Objective of this paper is a study of the impact of heat and mass transfer on time-dependent flow of a third-grade convective fluid due to an infinitely rotating upright cone. An interesting fact is observed that the similarity solutions only exist, if we take the angular velocities of the cone and far away from the fluid as an inverse function of time. The analytical solutions of the reduced ordinary differential equations of third-grade fluids are offered by the optimal homotopy analysis method (OHAM). The results for important parameters are illustrated graphically as well as in tabular form. The precision of the present results is also checked by comparison with the numerical outcomes published earlier. The impact of non-Newtonian fluid parameters is found to decrease the primary skin-friction coefficient. There is an aggregate in Nusselt and Sherwood numbers for increasing the ratio of the buoyancy forces.
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