International Journal of Advanced and Applied Sciences

Int. j. adv. appl. sci.

EISSN: 2313-3724

Print ISSN: 2313-626X

Volume 4, Issue 4  (April 2017), Pages:  67-72

Title: Analytic study of MHD flow and boundary layer control over a nonisothermal flat plate

Author(s):  M. Shanmugapriya *


Department of Mathematics, SSN College of Engineering, Chennai, India

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The objective of the present work is to investigate the boundary layer flow and heat transfer over a moving flat plate in the presence of a transverse magnetic field. Gyarmati’s variational principle developed on the thermodynamic theory of irreversible processes is employed to solve the problem numerically. The governing boundary layer equations are approximated as simple polynomial functions, and the functional of the variational principle is constructed. The Euler-Langrange equations are reduced to simple polynomial equations in terms of boundary layer thicknesses. The velocity and temperature as well as skin friction and heat transfer parameters are analysed for any given values of Prandtl number Pr, magnetic parameter M, Eckert number Ec, moving parameter Ɛ and n. The obtained numerical solutions are compared with known numerical solutions and the comparison is found to be satisfactory. 

© 2017 The Authors. Published by IASE.

This is an open access article under the CC BY-NC-ND license (

Keywords: Gyarmati’s variational principle, MHD boundary layer, Heat transfer, Non-isothermal

Article History: Received 16 December 2016, Received in revised form 12 February 2017, Accepted 20 February 2017

Digital Object Identifier:


Shanmugapriya M (2017). Analytic study of MHD flow and boundary layer control over a nonisothermal flat plate. International Journal of Advanced and Applied Sciences, 4(4): 67-72


Afzal N, Badaruddin A, and Elgarvi AA (1933). Momentum and heat transport on a continuous flat surface moving in a parallel stream. International Journal of Heat and Mass Transfer, 36(13): 3399-3403
Blasius H (1908). Grenschichten in flussigkeiten mit kleiner Reibung. Zeitschrift für Angewandte Mathematik und Physik, 56: 1-37.
Chandrasekar M (2003). Analytical study of heat transfer and boundary layer flow with suction and injection. Heat and Mass Transfer, 40(1-2): 157-165.
Cortell R (2005). Numerical solutions of the classical Blasius flat-plate problem. Applied Mathematics and Computation, 170(1): 706-710.
Erickson LE, Fan LT, and Fox VG (1966). Heat and mass transfer on moving continuous flat plate with suction or injection. Industrial and Engineering Chemistry Fundamentals, 5(1): 19-25.
Gyarmati I (1969). On the "governing principle of dissipative processes" and its extension to non‐linear problems. Annalen der Physik, 478(7‐8): 353-378.
Gyarmati I (1979). Non-equilibrium Thermodynamics: Field Theory and Variational Principles. Springer-Verlag, Berlin, Germany: 36-97.
Ishak N, Yacob NA, and Bachok N (2011). Radiation effects on the thermal boundary layer flow over a moving plate with convective boundary condition. Meccanica, 46(4): 795-801.
Jat RN and Neemawat A (2014). MHD boundary layer flow and heat transfer over a moving non-isothermal flat plate. Computational Mathematics and Modeling, 25(4): 514-520.
Kumari M and Nath G (2001). MHD boundary-layer flow of a non-Newtonian fluid over a continuously moving surface with a parallel free stream. Acta Mechanica, 146(3): 139-150.
Onsager L (1931a). Reciprocal relations in irreversible processes. I. Physical Review, 37(4): 405-406.
Onsager L (1931b). Reciprocal relations in irreversible processes. II. Physical Review, 38(12): 2265-2266.
Sakiadis BC (1961). Boundary layer behaviour on continuous solid surfaces: 1. Boundary-Layer Equations for Two-Dimensional and Axisymmetric Flow. American Institute of Chemical Engineers Journal, 7(1): 26-28.
Shanmugapriya M and Chandrasekar M (2008). Analytic solution of a free and forced convection with suction and injection over a non-isothermal wedge. Bulletin of the Malaysian Mathematical Sciences Society, Second Series, 31(1): 11-24.
Tsou FK, Sparrow EM, and Goldstein RJ (1967). Flow and heat transfer in the boundary layer on a continuous moving surface. International Journal of Heat and Mass Transfer, 10(2): 219-235.