Document Type : Full Lenght Research Article

**Author**

Department of Mathematical Sciences, Federal University of Technology,P.M.B 704,Akure Ondo State, Nigeria

**Abstract**

The present paper seeks to examine a numerical method of solution called spectra quasi-linearization method (SQLM) to the problem of unsteady MHD boundary layer ﬂow of Casson ﬂuid due to an impulsively stretching surface under the inﬂuence of a transverse magnetic ﬁeld, which is an important physical phenomena in engineering applications. The study extends the previous models to account for a classical non-newtonian ﬂuid called Casson ﬂuid under the inﬂuence of a transverse magnetic ﬁeld. The ﬂow model is described in terms of a highly nonlinear partial diﬀerential equations. The method of solution Spectral quasi-linearization methods(SQLM) seeks to linearised the original system of PDEs using the Newton-Raphson based quasilinearization method (QLM). The numerical results for the surface shear stress are compared with those of the analytical approach results, and they are found to be in good agreement. The ﬂow controlling parameters are found to have a profound eﬀect on the resulting ﬂow proﬁles. It is observed that there is a smooth transition from the small time solution to the large time solution. The magnetic ﬁeld signiﬁcantly aﬀects the ﬂow ﬁeld and skin friction coeﬃcient. Indeed, skin friction coeﬃcient is found to decrease rapidly, initially, in small time interval before attaining a steady state for large time.

**Keywords**

- Casson fluid
- Magnetohydrodynamic flow
- Magnetic ﬁeld
- Boundary Layer
- Spectra quasi-linearization method
- Impulsively stretching sheet
- Separated by semicolons

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**Receive Date:**03 May 2015**Revise Date:**20 September 2015**Accept Date:**20 June 2016