Thermal Science 2011 Volume 15, Issue suppl. 1, Pages: 5-20
https://doi.org/10.2298/TSCI11S1005H
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Starting radial subdiffusion from a central point through a diverging medium (a sphere): Heat-balance integral method
Hristov Jordan (Department of Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia, Bulgaria)
The work presents an integral solution of the time-fractional subdiffusion
equation as alternative approach to those employing hypergeometric functions.
The integral solution suggests a preliminary defined profile with unknown
coefficients and the concept of penetration (boundary layer) well known from
the heat diffusion and hydrodynamics. The profile satisfies the boundary
conditions imposed at the boundary of the boundary layer that allows its
coefficients to be expressed through the boundary layer depth as unique
parameter describing the profile. The technique is demonstrated by a solution
of a time fractional radial equation concerning anomalous diffusion from a
central point source in a sphere.
Keywords: radial subdiffusion, integral method, heat-balance integral, fractional Fourier number