Laminar free convective heat transfer from isothermal spheres: a new analytical method

Abstract-A simple but accurate approximate analytical method based on a linearization of the energy equation is developed for the area mean Nusselt number for free convection heat transfer from isothermal spheres for the range of Kayleigh number 0 < Ra < lo8 and all Prandtl numbers. In the process of linearization, the energy equation is reduced to the form of the transient heat conduction equation for which the solution exists. Comparison of the final correlation of Nu against Ra (which is an explicit form of linear superposition of the diffusive limit and boundary layer solution) with other correlation and experimental air data reveals very good agreement with a maximum difference of less than 5%