THERMAL SCIENCE

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Jordan Y. Hristov

HEAT-BALANCE INTEGRAL TO FRACTIONAL (HALF-TIME) HEAT DIFFUSION SUB-MODEL

ABSTRACT
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 profile 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 approximating profile as function of the thermal layer depth. This allows the exponent of the parabolic profile to be defined by a straightforward manner. The elegant solution performed by the fractional heat-balance integral method has been analyzed and the main efforts have been oriented towards the evaluation of fractional (half-time) derivatives by use of approximate profile across the penetration layer.
KEYWORDS
fractional equation, heat diffusion, half-time fractional derivative, heat-balance integral method
PAPER SUBMITTED: 2010-02-15
PAPER REVISED: 2010-03-16
PAPER ACCEPTED: 2010-05-03
DOI REFERENCE: https://doi.org/10.2298/TSCI1002291H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2010, VOLUME 14, ISSUE Issue 2, PAGES [291 - 316]
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Heat-balance integral to fractional (half-time) heat diffusion sub-model

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