Isothermal spheres

Kattawar, G. W., and M. Eisner, 1970. Radiation from a homogeneous isothermal sphere, Appl. Opt., 9, 2685-2690. 

For a quasi-steady-state heat conduction between an isothermal sphere and an infinitely large and quiescent fluid, the temperature distribution in the fluid phase is governed by... 

Isothermal sphere of radius r buried in infinite medium... 

Isothermal sphere buried in semi-infinite medium with insulated surface Insulated 4 ITT I + r 2D ... 

At a certain location the thermal conductivity of the earth is 1.5 W/m °C. At this location an isothermal sphere having a temperature of 5°C and a diameter of 2.0 m is buried at a centerline depth of 5.0 m. The earth temperature is 25°C. Calculate the heat lost from the sphere. 

Vliet.G. C.,andG. Leppert Forced Convection Heat Transfer from an Isothermal Sphere to Water, J. Heat Transfer, serv. C. vol. 83, p. 163, 1961. 

Amato, W. S., and C. V. Tien Free Convection Heat Transfer from Isothermal Spheres in Water, Int. J. Heat Mass Transfer, vol. 15, p. 327, 1972. 

The average Nusselt number over the entire surface can be determined from Eq. 9-25 [Churchill and Chu (1975)] for an isothermal horizontal cylinder, and from Eq. 9-26 for an isothermal sphere [Churchill (1983)] both given in Table 9-1. 

SOLUTION An isothermal sphere is suspended in air. The total blackbody emissive power, the total radiation emitted in 5 min, and the spectral blackbody emissive power at 3 p.m are to be determined. 

A.25 [25] G. C. Vliet and G. Leppert. Forced convection heat transfer from an isothermal sphere to water. J. Heat Transfer, C83,1961. 

Correlations for Spheres in a Thermally Stratified Medium. Consider the case of an isothermal sphere in a thermally stratified medium with constant vertical temperature gradient dTJdz and with a temperature difference at the mid-height of the sphere of AT. A Nusselt number Nuiso is first calculated for an isothermal sphere in an isothermal environment... 

Spheres (Fig. 4.41c). Cheng [46] reports the similarity solution for heat transfer from an isothermal sphere to be... 

Eventually the cooling wave eats the isothermal sphere completely away and the entire fireball becomes transparent to its own radiation. Now it cools more slowly. Below about 9000°F it can cool no more. Then, concludes Bethe, any further cooling can only be achieved by the rise of the fireball due to its buoyancy, and the turbulent mixing associated with this rise. This is a slow process, taking tens of seconds. ... 

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