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This article deals with the laminar flow of a viscous fluid and heat transfer analysis due to a porous stretching/shrinking cylinder with partial slip condition. The flow equations corresponding to momentum and energy equations are transformed into a set of highly nonlinear ordinary differential equations by means of similarity transformations, which are then, solved numerically using Runge–Kutta–Fehlberg method. The physical significance of the various involved parameters on the flow velocity and temperature distribution is discussed through graphs and tables in detail. It is found that the dual solutions exist for the shrinking cylinder, while a unique solution exists for stretching cylinder. Comparison of the present results with the existing previous results is given and found to be in good agreement.