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The purpose of the paper is to investigate the effects of magnetic field on the flow driven by the combined mechanism of buoyancy and thermocapillary flow in an open enclosure with localized heating from below and symmetrical cooling from the sides.

The governing equations are discretized by the control volume method with power-law scheme and solved numerically by SIMPLE algorithm for the pressure-velocity coupling together with under-relaxation technique.

In this work, it is observed that, the average Nusselt number, decreases with an increase of Hartmann number Ha, and increases with increase of Prandtl and Grashof number. At large Marangoni number Ma, a prominent secondary eddies are observed at the top of the enclosure due to the effect of surface tension.

The study combines many external forces on thermocapillary flow.

The purpose of this study is to determine the thermal behavior of a hemispherical electronic device contained in a concentric hemispherical enclosure, cooled by means of free convection through a porous medium saturated with a water–copper nanofluid. Influence of various parameters on the thermal state of this device is processed in this work. The high power generated by the dome leads to a Rayleigh number varying in the 5.2 × 10⁷-7.29 × 10¹⁰ range. The volume fraction of the monophasic nanofluid varies between 0 (pure water) and 10 per cent while the base of the hemispherical cavity (disc) is inclined between 0° (horizontal disc with dome facing upward) and 180° (horizontal disc with dome facing downward).

The three-dimensional numerical approach is carried out by means of the volume control method associated to the SIMPLE algorithm.

The work shows that the average temperature of the active component increases with the Rayleigh number according to a conventional law of the power type. The increase in the angle of inclination also goes with a systematic rise in the average temperature. However, increasing the ratio of the solid–fluid thermal conductivities decreases the average temperature of the component, given the respective contributions of the conductive and natural convective phenomena occurring through the nanofluid saturated porous media. The values of this ratio vary in this work between 0 (interstice between the two hemispheres without porous medium) and 70.

The correlation proposed in this work allows to calculate the temperature of the active electronic component for all the combinations of the four influence parameters which vary in wide ranges.