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The effects of magnetic field on boundary layer nano-fluid flow over stretching sheet have been investigated. Different factors affecting the nano-fluid’s motion and particles have been studied, mainly the changes in the stretching sheet caused by an external magnetic field with nano-particles such as Cu. Therefore, we modified and improved a model to study boundary layers nano- fluid flow. That model’s partial differential equations (PDEs) will be transformed into a non-linear higher-order system of ordinary differential equations (h-order ODEs) using similarities transformation. The obtained system will be approximated using an efficient and accurate spectral residual method. This method is a generalization of the spectral monic Chebyshev approximation for h-order ODEs. The obtained results are graphically represented. Various effects of different parameters, Prandtl, Lewis, Brownian motion, and thermophoresis, with the magnetic field’s parameter, are reported. The reported effects on streamwise velocity, volume friction, temperature, and stream function behavior of nano-particles have been studied.

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