We investigated the dynamics of nanofluid and heat transfer in a three-dimensional circular annular using the κ−ε turbulence model and energy equations. The pipe contained two concentric and rotating cylinders with a constant speed in the tangential direction. A heat flux boundary condition was executed at the inner cylinder of the annular. The pipe was settled vertically, and water alumina nanofluid was allowed to enter, with the initial velocity depending on the Reynolds number, ranging from 30,000 to 60,000. The volume fraction of the solid particles was tested from 0.001 to 0.1. The speed of the rotation of the cylinders was tested in the range from 0.5 to 3.5. The simulations were developed using COMSOL Multiphysics 5.6, adopting the finite element procedure for governing equations. The results were validated using the mesh independent study and the average Nusselt number correlations. We found that the average Nusselt number in the middle of the channel decreases linearly with the increase in the volume fraction of the water alumina nanofluid. The novelty of the present work is that various correlations between the average Nusselt number and volume fraction were determined by fixing the Reynolds number and the rotation of the inner cylinder. We also found that fixing the Reynolds number and the volume fraction improves the average Nusselt number at the outlet linearly. In addition, it was stated that the increase in the total mass of the nanofluid would decrease the average temperature at the outer cylinder of the annular. Moreover, the maximum average improvement percentage in the average Nusselt number, which is about 21%, was observed when the inner cylinder rotation was changed from 1.5 to 2.5 m/s.

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