Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-25T09:21:00.951Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Prediction of Natural Convection Flow in the Presence of Weak Magnetic Prandtl Number and Strong Magnetic Field with Algebraic Decay in Mainstream Velocity

Part of: Optics, electromagnetic theory - General

Published online by Cambridge University Press:  09 January 2017

Muhammad Ashraf ,
Iram Iqbal ,
M. Masud  and
Nazara Sultana
Muhammad Ashraf*
Affiliation:
Department of Mathematics, Faculty of Science, University of Sargodha, Sargodha, Pakistan
Iram Iqbal
Affiliation:
Department of Mathematics, Faculty of Science, University of Sargodha, Sargodha, Pakistan
M. Masud
Affiliation:
Department of Mathematics, Faculty of Science, University of Sargodha, Sargodha, Pakistan
Nazara Sultana
Affiliation:
Department of Mathematics, Faculty of Science, University of Sargodha, Sargodha, Pakistan
*
*Corresponding author. Email:mashraf682003@yahoo.com (M. Ashraf)
Get access

Abstract

In present work, we investigate numerical simulation of steady natural convection flow in the presence of weak magnetic Prandtl number and strong magnetic field by involving algebraic decay in mainstream velocity. Before passing to the numerical simulation, we formulate the set of boundary layer equations with the inclusion of the effects of algebraic decay velocity, aligned magnetic field and buoyant body force in the momentum equation. Later, finite difference method with primitive variable formulation is employed in the physical domain to compute the numerical solutions of the flow field. Graphical results for the velocity, temperature and transverse component of magnetic field as well as surface friction, rate of heat transfer and current density are presented and discussed. It is pertinent to mention that the simulation is performed for different values of algebraic decay parameter α, Prandtl number Pr, magnetic Prandtl number Pm and magnetic force parameter S.

Keywords

Natural convectionmagnetized plateskin frictioncurrent densityheat transferalgebraic decay in main stream velocity

MSC classification

Secondary: 78A48: Composite media; random media
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 2 , April 2017 , pp. 349 - 361
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Ackerberg, R. C., The viscous incompressible flow inside a cone, J. Fluid Mech., 21 (1971), pp. 47–81.Google Scholar
[2] Ali, F. M., Nazar, R., Arfin, N. M. and Pop, I., MHD stagnation point flow and heat transfer towards stretching sheet with induced magnetic field, Appl. Math. Mech., 32 (2011), pp. 409–418.CrossRefGoogle Scholar
[3] Ashraf, M., Asghar, S. and Hossain, M. A., Thermal radiation effects on hydromagnetic mixed convection flow along a magnetized vertical porous plate, Math. Problems Eng., Article ID 686594, DOI: 10.1155/2010/686594, (2010).CrossRefGoogle Scholar
[4] Ashraf, M., Asghar, S. and Hossain, M. A., Computational study of combined effects of conduction-radiation and hydromagnetics on natural convection flow past magnetized permeable plate, Appl. Math. Mech., 33 (2012), pp. 731–750.CrossRefGoogle Scholar
[5] Ashraf, M., Asghar, S. and Hossain, M. A., Fluctuating hydromagnetic natural convection flow past a magnetized vertical surface in the presence of thermal radiation, Thermal Sci. J., 16 (2012), pp. 1081–1096.Google Scholar
[6] Ashraf, M., Ahmad, U., Ahmad, M. and Sultana, N., Computational study of mixed convection flow with algebraic decay of mainstream velocity in the presence of applied magnetic field, J. Appl. Mech. Eng., 4 (2015), 175. doi: 10.4172/2168-9873.1000175.Google Scholar
[7] Bikash, S. and Sharma, H. G., MHD flow and heat transfer from continuous surface in uniform free stream of non newtonian fluid, Appl. Math. Mech., 28 (2007), pp. 1467–1477.Google Scholar
[8] Brown, S. and Stewartson, K., On similarity solutions of the boundary-layer equations with algebraic decay, J. Fluid Mech., 23 (1965), pp. 673–687.Google Scholar
[9] Buckmaster, J., Separation and magnetohydrodynamics, J. Fluid Mech., 38 (1969), pp. 481–498.CrossRefGoogle Scholar
[10] Chawla, S. S., Fluctuating boundary layer on a magnetized plate, Proc. Comb. Phil. Soc., 63 (1967), 513.Google Scholar
[11] Clarke, J. F., Transpiration and natural convection the vertical plate problem, J. Fluid Mech., 57 (1973), pp. 45–61.Google Scholar
[12] Clarke, J. F. and Riley, N., Natural convection induced in a gas by the presence of a hot porous horizontal surface, Quart. J. Mech. Appl. Math., 28 (1975), pp. 373–396.CrossRefGoogle Scholar
[13] Davies, T. V., The magnetohydrodynamic boundary layer in two-dimensional steady flow past a semi-infinite flat plate, Part I, Uniform conditions at infinity, Proceeding of the Royal Society of London Series A, 273 (1963), pp. 496–507.Google Scholar
[14] Davies, T. V., The magnetohydrodynamic boundary layer in two-dimensional steady flow past a semi-infinite flat plate, Part III, Influence of adverse magneto-dynamic pressure gradient, Proceeding of the Royal Society of London Series A, 273 (1963), pp. 518–537.Google Scholar
[15] Ali, F., Khan, I., Samiulhaq, and Shafie, S., Conjugate effects of heat transfer on MHD free convection flow over an inclined plate embeded in porous media, 8 (2013).Google Scholar
[16] Ali, F., Khan, I., Samiulhaq, and Shafie, S., Effects of wall shear stress on unsteady MHD conjugate flow in porous medium with ramped wall temperature, Plos One, 9 (2014), 90280.Google Scholar
[17] Glauert, M. B., The boundary layer on a magnetized plate, J. Fluid Mech., 12 (1962), 625.CrossRefGoogle Scholar
[18] Goldstein, S., On backward boundary layers and flow in converging passages, J. Fluid Mech., 21 (1965), pp. 33–45.Google Scholar
[19] Gupta, A. S., Misra, J. C. and Reza, M., Magnetohydrodynamic shear flow along a flat plate with uniform suction or blowing, ZAMP, 56 (2005), pp. 1030–1047.Google Scholar
[20] Hildyard, T., Falkner-Skan problem in magnetohydrodynamics, Phys. Fluids, 15 (1972), pp. 1023–1027.CrossRefGoogle Scholar
[21] Ingham, D. B., The magnetogasdynamic boundary layer for a thermally conducting plate, Quart. J. Mech. Appl. Math., 20 (1967), pp. 347–364.Google Scholar
[22] Merkin, J. H., On solutions of the boundary-layer equations with algebraic decay, J. Fluid Mech., 88 (1978), pp. 309–321.Google Scholar
[23] Merkin, H. J., The effects of blowing and suction on free convection boundary layers, Int. J. Heat Mass Transfer, 18 (1975), pp. 237–244.CrossRefGoogle Scholar
[24] Shit, G. C. and Haldar, R., Effect of thermal radiation on MHD viscous fluid flow and heat transfer over non linear shirking porous plate, Appl. Math. Mech., 32 (2011), pp. 677–688.Google Scholar
[25] Sparrow, E. M. and Cess, R. D., Free convection with blowing or suction, J. Heat Transfer, 83 (1961), pp. 387–396.Google Scholar
[26] Su, X. H. and Zheng, L. C., Approximate solution to MHD Falkner-Skan flow over permeable wall, Appl. Math. Mech., 32 (2011), pp. 401–408.Google Scholar
[27] Tan, C. W. and Wang, C. T., Heat transfer in aligned-field magnetohydrodynamic flow past a flat plate, Int. J. Heat Mass Transfer, 11 (1967), pp. 319–329.Google Scholar
[28] Uddin, M. J., Waqar Khan, A. and Ismail, I. A., MHD free convection boundary layer flow of nanofluid past a flat vertical plate with newtonian heating boundary conditions, Plos One, 7 (2012), 49499.Google Scholar
[29] Vedhanayagam, M., Altenkrich, R. A. and Eichhorn, R., A transformation of the boundary layer equations for free convection past a vertical flat plate with arbitrary blowing and wall temperature variations, Int. J. Heat Mass Transfer, 23 (1980), pp. 1286–1288.Google Scholar
[30] Zueco, J. and Ahmed, S., Combined heat and mass transfer by convection MHD flow along a porous plate with chemical reaction in presence of heat source, Appl. Math. Mech., 31 (2010), pp. 1217–1230.CrossRefGoogle Scholar