The energy equation of a sphere in an unsteady and nonuniform temperature field

✍ Scribed by par Z.-G. Feng; E.E. Michaelides; M.-F. Scibilia

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 950 KB
• Volume: 35
• Category: Article
• ISSN: 0035-3159
• DOI: 10.1016/s0035-3159(96)80036-5

✦ Synopsis

The equation for the unsteady heat transfer from a sphere in a viscous/conducting fluid at finite Blot numbers is developed. This process has two characteristic times, one for the diffusion of heat inside the sphere and the other for the diffusion of heat in the external fluid. The solution of the governing equations proves that a general analytical solution may be obtained in the Laplace domain, but not in the time domain. This is due to the complexity of the heat transfer process and the two time scales involved. Asymptotic analytical solutions may be obtained at short and long times. It is observed that the complete form of the energy equation of a small sphere, even at zero Peclet numbers (creeping flow condition) is very complex. Several history terms appear in the energy equation. These emanate from temperature gradients diffused in the two media since the commencement of the heat transfer process.