Transient natural convection heat transfer of fluids with variable viscosity between concentric and vertically eccentric spheres

Thermal blob convection in spherical shells

“…We would expect therefore that some type of convectively driven flow will be established, acting to transport heat from the outer sphere to the inner. This simple system is thus well suited to studying natural convection and heat transfer, with many of the key results directly transferable to engineering and industrial applications [1][2][3].…”

“…Large Prandtl numbers were considered by Chu and Lee [13], Chiu and Chen [14], and Wu et al [3], who focussed more on the initial transients rather than the final solutions though, and also included features such as taking the inner sphere to be off-center, either raised or lowered relative to the outer sphere.…”

Effects of Temperature-Dependent Viscosity on Natural Convection in Porous Media

“…However, there have been few articles published concerning the effect of Prandtl numbers on heat transfer with variable viscosity of fluid inside the porous media between two concentric spheres; thus, this paper discusses such a topic. Furthermore, the differences between the present study and the above-mentioned paper [6] are that the present study deals with porous media changing the radius ratio but the referenced paper did with non-porous media and constant radius ratio. Owing to the concentric sphere characteristic, the present paper directly discretized the governing equations with a spherical shell grid instead of grid generation by the coordinate transformation process.…”

“…Jang and Mollendorf [5] concluded that variable viscosity tended to stabilize a vertical boundary layer of natural convection. Wu, Tsai, and Chou [6] studied the natural convection of variable-viscosity fluids between concentric and vertically eccentric spheres. They found that there was thermal convection enhancement of the fluid with variable viscosity and higher Prandtl numbers and the enhancement was more distinct as the Rayleigh number increased.…”

Effect of Temperature Dependent Properties on Natural Convection of Water Near its Density Maximum in Enclosures

“…They found that heat transfer rate is slightly smaller than that in the constant property case as the viscosity variation become large. Wu et al [21] studied transient natural convection with variable viscosity between concentric and vertically eccentric spheres. They found that the effect of variable viscosity enhances the result of convection and increases rate of heat transfer.…”