- 382007, India

2 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, South Africa

3 Department of Mathematics, University of Swaziland, Swaziland


Present study explores the effect of Hall current, non-linear radiation, irregular heat source/sink on magnetohydrodynamic flow of Casson nanofluid past a nonlinear stretching sheet. Viscous and Joule dissipation are incorporated in the energy equation. An accurate numerical solution of highly nonlinear partial differential equations, describing the flow, heat and mass transfer, by a new Spectral Paired Quasi-linearization method is obtained and effect of various physical parameters such as hall current parameter, radiation parameter, Eckert number, Prandtl number, Lewis number, thermophoresis parameter and Brownian motion parameter on the thermal, hydro-magnetic and concentration boundary layers are observed. The analysis shows that variation of different thermo-magnetic parameter induces substantial impression on the behaviour of temperature and nanoparticle distribution. Thermal boundary layer is greatly affected by conduction radiation parameter.


Main Subjects

[1] Turkyilmazoglu, M., Mixed convection flow of magnetohydrodynamic micropolar fluid due to a porous heated/cooled deformable plate: exact solutions, International Journal of Heat and Mass Transfer, 106, 2017, 127-134.
[2] Turkyilmazoglu, M., Analytical solutions to mixed convection MHD fluid flow induced by a nonlinearly deforming permeable surface, Communications in Nonlinear Science and Numerical Simulation, 63, 2018, 373-379.
[3] Shit, G.C., Haldar, R., Combined Effects of Thermal Radiation and Hall Current on MHD Free-Convective Flow and Mass Transfer over a Stretching Sheet with Variable Viscosity, Journalof Applied Fluid Mechanics, 5(2), 2012, 113-121.
[4] Salem, A.M., Abd el Aziz, M., Effect of Hall currents and chemical reaction on hydromagnetic flow of a stretching vertical surface with internal heat generation/absorption, Applied Mathematical Modelling, 32, 2008, 1236-1254.
[5] Sreedevi, R., Rao, R.R., Prasad Rao, D.R.V., Chamkha, A.J., Combined influence of radiation absorption and Hall current effects on MHD double-diffusive free convective flow past a stretching sheet, Ain Shams Engineering Journal, 7(1), 2016, 383-397.
[6] Su, X., Hall and ion-slip effects on the unsteady MHD mixed convection of Cu-water nanofluid over a vertical stretching plate with convective heat flux, Indian Journal of Pure and Applied Physics, 55, 2017, 564- 573.
[7] Prasad, K.V., Vajravelu, K., Vaidya, H., Hall Effect on MHD Flow and Heat Transfer over a Stretching Sheet with Variable Thickness, International Journal Computational Methods in Engineering Science and Mechanics, 17(4), 2016, 288-297.
[8] Abd el Aziz M., Flow and heat transfer over an unsteady stretching surface with Hall Effect, Meccanica, 45(1), 2010, 97-109.
[9] Vajravelu, K., Prasad, K.V., Vaidya, H., Influence of Hall Current on MHD Flow and Heat Transfer over a slender stretching sheet in the presence of variable fluid properties, Communications in Numerical Analysis, 2016(1), 2016, 17-36.
[10] Ali, M., Alam, M.S., Soret and Hall effect on MHD flow heat and mass transfer over a vertical stretching sheet in a porous medium due to heat generation, ARPN Journal of Engineering and Applied Science, 9(3), 2014, 361-371.
[11] Pal, D., Hall current and MHD effects on heat transfer over an unsteady stretching permeable surface with thermal radiation, Computers and Mathematics with Applications, 66(7), 2013, 1161-1180.
[12] Shateyi, S., Marewo, G.T., On a new numerical analysis of the Hall effect on MHD flow and heat transfer over an unsteady stretching permeable surface in the presence of thermal radiation and heat source/sink, Boundary Value Problems, 2014, 2014, 170.
[13] Sheikholeslami, M., Rokni, H.B., Effect of melting heat transfer on nanofluid flow in existence of magnetic field considering Buongiorno Model, Chinese Journal of Physics, 55(4), 2017, 1115-1126.
[14] Sheikholeslami, M., New computational approach for energy and entropy analysis of nanofluid under the impact of Lorentz force through a porous media, Computer Methods in Applied Mechanics and Engineering, 344, 2019, 319-333.
[15] Sheikholeslami, M., Shehzad, S.A., Li, Z., Shafee, A., Numerical modeling for alumina nanofluid magnetohydrodynamic convective heat transfer in a permeable medium using Darcy law, International Journal of Heat and Mass Transfer, 127, 2018, 614-622.
[16] Sheikholeslami, M., Rokni, H.B., Magnetic nanofluid flow and convective heat transfer in a porous cavity considering Brownian motion effects, Physics of Fluids, 30(1), 2018, 012003.
[17] Sheikholeslami, M., Application of Darcy law for nanofluid flow in a porous cavity under the impact of Lorentz forces, Journal of Molecular Liquids, 266, 2018, 495-503.
[18] Sheikholeslami, M., Numerical approach for MHD Al2O3-water nanofluid transportation inside a permeable medium using innovative computer method, Computer Methods in Applied Mechanics and Engineering, 344, 2019, 306-318.
[19] Sheikholeslami, M., Numerical investigation of MHD nanofluid free convective heat transfer in a porous tilted enclosure, Engineering Computations, 34(6), 2017, 1939-1955.
[20] Turkyilmazoglu, M., Buongiorno Model in a nanofluid filled asymmetric channel fulfilling zero net particle flux at the walls, International Journal of Heat and Mass Transfer, 126, 2018, 974-979.
[21] Abd el-Aziz, M., Effects of Hall current on the flow and heat transfer of a nanofluid over a stretching sheet with partial slip, International Journal of Modern Physics C, 24(7), 2013, 1350044.
[22] Su, X., Zheng, L., Hall effect on MHD flow and heat transfer of nanofluids over a stretching wedge in the presence of velocity slip and Joule heating, Central European Journal of Physics, 11(12), 2013, 1694-1703.
[23] Abdel-Wahed, M., Akl, M., Effect of hall current on MHD flow of a nanofluid with variable properties due to a rotating disk with viscous dissipation and nonlinear thermal radiation, AIP Advances, 6, 2016, 095308.
[24] Makinde, O.D., Iskander, T., Mabood, F., Khan, W.A., Tshehla, M.S., MHD Couette- Poiseuille flow of variable viscosity nanofluids in a rotating permeable channel with Hall effects, Journal of Molecular liquids, 221, 2016, 778-787.
[25] Hayat, T., Shafique, M., Tanveer, A., Alsaedi, A.,Hall and ion slip effects on peristaltic flow of Jeffrey nanofluid with Joule heating,Journal of Magnetism and Magnetic Materials, 407, 2016, 51.
[26] Gireesha, B.J., Mahanthesh, B., Krupalakshmi, K.L., Hall effect on two- phase radiated flow of magneto-dusty-nanoliquid with irregular heat generation/ consumption, Results in Physics, 7, 2017, 4340-4348.
[27] Ullah, I., Bhattacharyya, K, Shafie, S., Khan, I., Unsteady MHD Mixed Convection Slip Flow of Casson Fluid over Nonlinearly Stretching Sheet Embedded in a Porous Medium with Chemical Reaction, Thermal Radiation, Heat Generation/ Absorption and Convective Boundary Conditions, PLoS ONE, 11(10), 2016, e0165348.
[28] Nadeem S., Ul Haq, R., Akbar, N.S., MHD three-dimensional boundary layer flow of Casson nanofluid past a linearly stretching sheet with convective boundary condition, IEEE Transactions on Nanotechnology, 13, 2014, 109-115.
[29] Hussain, T., Shehzad, S.A., Alsaedi, A., Hayat, T., Ramzan, M., Flow of Casson nanofluid with viscous dissipation and convective conditions: a mathematical model, Journal of Central South University, 22, 2015, 1132-1140.
[30] Mustafa, M., Khan, J. A., Model for flow of Casson nanofluid past a non-linearly stretching sheet considering magnetic field effects, AIP Advances, 5, 2015, 077148.
[31] Ullah, I., Khan, I. Shafie, S., MHD Natural Convection Flow of Casson Nanofluid over Nonlinearly Stretching Sheet Through Porous Medium with Chemical Reaction and Thermal Radiation, Nanoscale Research Letters, 11, 2016, 527.
[32] Ibrahim, W., Makinde, O.D., Magnetohydrodynamic Stagnation Point Flow and Heat Transfer of Casson Nanofluid Past a Stretching Sheet with Slip and Convective Boundary Condition, Journal of Aerospace Engineering, 29(2), 2016, 04015037.
[33] Sulochana, C., Ashwinkumar, G.P., Sandeep, N., Similarity solution of 3D Casson nanofluid flow over a stretching sheet with convective boundary conditions, Journal of Nigerian Mathematical Society, 35, 2016, 128-141.
[34] Hayat, T., Aziz, A., Muhammad, T., Alsaedi, A., Active and passive controls of Jeffrey nanofluid flow over a nonlinear stretching surface, Results in Physics, 7, 2017, 4071-4078.
[35] Cowling, T. G., Magnetohydrodynamics, Interscience, New York, 1957.
[36] Kuznetsov, A.V., Nield, D.A., Natural convective boundary-layer flow of a nanofluid past a vertical plate, International Journal of Thermal Sciences, 49, 2010, 243-247.
[37] Rahman, M.M., Eltayeb, I.A., Radiative heat transfer in a hydromagnetic nanofluid past a non-linear stretching surface with convective boundary condition, Meccanica, 48, 2013, 601-615.
[38] Gireesha, B.J., Krishnamurthy, M.R., Prasannakumara, B.C., Gorla, R.S.R., MHD flow and non-linear radiative heat transfer of a Casson nanofluid past a nonlinearly stretching sheet in the presence of a chemical reaction, Nanoscience and Technology: An International Journal, 9 (3), 2018, 207-229.
[39] Hayat, T., Qayyum, S., Alsaedi, A., Asghar, S., Radiation effects on the mixed convection flow induced by an inclined stretching cylinder with non-uniform heat source/sink, PLoS One, 12(4), 2017, e0175584.
[40] Motsa, S.S., Animasaun, I.L., Paired quasi-linearization analysis of heat transfer in unsteady mixed convection nanofluid containing both nanoparticles and gyrotactic microorganisms due to impulsive motion, Journal of Heat Transfer, 138(11), 2016, 114503.
[41] Otegbeye, O., Motsa, S.S., A paired quasilinearization method for solving boundary layer flow problems, AIP Conference Proceedings, 1975(1), 2018, 030020.
[42] Bellman, R.E., Kalaba, R.E., Quasilinearisation and non-linear boundary-value problems, Elsevier, New York, 1965.
[43] Boyd, J.P., Chebyshev and Fourier spectral methods, Dover Publications, 2001.
[44] Trefethen, L.N., Spectral methods in MATLAB, SIAM, 10th ed., 2000.
[45] Canuto, C., Husseini, M.Y., Quarteroni, A., Zang, T.A., Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin, 1988.