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This paper aims to investigate numerically the free convective heat transfer efficiency inside a rectotrapezoidal enclosure filled with Al₂O₃–Cu/water hybrid fluid. The bottom wall of the cavity is uniformly heated, the upper horizontal wall is insulated, and the remaining walls are considered cold. A new thermophysical relation determining the thermal conductivity of the hybrid nanofluid has been established, which produced results those match with experimental ones.

The governing partial differential equations are solved using the finite element method of Galerkin type. The simulated results in terms of streamlines, heat lines and isotherms are displayed for various values of the model parameters, which govern the flow.

The Nusselt number, friction factor and the thermal efficiency index are also determined for the pertinent parameters varying different ratios of the hybrid nanoparticles. The simulated results showed that thermal buoyancy significantly controls the heat transfer, friction factor and thermal efficiency index. The highest thermal efficiency is obtained for the lowest Rayleigh number.

This theoretical study is significantly relevant to the applications of the hybrid nanofluids electronic devices cooled by fans, manufacturing process, renewable energies, nuclear reactors, electronic cooling, lubrication, refrigeration, combustion, medicine, thermal storage, etc.

The results showed that nanoparticle loading intensified the rate of heat transfer and thermal efficiency index at the expense of the higher friction factor or higher pumping power. The results further show that the heat transmission in Al₂O₃–Cu/water hybrid nanofluid at a fixed value of intensified $\phi_{hnf}$ compared to the Al₂O₃/water nanofluid when an amount of higher conductivity nanoparticles (Cu) added to it. Besides, the rate of heat transfer in Cu/water nanofluid declines when the lower thermal conductivity Al₂O₃ nanoparticles are added to the mixture.

The purpose of this study is to investigate the enhancement and suppression of heat transfer for hybrid nanofluids (Cu–Al2O3/water) in a square enclosure containing a thermal-conductive cylinder when the Lorentz force is applied to the hybrid nanofluids.

Since the inner conductive cylinder in present research has a complex geometry, an in-house meshless method, namely, the local radial basis function (LRBF) method, is applied to solve the 2 dimensional (2D) incompressible Navier–Stokes equation in the fluid domain and Fourier heat conduction equation in solid domain. The solid–fluid interface remains the physical continuity of temperature and heat flux. Only the Lorentz force is considered for the presence of the magnetic field. The conjugate natural convection is assumed to be steady, thus only fully developed heat exchange from the nanofluids to solid or vice versa is comprehensively investigated.

It can be concluded that Lorentz force plays a more significant role than hybrid nanofluids in enhancing/suppressing heat transfer when the orientation of magnetic field is the same to the x direction. The thermal conductivity ratio can dramatically change the isotherms and streamlines as well as the mean value of the Nusselt number, resulting in totally different heat transfer phenomena. The included angle of magnetic field also has a significant effect on the heat transfer rate when it changes from horizontal to vertical.

The constant thermo-physical properties of incompressible fluid and the 2D steady flow are considered in this study.

The conjugate MHD natural convection of hybrid nanofluids is numerically investigated by an in-house meshless LRBF method. The enhancement and suppression of heat transfer under the combined influence of the volume fraction of nanoparticles, Hartmann number and the thermal conductivity ratio are comprehensively investigated.