Unsteady Natural Convection between Two Eccentric Hemispheres

Abstract

Natural convection heat transfer in open or closed cavities takes place in different engineering areas. The hemispherical cavity is a part of basic geometries although it is not widely studied. The present paper reports the numerical study of natural convection in a closed hemispherical annulus delimited by two vertically eccentric hemispheres filled with Newtonian fluid (air in this case with Pr = 0.7) is conducted. The inner hemisphere is heated by a heat flux of constant density and the outer one is maintained isothermal. Based on the Boussinesq assumptions, the governing equations are numerically studied using unsteady natural convection formulated with vorticity and stream-function variables. These equations are written by using bispherical coordinates system and solved by using a finite difference method. The effect of the control parameters such as the Rayleigh number ( 3 6 10 10 Ra ≤ ≤ ) or the eccentricity (e = ±0.2, ±0.5, 0) in the dynamic and thermal behaviours of the fluid is investigated.

Numerical Simulation of Natural Air Convection in Inclined Eccentric Hemispheres Enclosure

“…When the Rayleigh number is fixed at 10 5 and the eccentricity at −0.5. We notice that streamlines for configurations 0 ϕ = and ϕ = π (Figure 6 and Figure 10) has a unicellular flow what is in agreement with those of [13]. The isotherms are increasingly deformed over time.…”

“…His results showed that the inclinaison angle of the device affects only weakly the heat exchange and the natural convection heat transfers are also quantified by means of the Nusselt number. Recently, by studying natural convection between two eccentric hemispheres, Koita et al, [13] observed that the parameters of fluid depend strongly on the modified Rayleigh number as well as of the eccentricity. Also, the effects of eccentricity showed the center of rotation moves toward the top of enclosure when the eccentricity increases and the Nusselt number increases with the modified Rayleigh number.…”

Numerical modeling of the magneto convection of a Newtonian fluid confined between two vertically eccentric hemispheres

“…However, we will also note its decrease for larger Rayleigh numbers. Moreover, our values are slightly higher than those of [9] and [19]. For the same Rayleigh numbers that we used previously, Figure 3(b) gives, as a function of dimensionless time, the evolution of the minimum flux function.…”

“…The results presented in Table 3 provide information on the values of the mean Nusselt number, calculated and then given for different Rayleigh numbers. We compared these results with those of [19] for the study of transient laminar convection between two vertically eccentric hemispheres. These comparisons show a relative difference of 02.72% for all the cases presented.…”

“…The heat exchange characterized by the Nusselt number increases with the modified Rayleigh number. [19] studied the case of a hemisphere. The results show that the center of the vortex moves upwards for larger eccentricities.…”