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

**M. O Ibrahim**^{1}, **K. K. Asogwa**^{2,}, **I. J Uwanta**^{3}, **B. G Dan Shehu**^{4}

^{1}Department of Mathematics, University of Ilorin, Kwara State, Nigeria

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

^{3}Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria

^{4}Sokoto Energy Research Centre, Usmanu Danfodiyo University, Sokoto, Nigeria

*American Journal of Modeling and Optimization*, **2013** 1 (3),
pp 36-42

DOI: 10.12691/ajmo-1-3-3

Received July 28, 2013; Revised August 05, 2013; Accepted August 09, 2013

Corresponding author: kanasogwa@yahoo.com |

## Cite This Article:

- Ibrahim, M. O, et al. "Radiative Effect on MHD Fluid Flow in a Vertical Channel under Optically Thick Approximation."
*American Journal of Modeling and Optimization*1.3 (2013): 36-42.

- Ibrahim, M. O. , Asogwa, K. K. , Uwanta, I. J. , & Shehu, B. G. D. (2013). Radiative Effect on MHD Fluid Flow in a Vertical Channel under Optically Thick Approximation.
*American Journal of Modeling and Optimization*,*1*(3), 36-42.

- Ibrahim, M. O, K. K. Asogwa, I. J Uwanta, and B. G Dan Shehu. "Radiative Effect on MHD Fluid Flow in a Vertical Channel under Optically Thick Approximation."
*American Journal of Modeling and Optimization*1, no. 3 (2013): 36-42.

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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 *a*_{i} and τ_{2} 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

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