This paper presents the homotopy series solution of the Navier–Stokes and energy equations for non-Newtonian flows. Three different problems, Couette flow, Poiseuille flow and Couette–Poiseuille flow have been investigated. For all three cases, the nonlinear momentum and energy equations have been solved using the homotopy method and analytical approximations for the velocity and the temperature distribution have been obtained. The current results agree well with those obtained by the homotopy perturbation method derived by Siddiqui et al (2008 Chaos Solitons Fractals 36 182–92). In addition to providing analytical solutions, this paper draws attention to interesting physical phenomena observed in non-Newtonian channel flows. For example, it is observed that the velocity profile of non-Newtonian Couette flow is indistinctive from the velocity profile of the Newtonian one. Additionally, we observe flow separation in non-Newtonian Couette–Poiseuille flow even though the pressure gradient is negative (favorable). We provide physical reasoning for these unique phenomena.

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