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Purpose – The purpose of this paper is to study the generalized Couette flow of Eyring-Powell fluid. The paper aims to discuss diverse issues befell for the heat transfer, magnetohydrodynamics and slip. Design/methodology/approach – A hybrid technique based on pseudo-spectral collocation is applied for the solution of nonlinear resulting system. Findings – Viscous fluid results which are yet not available can be taken as a limiting case of presented problem. The results for the case of Hartmann flow can be obtained as a special case when plate velocity is zero, i.e. pressure gradient induced flow. The results for the zero fluid slip and no thermal slip also become special cases of this work, and the results can be recovered by setting, and to zero. These solutions are valid not only for small but also for large values of all emerging parameters. Originality/value – This model is investigated for the first time, as the authors know.

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This paper shows that the homotopy analysis method, the wellknown method to solve ODEs and PDEs, can be applied as well as to solve linear and nonlinear integral equations with high accuracy. Comparison of the present method with Adomian decomposition method (ADM), which is well-known in solving integral equations, reveals that the ADM is only special case of the present method. Also, some linear and nonlinear examples are presented to show high efficiency and illustrate the steps of the problem resolution.