Magnetohydrodynamics Fluid Flow and Heat Transfer over a Permeable Shrinking Sheet with Joule dissipation: Analytical Approach

Document Type: Research Paper

Authors

1 Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran

2 Department of Mechanical Engineering, Faculty of Imam Khomeini, Behshahr Branch, Technical and Vocational University (TVU), Mazandaran, Iran

Abstract

A laminar, two dimensional, steady boundary layer Newtonian conducting fluid flow passes over a permeable shrinking sheet in the presence of a uniform magnetic field is investigated. The governing equations have converted to ordinary nonlinear differential equations (ODE) by using appropriate similarity transformations. The main idea is to transform ODE with infinite boundary condition into other sets of variables in a way that infinite boundary condition becomes a finite boundary condition. The effects of physical parameters affecting the velocity and temperature are shown. The results show that with increasing the magnetic and suction parameters, the normal velocity component of fluid increases over the sheet whereas the tangential velocity component of fluid decreases. Moreover, when the suction parameter, the Prandtl and Eckert numbers increase, the rate of the heat transfer increases. However, when the magnetic parameter increases, the rate of heat transfer reduces. Finally, the solution shows that the results of the analytical method using a special technique have an excellent agreement with numerical solutions.

Keywords

Main Subjects

[1] B.G. Mahanthesh, B. J., Animasaun, I. L., Exploration of Non-Linear Thermal Radiation and Suspended Nanoparticles Effects on Mixed Convection Boundary Layer Flow of Nanoliquids on a Melting Vertical Surface, Journal of Nanofluids, 7 (2018) 833-843.

[2] B.G. Mahanthesh, B. J., Sheikholeslami, M., Shehzad, S. A., Kumar, P. B. S., Nonlinear Radiative Flow of Casson Nanoliquid Past a Cone and Wedge with Magnetic Dipole: Mathematical Model of Renewable Energy, Journal of Nanofluids, 7 (2018) 1089-1100.

[3] B.J. Gireesha, B. Mahanthesh, G.T. Thammanna, P.B. Sampathkumar, Hall effects on dusty nanofluid two-phase transient flow past a stretching sheet using KVL model, Journal of Molecular Liquids, 256 (2018) 139-147.

[4] X. Chen, Y. Ye, X. Zhang, L. Zheng, Lie-group similarity solution and analysis for fractional viscoelastic MHD fluid over a stretching sheet, Computers & Mathematics with Applications, 75 (2018) 3002-3011.

[5] Y. Liu, B. Guo, Effects of second-order slip on the flow of a fractional Maxwell MHD fluid, Journal of the Association of Arab Universities for Basic and Applied Sciences, 24 (2017) 232-241.

[6] B. Mahanthesh, B.J. Gireesha, R.S.R. Gorla, F.M. Abbasi, S.A. Shehzad, Numerical solutions for magnetohydrodynamic flow of nanofluid over a bidirectional non-linear stretching surface with prescribed surface heat flux boundary, Journal of Magnetism and Magnetic Materials, 417 (2016) 189-196.

[7] B. Mahanthesh, B.J. Gireesha, R.S.R. Gorla, Heat and mass transfer effects on the mixed convective flow of chemically reacting nanofluid past a moving/stationary vertical plate, Alexandria Engineering Journal, 55 (2016) 569-581.

[8] B.J. Gireesha, B. Mahanthesh, I.S. Shivakumara, K.M. Eshwarappa, Melting heat transfer in boundary layer stagnation-point flow of nanofluid toward a stretching sheet with induced magnetic field, Engineering Science and Technology, an International Journal, 19 (2016) 313-321.

[9] B.J.G. Gireesha, Rama Subba Reddy, Mahanthesh, B., Effect of Suspended Nanoparticles on Three-Dimensional MHD Flow, Heat and Mass Transfer of Radiating Eyring-Powell Fluid Over a Stretching Sheet, Journal of Nanofluids, 4 (2015) 474-484.

[10] B.M. B. J. Gireesha, M. M. Rashidi, MHD boundary layer heat and mass transfer of a chemically reacting Casson  fluid over a permeable stretching surface with non-uniform heat source/sink, International Journal of Industrial Mathematics, 7 (2015) 247-260.

[11] B.C. Sakiadis, Boundary-layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface, AIChE Journal, 7 (1961) 221-225.

[12] B.C. Sakiadis, Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow, AIChE Journal, 7 (1961) 26-28.

[13] P.S. Gupta, A.S. Gupta, Heat and mass transfer on a stretching sheet with suction or blowing, The Canadian Journal of Chemical Engineering, 55 (1977) 744-746.

[14] M.E. Ali, On thermal boundary layer on a power-law stretched surface with suction or injection, International Journal of Heat and Fluid Flow, 16 (1995) 280-290.

[15] E. Magyari, B. Keller, Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface, Journal of Physics D: Applied Physics, 32 (1999) 577.

[16] K. Vajravelu, J.R. Cannon, D. Rollins, Analytical and Numerical Solutions of Nonlinear Differential Equations Arising in Non-Newtonian Fluid Flows, Journal of Mathematical Analysis and Applications, 250 (2000) 204-221.

[17] K. Vajravelu, D. Rollins, Hydromagnetic flow of a second grade fluid over a stretching sheet, Applied Mathematics and Computation, 148 (2004) 783-791.

[18] R. Cortell, Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and to a transverse magnetic field, International Journal of Heat and Mass Transfer, 49 (2006) 1851-1856.

[19] C.Y. Wang, Stagnation flow towards a shrinking sheet, International Journal of Non-Linear Mechanics, 43 (2008) 377-382.

[20] S. Aïboud, S. Saouli, Second Law Analysis of Viscoelastic Fluid over a Stretching Sheet Subject to a Transverse Magnetic Field with Heat and Mass Transfer, Entropy, 12 (2010) 1867.

[21] B. Sahoo, Effects of slip on sheet-driven flow and heat transfer of a non-Newtonian fluid past a stretching sheet, Computers & Mathematics with Applications, 61 (2011) 1442-1456.

[22] B.I. Olajuwon, Convection heat and mass transfer in a hydromagnetic flow of a second grade fluid in the presence of thermal radiation and thermal diffusion, International Communications in Heat and Mass Transfer, 38 (2011) 377-382.

[23] B. Sahoo, S. Poncet, Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition, International Journal of Heat and Mass Transfer, 54 (2011) 5010-5019.

[24] T.E. Akinbobola, S.S. Okoya, The flow of second grade fluid over a stretching sheet with variable thermal conductivity and viscosity in the presence of heat source/sink, Journal of the Nigerian Mathematical Society, 34 (2015) 331-342.

[25] M. Mustafa, Viscoelastic Flow and Heat Transfer over a Non-Linearly stretching sheet: OHAM Solution, Journal of Applied Fluid Mechanics, 9 (2016) 1321-1328.

[26] T. Hayat, Z. Abbas, M. Sajid, On the Analytic Solution of Magnetohydrodynamic Flow of a Second Grade Fluid Over a Shrinking Sheet, Journal of Applied Mechanics, 74 (2007) 1165-1171.

[27] T. Fang, J. Zhang, Closed-form exact solutions of MHD viscous flow over a shrinking sheet, Communications in Nonlinear Science and Numerical Simulation, 14 (2009) 2853-2857.

[28] K. Bhattacharyya, Effects of radiation and heat source/sink on unsteady MHD boundary layer flow and heat transfer over a shrinking sheet with suction/injection, Frontiers of Chemical Science and Engineering, 5 (2011) 376-384.

[29] Muhaimin, R. Kandasamy, A.B. Khamis, Effects of heat and mass transfer on nonlinear MHD boundary layer flow over a shrinking sheet in the presence of suction, Applied Mathematics and Mechanics, 29 (2008) 1309.

[30] S. Mukhopadhyay, MHD boundary layer flow and heat transfer over an exponentially stretching sheet embedded in a thermally stratified medium, Alexandria Engineering Journal, 52 (2013) 259-265.

[31] W. Ibrahim, B. Shanker, Magnetohydrodynamic Boundary Layer Flow and Heat Transfer of a Nanofluid Over Non-Isothermal Stretching Sheet, Journal of Heat Transfer, 136 (2014) 051701-051701.

[32] O. Pourmehran, M. Rahimi-Gorji, M. Gorji-Bandpy, D.D. Ganji, Analytical investigation of squeezing unsteady nanofluid flow between parallel plates by LSM and CM, Alexandria Engineering Journal, 54 (2015) 17-26.

[33] M. Rahimi-Gorji, O. Pourmehran, M. Gorji-Bandpy, D.D. Ganji, An analytical investigation on unsteady motion of vertically falling spherical particles in non-Newtonian fluid by Collocation Method, Ain Shams Engineering Journal, 6 (2015) 531-540.

[34] S.M. Ebrahimi, M. Abbasi, M. Khaki, Fully Developed Flow of Third-Grade Fluid in the Plane Duct with Convection on the Walls, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 40 (2016) 315-324.

[35] S.A.R. Sahebi, H. Pourziaei, A.R. Feizi, M.H. Taheri, Y. Rostamiyan, D.D. Ganji, Numerical analysis of natural convection for non-Newtonian fluid conveying nanoparticles between two vertical parallel plates, The European Physical Journal Plus, 130 (2015) 238.

[36] M. Hatami, K. Hosseinzadeh, G. Domairry, M.T. Behnamfar, Numerical study of MHD two-phase Couette flow analysis for fluid-particle suspension between moving parallel plates, Journal of the Taiwan Institute of Chemical Engineers, 45 (2014) 2238-2245.

[37] P.G. Moakher, M. Abbasi, M. Khaki, Fully developed flow of fourth grade fluid through the channel with slip condition in the presence of a magnetic field, Journal of Applied Fluid Mechanics, 9 (2016) 2239-2245.

[38] J. Rahimi, D.D. Ganji, M. Khaki, K. Hosseinzadeh, Solution of the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linear stretching sheet by collocation method, Alexandria Engineering Journal, 56(4) (2017) 621-627.