Heat transfer from a vertically eccentric hot sphere to its enclosed spherical cavity

Heat transfer from a sphere to its spherical enclosure is a fundamental problem with numerous applications. This study investigated the heat transfer mechanism for eccentric sphere configurations encompassing Raleigh number from 22 to 2.6×10 ⁴. Experiments were performed for three radius ratios (1.22, 2, and 3.36) across various eccentricities and compared with a quasi-steady state model. The Nusselt number is determined from the change in the inner sphere temperature using a lumped capacity method. For low Ra numbers (conduction-dominated regime), the Nusselt number is highly eccentricity dependent, and the quasi-steady state assumption is valid. In the transition regime, the Nusselt number is nearly doubled, and the model prediction starts to deviate resulting from the enhanced buoyancy effects. For a radius ratio of 3.36, the effect of eccentricity is less pronounced, especially for negative ones resulting from the intense convection flow within the annulus. The findings are contextualized by comparing them with the evaporation dynamics of a Leidenfrost droplet inside a liquid pool, where accurate heat transfer modeling is crucial. It demonstrates that the convection at the moderate Ra number cannot be neglected. The corresponding Nusselt relation needs to be obtained to predict the later evaporation stage of the Leidenfrost droplet accurately.