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The above equation applies also to the case of mass transfer simply by replacing Nu by the Sherwood number Sh. Morrison and Reed ( 1974) derived a solution for the conductive heat transfer from two touching spheres. They found that the Nusselt number of a sphere was reduced by the presence of a touching sphere according to the following 2ln 2 Nu  (2) The problem of two, three and multi-sphere or multi-bubble system are now being addressed by a number of research workers e.g. Ruzicka ( 2000) and Ramachandran et al. ( 1989) who solved the forced convective heat transfer to a linear array of three spheres by using the finite element method. In general, an increased rate of convective heat or mass transfer with sphere separation was obtained. The molecular heat conductin and mass diffusion of the two spheres are governed by the following phenomenon: t he diffusion of heat or mass from one sphere moderates the gradient of temperature and concentration around the other sphere and thus Nu or Sh are decreased with the separation distance between spheres. This phenomenon is encountered in low Reynolds number flow (e.g. Chen and Pfeiffer (1970), Aminzadeh et al. (1974) and Ramachandran and Kleinstreuer ( 1985) . The following conclusions were deduced from the literature review: a. Aconfusion exists as to the increase or decrease of heat transfer with sphere spacing. (see for example Mulholand et al. (1988). b. The majority of the theoretical research was confined to the numerical solution of the conservation equations, except for the work of Kendoush (2007). c. Two-sphere interactions were not treated experimentally, except for the works of Wang and Liu Abstract: An analytical solution to the heat conduction equation applied to two spheres was obtained. Bispherical coordinates system were used. The derived solution applies to both fluid and solid spheres. The solution revealed a decrease in the heat conduction between the two spheres when they approach one another. The solution compared well with the available theoretical models

The Molecular Diffusion of Heat and Mass from Two Spheres