Magneto-hydrodynamic natural convection in an inclined T-shaped enclosure for different nanofluids and subjected to a uniform heat source

This paper examines numerically by using the finite difference method the laminar steady magneto-hydrodynamic natural convection in an inclined T-shaped enclosure filled with different types of nanofluids. A uniform heat source is embedded on a part of the upper wall of the enclosure. Both left and right sidewalls of the enclosure leg are maintained at a constant cold temperature, while the other portions of the enclosure walls are considered adiabatic. A magnetic field is applied vertically downward on the bottom wall of the enclosure. Based on the numerical results, the effects of the dominant parameters such as Rayleigh number, Hartmann number, inclination angle, solid volume fraction, location and length of the heat source and enclosure aspect ratio are examined. The numerical results are obtained for Hartmann number varying as 0 ⩽ Ha ⩽ 100, inclination angle varying as 0 ⩽ Φ ⩽ 90°, Rayleigh numbers varying as 103 ⩽ Ra ⩽ 106, aspect ratio 0.3 ⩽ AR ⩽ 0.9, heat source length 0.2 ⩽ B ⩽ 0.8, heat source location 0.2 ⩽ D ⩽ 0.5 and the solid volume fractions varying as 0 ⩽ ϕ ⩽ 0.2. Comparison with previously published numerical work is performed and a good agreement between the results is observed. It is found that the mean Nusselt number increases with the increase of Rayleigh number, inclination angle, aspect ratio, heat source location and volume fraction of nanoparticles, while, it decreases when the Hartmann number and heat source length increase.