Unsteady Mixed Convection Flow of a Rotating Second-Grade Fluid on a Rotating Cone S. Nadeem and S. Saleem Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, Pakistan In the present article, we have investigated the unsteady mixed convection flow of a rotating second-grade fluid in a rotating cone with time-dependent angular velocities. Two cases of heat transfer are presented which are known as (i) prescribed wall temperature (PWT) and (ii) prescribed heat flux (PHF). The governing coupled nonlinear partial differential equations are simplified with the help of transformations and non-dimensional similar and non-similar variables, and solved analytically with the help of the homotopy analysis method (HAM). The effects of pertinent parameters on the velocity, temperature, concentration, skin friction coefficients, Nusselt number, and Sherwood number have been examined through graphs. © 2013 Wiley Peri- odicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21072 Key words: unsteady flow, mixed convection, rotating cone, second-grade fluid, HAM solutions 1. Introduction It is now generally recognized that in practical applications non-Newtonian fluids are more significant and useful than Newtonian fluids. The flows of non-Newtonian fluids offer mathemati- cians, engineers, and numerical specialists varied challenges, and they are developing appropriate analytical and numerical solutions. This class of possible solution is still narrowed down for non-Newtonian fluids on account of the highly nonlinear nature of the governing equations. There is no single model which completely explains all the properties of non-Newtonian fluids; thus numerous models have been developed for these fluids with their constitutive equations varying greatly in complexity. However, differential-type non-Newtonian fluids such as second-grade fluids and third- grade fluids have achieved a lot of success. Some important applications of non-Newtonian fluids are food mixing and chyme movement in the intestine, polymer solutions, paint, flow of plasma, flow of blood, flow of nuclear fuel slurries, flow of liquid metals and alloys, flow of mercury amalgams, and lubrications with heavy oils and greases. Some fundamental studies on non-Newtonian fluids are available in Refs. 1–9. Mixed convection flow is another important area which has attracted the attention of researchers due to its applications in industry and technology. A few of these applications are solar central receivers exposed to wind currents, electronic devices cooled by fans, nuclear reactors cooled during emergency shutdown, and heat exchangers placed in a low-velocity environment [10]. However, the convective heat transfer in a rotating flow over a rotating cone is also a very important © 2013 Wiley Periodicals, Inc. Heat Transfer—Asian Research 1