Main Article Content



In this paper, we re-investigate the problem describing effects of radiation, Joule heating and viscous dissipation on MHD Marangoni convection boundary layer over a flat surface with suction/injection. The analytical solution obtained for the reduced system of nonlinear-coupled differential equations governing the problem. Laplace transform successfully implemented to get the exact expression for the temperature profile. Furthermore, comparing the current exact results with approximate numerical results obtained using Runge-Kutta-Fehlberg method is introduced. These comparisons declare that the published numerical results agree with the current exact results. In addition, the effects of various parameters on the temperature profile are discussed graphically.

Article Details

How to Cite
KHALED, S. M.. THE EXACT EFFECTS OF RADIATION AND JOULE HEATING ON MHD MARANGONI CONVECTION OVER A FLAT SURFACE. Thermal Science, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <>. Date accessed: 23 june 2017. doi:
Received 2017-03-06
Accepted 2017-03-13
Published 2017-03-13


[1] T.S. Khaleque, M.A. Samad, Effects of radiation, heat generation and viscous dissipation on MHD free convection flow along a stretching sheet, Journal of Applied Sciences, Engineering and Technology, 2(4) (2010) 368-377.
[2] M. Amkadni, A. Azzouzi, On a similarity solution of MHD boundary layer flow over a moving vertical cylinder, Journal of Differential Equations and Nonlinear Mechanics, Volume 2006, Article ID 52765, pp: 1-9.
[3] R. Rajeswari, B. Jothiram, V.K. Nelson, Chemical reaction, heat and mass transfer on nonlinear MHD boundary layer flow through a vertical porous surface in the presence of suction, Applied Mathematical Sciences, 3(50) (2009) 2469-2480.
[4] K. Bhattacharyya, G.C. Layek, Chemically reactive solute distribution in MHD boundary layer flow over a permeable stretching sheet with suction or blowing, Chemical Engineering Communications, 197(12) (2010) 1527-1540.
[5] A. Al-Mudhaf, A.J. Chamkha, Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation or absorption effects, Heat Mass Transfer, 42 (2005) 112-121.
[6] C.Sulochana, N.Sandeep, Dual solutions for radiative MHD forced convective flow of a Nanofluid over a slandering stretching sheet in porous medium, J. Naval Architecture and Marine Eng., 12(2015) 115-124.
[7] A.Veerasuneela Rani, V.Sugunamma and N.Sandeep, Hall Current effects on convective heat and mass transfer flow of viscous fluid in a vertical wavy channel, International Journal of Emerging trends in Engineering and Development 4(2), 252-278, 2012
[8] G. Pathak, C.H. Maheshwari, Effect of radiation on unsteady free convection flow bounded by an oscillating plate with variable wall temperature, International Journal of Applied Mechanics and Engineering, 11(2) (2006) 371-382.
[9] C.Sulochana, M.K.Kishore Kumar, N.Sandeep, Nonlinear thermal radiation and chemical reaction effects on MHD 3D Casson fluid flow in porous medium, Chemical and process engineering research, 37, 24-36,2015.
[10] N.Sandeep, A.Vijaya Bhaskar Reddy and V Sugunamma, Effect of Radiation and Chemical Reaction on Transient MHD Free Convective flow over a Vertical Plate through Porous Media, Chemical and Process Engineering Research 2, 1-9, 2012.
[11] S. Shateyi, Thermal radiation and buoyancy effects on heat and mass transfer over a semi-infinite stretching surface with suction and blowing, Journal of Applied Mathematics, Article ID 414830, (2008), pp: 12.
[12] S. Suneetha, N.B. Redd, V.R. Prasad, Thermal radiation effects on MHD free convection flow past an impulsively started vertical plate with variable surface temperature and concentration, Journal of Naval Architecture and Marine Engineering, 2 (2008) 57-70.
[13] M.A. Alim, M.D. Alam, A. Mamun, Joule heating effect on the coupling of conduction with magnetohydrodynamic free convection flow from a vertical flat plate, Nonlinear Analysis: Modelling and Control, 12(3) (2007) 307-316.
[14] V.D. Borisevich, E.P. Potanin, Effects of viscous dissipation and Joule heat on heat transfer near a rotating disk in the presence of intensive suction, Moscow Engineering Physics Institute, Translated from Inzhenerno-Fizicheskii Zhurnal., 55(5) (1988) 740-743.
[15] H.M. Duwairi, Viscous and joule heating effects on forced convection flow from radiate isothermal porous surfaces, International Journal of Numerical Methods for Heat and Fluid Flow, 15(5) (2005) 429-440.
[16] C.H. Chen, Combined effects of Joule heating and viscous dissipation on magnetohydrodynamic flow past a permeable, stretching surface with free convection and radiative heat transfer, Journal of Heat Transfer, 132 (2010) 1-5, 064503.
[17] M. Turkyilmazoglu, Exact solutions corresponding to the viscous incompressible and conducting fluid flow due to a porous rotating disk, Journal of Heat Transfer, 131 (2009) 091701.
[18] Yan ZHANG et al., Analysis of Marangoni convection of non-Newtonian power law fluids with linear temperature distribution, Thermal Science, Year 2011, Vol. 15, pp. S45-S52.
[19] Rohana Abdul Hamid, Norihan Md Arifin, Roslinda Nazar, Effects of Radiation, Joule Heating and Viscous Dissipation on MHD Marangoni Convection over a Flat Surface with Suction and Injection, World Applied Sciences Journal 21 (6) (2013) 933-938.
[20] A. Ebaid, Remarks on the homotopy perturbation method for the peristaltic flow of Jeffrey fluid with Nano-particles in an asymmetric channel, Comput. Math. Applic. 68 (2014) (3), 77-85.
[21] A. Ebaid, S.M. Khaled, An Exact Solution for a Boundary Value Problem with Application in Fluid Mechanics and Comparison with the Regular Perturbation Solution, Abstract and Applied Analysis, (2014).
[22] E.H. Aly, A. Ebaid, Effect of the Velocity Second Slip Boundary Condition on the Peristaltic Flow of Nanofluids in an Asymmetric Channel: Exact Solution, Abstract and Applied Analysis, (2014).
[23] E.H. Aly, A. Ebaid, Exact Analytical Solution for the Peristaltic Flow of Nanofluids in An Asymmetric Channel with Slip Effect of the Velocity, Temperature and Concentration, Journal of Mechanics, (2014) 1-12.
[24] Brewster, M. Q., 1992. Thermal radiative transfer properties, Wiley, New York.
[25] A. Ebaid, F. Al Mutairi, S.M. Khaled, Effect of velocity slip boundary condition on the flow and heat transfer of Cu-water and TiO2-water Nanofluids in the presence of a magnetic field, Advances in Mathematical Physics, Volume, 2014, Article ID 538950, 9 pages,
[26] A. Ebaid, E.H. Aly, Exact Analytical Solution of the Peristaltic Nanofluids Flow in an Asymmetric Channel with Flexible Walls and Slip Condition: Application to the Cancer Treatment, Computational and Mathematical Methods in Medicine, Volume 2013, Article ID 825376, 8 pages,
[27] E.H. Aly, A. Ebaid, Exact analytical solution for suction and injection flow with thermal enhancement of five Nanofluids over an isothermal stretching sheet with effect of the slip model: a comparative study, Abstract and Applied Analysis, Volume 2013, Article ID 721578, 14 pages,
[28] A. Ebaid, S.H. Alatawi, Influence of Wall Properties on the Peristaltic Flow of a Nanofluid in View of the Exact Solutions: Comparisons with Homotopy Analysis Method, Z. Nature. A., 69 (5-6) (2014), 199-206.