Purpose This study aims to investigate the numerical analysis of mixed convection within the horizontal annulus in the presence of water-based fluid with nanoparticles of aluminum oxide, copper, silver and titanium oxide. Numerical solution is performed using a finite-volume method based on the SIMPLE algorithm, and the discretization of the equations is generally of the second order. Inner and outer cylinders have a constant temperature, and the inner cylinder temperature is higher than the outer one. The two cylinders can be rotated in both directions at a constant angular velocity. The effect of parameters such as Rayleigh, Richardson, Reynolds and the volume fraction of nanoparticles on heat transfer and flow pattern are investigated. The results show that the heat transfer rate increases with the increase of the Rayleigh number, as well as by increasing the volume fraction of the nanoparticles, the heat transfer rate increases, and this increase is about 8.25 per cent for 5 per cent volumetric fraction. Rotation of the cylinders reduces the overall heat transfer. Different directions of rotation have a great influence on the flow pattern and isotherms, and ultimately on heat transfer. The addition of nanoparticles does not have much effect on the flow pattern and isotherms, but it is quantitatively effective. The extracted results are in good agreement with previous works. Design/methodology/approach Studying mixed convection heat transfer in the horizontal annulus in the presence of a water-based fluid with aluminum oxide, copper, silver and titanium oxide nanoparticles is carried out quantitatively using a finite-volume method based on the SIMPLE algorithm. Findings Increasing the Rayleigh number increases the Nusselt number. Increasing the Richardson number increases heat transfer. Adding nanoparticles does not have much effect on the flow pattern but is effective quantitatively on heat transfer parameters. The addition of nanoparticles sometimes increases the heat transfer rate by about 8.25 per cent. In constant Rayleigh numbers, increasing the Reynolds number reduces heat transfer. The Rayleigh and Reynolds numbers greatly affect the isotherms and streamlines. In addition to the thermal conductivity of nanoparticles, the thermo-physical properties of nanoparticles has great effect in the formation of isotherms and streamlines and ultimately heat transfer. Originality/value Studying the effect of different direction of rotation on the isotherms and streamlines, as well as the comparison of different nanoparticles on mixed convection heat transfer in annulus.

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