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 (103 ≤ Ra ≤ 106) or the eccentricity (e = ±0.2, ±0.5, 0) in the dynamic and thermal behaviours of the fluid is investigated.
Highlights
For several decades, heat transfer by natural convection has been the subject of much research and offers a diverse field of application as electronics, nuclear industry, building or solar energy
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 is conducted
By studying transient natural convection heat transfer between concentric and vertically eccentric spheres, Chiu and Chen [4] observed that for a range of Rayleigh numbers ( 103 < Ra < 105 ), for a Prandtl number and a radius ratio equal respectively 0.7 and 2, the heat and flow fields are dependent on the Rayleigh number and the eccentricity of the annulus
Summary
Heat transfer by natural convection has been the subject of much research and offers a diverse field of application as electronics, nuclear industry, building or solar energy. Mack and Hardee [7] studied natural convection between concentric at low Rayleigh numbers They discussed and illustrated streamline configuration, velocity and temperature distributions, and both local and overall heat transfer rates. They showed that negative eccentricities have been to enhance convection while positive eccentricities have the reverse effect and the heat transfer increases slightly for very high positive eccentricities where conduction plays an important role For their part, Sow et al [8] by studying geometrical and Rayleigh number effect free convection between two vertically eccentric spheres confirms that the convection motion is reinforced for the geometries characterized by positive values of the eccentricity with heat exchange increasing and the fluids flow depends strongly on the eccentricity and the modified Rayleigh number. The governing equations are formulated in terms of vorticity and stream function
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