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A Short-Distance Integral-Balance Solution To A Strong Subdiffusion Equation: A Weak Power-Law Profile, Jordan Hristov
A Short-Distance Integral-Balance Solution To A Strong Subdiffusion Equation: A Weak Power-Law Profile, Jordan Hristov
Jordan Hristov
The work presents an integral solution of the time-fractional subdiffusion through a preliminary defined profile with unknown coefficients and the concept of penetration layer well known from the heat diffusion The profile satisfies the boundary conditions imposed at the boundary of the boundary layer in a weak form 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 subdiffusion equation in rectilinear 1-D conditions.
Heat-Balance Integral To Fractional (Half-Time) Heat Diffusion Sub-Model, Jordan Hristov
Heat-Balance Integral To Fractional (Half-Time) Heat Diffusion Sub-Model, Jordan Hristov
Jordan Hristov
The fractional (half-time) sub-model of the heat diffusion equation, known as Dirac-like evolution diffusion equation has been solved by the heat-balance integral method and a parabolic pro file with unspecified exponent. The fractional heat-balance integral method has been tested with two classic examples: fixed temperature and fixed flux at the boundary. The heat-balance technique allows easily the convolution integral of the fractional half-time derivative to be solved as a convolution of the time-independent approximating function. The fractional sub-model provides an artificial boundary condition at the boundary that closes the set of the equations required to express all parameters of the …