Open Access Peer-reviewed

Radiative Effect on MHD Fluid Flow in a Vertical Channel under Optically Thick Approximation

M. O Ibrahim1, K. K. Asogwa2,, I. J Uwanta3, B. G Dan Shehu4

1Department of Mathematics, University of Ilorin, Kwara State, Nigeria

2Department of Physical and Computer Sciences, College of Natural and Applied Science, McPherson University, Abeokuta. Ogun State, Nigeria

3Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria

4Sokoto Energy Research Centre, Usmanu Danfodiyo University, Sokoto, Nigeria

American Journal of Modeling and Optimization. 2013, 1(3), 36-42. DOI: 10.12691/ajmo-1-3-3
Published online: August 25, 2017


Many non linear problems that arise in real life situations defy analytical solution; hence numerical techniques are desirable to find the solution of such equations. In this study we use the Newton scheme method from Taylor series to solve fourth order non linear problem. The velocity profiles and temperature profile are studied for different physical parameters like, Magnetic parameter M, Radiation F and thermal Grashof number Ga. The results obtained after computation taking into cognizance of the parameters present shows that the Magnetic parameter M increases with increasing velocity, while the trend reverses with radiation and thermal Grashof number in a vertical channel under optically thick approximation. It also observed that temperature rise with increasing values of ai and τ2 and trend of heat transfer coefficient due to thermal conduction h increases with the rate of change of .


MHD, recurrence relation, vertical plate, radiation, flow rate
[1]  Abel, S., K. V. Prasad, and Mahaboob, A.: ‘‘Buoyancy force and thermal radiation effects in MHD boundary layer visco-elastic fluid flow over continuously moving stretching surface,’’ International Journal of Thermal Sciences, vol. 44, no. 5, pp. 465-476. 2005.View Article
[2]  Bharti RP, Chhabra RP, Eswaran V: ‘‘Steady flow of power-law fluids across a circular cylinder,’’ Can. J. Chem. Eng. 84(4) (in press) 2006.
[3]  Cogley, A. C. L., Vincenti, W. G., Gilles, E. S : ‘‘Differential approximation for radiative heat transfer in a non grey gas near equilibrium,’’ Am. Inst. Aeronat.Astronaut. J 6: 551-553. 1968.View Article
[4]  Crammer, K., Pai, S. I: ‘‘Magnetofluid dynamics for engineers and applied physicists,’’ McGraw-Hill Book Company. 1973.
[5]  Grief, R., Habib I. S. and Lin J.C.: ‘‘Laminar convection of a radiating gas in a vertical Channel,’’ Journal of Fluid Mechanics Vol. 46, pp 513-522. 1977.View Article
[6]  Ibrahim M.O. ; ‘‘Radiation effect on laminar convective flow of a radiating gas in a vertical channel under optically thick limit approximation’’’ M.Sc thesis , University of Ilorin, Nigeria. 1997.
[7]  Kearsley, A. J.: ‘‘A steady state model of Couette flow with viscous heating,’’ Int. J. Engng Sci. 32: 179-186. 1994.View Article
[8]  Makinde, O. D., Mhone, P. Y. ‘‘Heat transfer to MHD oscillatory flow in a channel filled with porous medium,’’ Romanian J. Physics 50 (9-10): 931-938. 2005.
[9]  Makinde, O. D., Osalusi, E (2006), MHD steady flow in a channel with slip at permeable boundaries, Romanian J. Physics 51(3-4): 319-328.
[10]  Moreau, R.: ‘‘Magnetohydrodynamics,’’ Kluwer Academic Publishers. 1990.View Article
[11]  Taiwo O.A. and Ogunlaran O.M.: ‘‘Numerical solution of fourth order linear ordinary differential equations by cubic spline collocation tau method,’’ Journal of Mathematics and Statistics 4 (4): 264-268, 2008.