Natural Convection Heat Transfer from Upward, Downward, and Sideward Solid/Hollow Hemispheres

Continuity, momentum, and energy equations have been solved to predict the natural convection heat transfer from an upward, downward, and sideward solid or hollow hemisphere either suspended in air or placed on the ground. The results have been plotted in terms of average surface Nusselt number Nu as a function of Rayleigh number Ra spanning from 10(4) to 10(7) in the laminar flow regime. The behavior of the flowfield and temperature distribution around the hemisphere at different orientations have been analyzed against Rayleigh number with the aid of velocity vector plot and temperature contour. It is found that the Nusselt number for the upward solid hemisphere is more than that of the downward and sideward hemispheres. However, the situation reverses when the hemisphere lies on the ground with an Ra less than 10(6). When a hollow hemisphere is being focused, the inner-surface Nusselt number for a hollow hemisphere becomes less than that of the outer surface for all Rayleigh numbers. The outer-surface Nusselt number for the upward-facing hollow hemisphere is marginally higher than that of the downward and sideward hemispheres; however, the inner-surface Nusselt number is significantly more for the sideward hemisphere compared to other cases. The Nusselt number for the solid or hollow hemisphere in air is higher than that of the hemisphere on the ground. The opposite scenario arises for the downward and sideward hollow hemispheres when the Ra is more than 10(6). When the hollow hemisphere is concerned with finite thickness, the Nusselt number for both the inner and outer surfaces remains constant against the thickness and thermal conductivity of the material. Finally, the correlation of Nusselt number as a function of Rayleigh number for both the hollow and solid hemispheres has been proposed, which could be referred to in academics and industrial practices.