**ABSTRACT**

This work presents numerical and analytical investigations of the two-dimensional unsteady flow of a nanofluid in a porous channel through expanding/contracting walls with large injection or suction under the influence of a transverse magnetic field. With the aid of similarity variables, the systems of the governing partial differential equations are reduced to a nonlinear fourth-order ordinary differential equation. The developed nonlinear differential equation is solved numerically and analytically using Chebyshev pseudospectral collocation method and differential transform methods, respectively. The results of the Chebyshev pseudospectral collocation method and that of the differential transform method show very good agreements. Also, the effects of permeation Reynolds number, wall expansion ratio, and magnetic parameter on the flow behavior of the fluid. The results of the present analysis will assist in expanding the understanding of the flow characteristics of nanofluid in a porous channel through expanding/contracting walls with large injection or suction in a magnetic environment.

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