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This paper considers the effect of transpiration on hybrid nanofluid flow and heat transfer over a stretching/shrinking sheet for uniform shear flow. The similarity equations are attained from the governing equations by using similarity transformation technique, and their solutions are obtained using the bvp4c solver in Matlab software. The effect of the several governing parameters on the flow and heat transfer characteristics are presented and interpreted theoretically. Results elucidate that dual solutions exist up to a certain range of the stretching/shrinking parameter. Moreover, the dual solutions are observed to occur for both stretching or shrinking cases in the present of suction parameter. An increasing of copper nanoparticle volume fractions generates an enhancement in the heat transfer coefficient, however dual behaviour is observed in the skin friction coefficient for the upper branch solutions. The temporal stability analysis is conducted to determine the stability of the dual solutions, and it is discovered that only one of them is stable and physically reliable. Keywords: Hybrid nanofluid, Transpiration, Uniform shear flow, Stretching/shrinking sheet, Dual solutions, Stability analysis