(A) study of natural convection in concentric vertical cylinders with heat genetating inner cylinder

Abstract

Heat transfer coefficients for natural convection in the enclosed space between two vertical cylinders maintained at different uniform temperatures such as $Ti=90\,^\circ\!C,\; To=30\,^\circ\!C$ were determined. Also, surface temperatures of the inner cylinder were calculated numerically for the same geometry having a constant uniform heat source q = 6803 KW/m$^3$ in the inner cylinder. In the former case, the effect of vertical position (ie. elevation) of the inner cylinder on heat transfer was studied. In the latter case, to see the effect of conductivity of the inner cylinder on the temperature distribution or heat flux of the inner surface, the conductivity of the inner cylinder were varied by a kind of material. For the enclosure geometry, the heat transfer media of two cases were air above and electric transformer oil below the interface which exists between those fluids. Rayleigh number of the oil for the inner cylinder, $4.1 \times 10^5$ was used. In results, in the case of the isothermal boundary, heat transfer coefficient was increased at the lowest position of the inner cylinder. In the case of the uniform heat source, if the conductivity of the inner cylinder is larger than 17 W/m$\,^\circ\!C$, the internal boundary condition can be assumed to be isothermal boundary condition on the inner surface.