Radiative and free convective heat transfer from a containerless sphere

A mathematical model is derived for heat loss due to radiation and free convection for a small copper sphere (approximately 0.3 to 0.4 cm diameter) cooled by a helium-argon gas mixture. A FORTRAN program written to simplify calculations and extend the range of applicability to experimentation is presented. Pressures used were less than 400 torr, and resulting temperatures ranged from 500 to 4600 K. Comparison of results for initial cooling by the gas mixture with experimental data showed a 5 percent error for temperature values and a 2.7 percent error for the temperature difference caused by the cooling. Results indicate that the accuracy could be increased significantly by using better estimates for thermal conductivities.