In this study, three-dimensional Bödewadt hybrid nanofluid flow has been investigated. Base fluids are water and hexanol which contain Fe$_3$O$_4$ and MoS$_2$. The governing nonlinear PDEs are converted into nonlinear ODEs and the nonlinear equations are solved by the homotopy perturbation method (HPM). The effects of nanoparticle volume fraction, Eckert number, base fluid and shape factor on entropy generation, Nusselt number, skin friction coefficient and Bejan number have been studied. Entropy generation is increased with an increment in Eckert number; while, it is decreased by growth in nanoparticle volume fraction and shape factor. In a similar situation, hexanol has higher rate of irreversibility, higher Bejan number and higher Nusselt number than water. The skin friction coefficient is not a function of the Eckert number and shape factor, but it is an increasing function of nanoparticle volume fraction. In this paper, by averaging the differences of Nusselt number and skin friction coefficient between water and hexanol, it can be observed that the Nusselt number and skin friction coefficient for hexanol are 11% and 5% more than water, respectively. Indeed, in a fixed situation, hexanol-based fluid flows have higher heat transfer and drag than water-based fluid flows.