Math. Sci. Lett. 5, No. 1, 1-7 (2016) 1 Mathematical Sciences Letters An International Journal http://dx.doi.org/10.18576/msl/050101 Mechanisms of Different Nanoclusters in Nanobased Fluids with Natural Convection and Variable surface M. Hassan 1 , R. Ellahi 1,2,∗ and Ahmad Zeeshan 1 1 Department of Mathematics & Statistics, IIUI, Islamabad, Pakistan. 2 Department of Mechanical Engineering, University of California Riverside, USA. Received: 8 Feb. 2015, Revised: 15 Oct. 2015, Accepted: 28 Oct. 2015 Published online: 1 Jan. 2016 Abstract: In this letter, the natural convection boundary layer flow with variable surface heat flux on nanofluids is investigated. Different nanoclusters containing different nano based fluids are taken into account. Analytic solutions are first obtained and then the role of sundry parameters such as heat flux gradient parameter, skin-friction, heat transfer coefficient and coefficient of nanofluid on velocity and temperature profiles are demonstrated through graphs and tables. Convergence of presenting series solutions has been conferred by means of error norm in their respective admissible range. Keywords: Natural convection, variable surface heat flux, nanoclusters, nanofluid, analytical solutions. 1 Introduction The problems concerning the flow of nanofluids have become more important nowadays. These fluids are widely encountered in the study of nanoparticles, nanofibers, nanotubes, nanowires, nanorods, nanosheet, or droplets etc. Nanofluids appear to have the potential to significantly increase the heat transfer rates in mechanical and electromechanical systems. Nanofluids are also found to possess enhanced thermophysical properties like thermal diffusivity, thermal conductivity, viscosity and convective heat transfer coefficients compared to those of base fluids like water and oil. It has demonstrated great potential applications in several other fields [1, 2, 3, 4, 5, 6, 7, 8, 9]. Moreover, noteworthy research efforts have been devoted to exploring the thermal transport characteristics of colloidal suspensions of nano-sized solid particles. Some recent studies having the related works on the topic can be mentioned by the efforts [10, 11, 12] Hong et al. [13] observed that the reduction of thermal conductivity of nanofluids is directly related to cluster of nanoparticles. In this study it has also mentioned that the thermal conductivity of Fe nanofluids increases nonlinearly by increasing the volume fraction of nanoparticles. The nonlinearity is attributed to the rapid clustering of nanoparticles in condensed nanofluids. The Fe nanofluids exposed a more rapid increase in thermal conductivity as compared to Cu nanofluids when the volume fraction of nanoparticles increased. They claim that the variations of cluster size and thermal conductivity both are functions of time. They also found that the thermal conductivity of nanofluids is closely related to the clustering of nanoparticles. With all said points in mind, we intend to strengthen our efforts to understand the problems having the more complicated nature. This is particularly in the modeling of different nanoclusters containing various nano-based fluids. To the best of authors’ knowledge no study is still accorded in available literature on the said topic. Motivated by these facts, the present work has been undertaken to analyze the fully developed flow of an incompressible nanofluid with different nanoparticle clustering containing free convection flow from a vertical circular cone with variable surface heat flux. To drive the solutions of nonlinear coupled equations, homotopy analysis method [14] has been used. Graphs for different flow parameters of interest are sketched and analyzed. 2 Mathematical formulation We consider two dimensional free convection flows past a vertical circular cone with variable surface heat flux ∗ Corresponding author e-mail: rellahi@engr.ucr.edu c  2016 NSP Natural Sciences Publishing Cor.