Joule and Viscous Dissipation Effects on MHD Boundary Layer Flow over a Stretching Sheet with Variable Thickness




Boundary Layer Flow, Heat Transfer Rate, MHD, Skin Friction, Stretching Sheet, Variable Thickness


This paper is aimed to investigate the influence of Joule and viscous dissipation effects on boundary layer flow over a stretching sheet with variable thickness and surface temperature. The flow is subjected to space dependent magnetic field applied normal to the sheet. Mathematical modeling is done under boundary layer approximations. The governing partial differential equations are transformed into ordinary differential equations via appropriate similarity transformations. The resulting set of nonlinear equations is solved numerically. The impact of various physical parameters on velocity and temperature profiles is analyzed. Also, their effects on skin friction coefficient and Nusselt number are presented and discussed.


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T. Altan, S. Oh, H. Gegel, Metal forming fundamentals and applications, American society for metals, metals park, Ohio, 1979.

E.G. Fisher, Extrusion of plastics, Wiley, New York, 1976.

M.V. Karwe, Y. Jaluria, Numerical simulation of thermal transport associated with a continuously moving flat sheet in materials processing, ASME J. of Heat Trans. 113(3), 612-619 (1991).

B.C. Sakiadis, Boundary layer behavior on continuous solid surface: II. Boundary-layer equations for two-dimensional and axisymmetric flow, J. of Americ. Inst. Of Chem. Engg. 7(2), 221-225 (1961).

L.J. Crane, Flow past a stretching plate, Zeitschrift fr angewandte Mathematik und Physik (ZAMP). 21, 645-647 (1970).

A. Chakrabarti, A.S. Gupta, Hydromagnetic flow and heat transfer over a stretching sheet, Quart. J. of Mech and Appl. Math. 37, 73-78 (1979).

A.K. Jhankal, M.Kumar, MHD boundary layer flow past a stretching plate with heat transfer, IJES, 2(3), 09-13 (2013).

E.M. Sparrow, R.D. Cess, The effect of a magnetic field on free convenction heat transfer, In. J. of Heat and Mass Trans. 3, 267-274 (1961).

T. C. Chaim, Magnetohydrodynamic heat transfer over a non-isothermal stretching sheet, Acta Mech. 122, 169-179 (1977).

Tiegang Fang, Ji Zhang, Yongfang Zhong, Boundary layer flow over a stretching sheet with variable thickness, Appl. Math. And Comput. 218, 7241-7252 (2012).

M. M. Khader, A. M. Megahed, Numerical solution for boundary layer flow due to a nonlinearly stretching sheet with variable thickness and slip velocity, Europ. Phys. J. Plus. 128, 100 (2013).

L. G. Grubka, K. M. Bobba, Heat transfer characteristics of a continuous stretching surface with variable temperature, ASME J. of Heat Trans. 107, 248-250 (1985).

S. P. Anjali Devi, M. Thiyagarajan, Steady nonlinear hydromagnetic flow and heat transfer over a stretching surface of variable temperature, Heat and Mass Trans. 42, 671-677 (2006).

S. P. Anjali Devi, M. Prakash, Steady nonlinear hydromagnetic flow over a stretching surface with variable thickness and variable surface temperature, J. KSIAM, 18(3), 245-256 (2014).

K. K. Jaber, Effects of viscous dissipation and Joule heating on MHD flow of a fluid with variable properties past a stretching vertical plate, European Scientific Journal, 10(33), 383-393 (2014).

G. Palani, K. Y. Kim, Joule heating and viscous dissipation effects on MHD flow past a semi-infinite plate with variable surface temperature, Journal of Engineering Thermophysics, 20(4), 501-517 (2011).

R. A. Hamid, N. M. Arifin, R. Nazar, F. M. Ali, Effects of Joule heating and viscous dissipation on MHD marangoni convection boundary layer flow, Journal of Science and Technology, 3(1), 67-77 (2011).

S. P. Anjali Devi, B. Ganga, Effects of viscous and Joule dissipation on MHD flow, heat and mass transfer past a stretching porous surface embedded in a porous medium, Nonlinear Analysis: Modelling and Control, 14(3), 303-314 (2009).

I. S. Awaluddin, A. Ishak, I. Pop, On the Stability of MHD Boundary Layer Flow of a Stretching/Shrinking Wedge, Scientific Reports, 8, 13622 (2018).

G. Narender, S. Misra, K. Govardhan, Numerical Solution of MHD Nanofluid over a Stretching Surface with Chemical Reaction and Viscous Dissipation, Chemical Engineering Research Bulletin, 21, 36 - 45 (2019).

R. P. Sharma, S. Shaw, MHD Non-Newtonian Fluid Past a Stretching Sheet under the Influence of Non-linear Radiation and Viscous Dissipation, Journal of Applied and Computational Mechanics, 8(3), 949 - 961 (2022).

H. B. Keller, Numerical Methods for Two-Point Boundary-Value Problems , Blaisdell, Waltham, MA, 1968.




How to Cite

Mahmood, A., Ahmed, S., & Iram, H. (2022). Joule and Viscous Dissipation Effects on MHD Boundary Layer Flow over a Stretching Sheet with Variable Thickness. International Journal of Emerging Multidisciplinaries: Mathematics, 1(2), 1–10.



Research Article