The heat-balance integral: 2. Parabolic profile with a variable exponent: The concept, analysis and numerical experiments
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2012-07-01
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Abstract
A heat-balance integral method employing a parabolic profile with a variable (self-adapting) exponent has been developed. The parabolic profile satisfies both the boundary conditions and the heat-balance integral at any value of the exponent, while the optimal solution requires minimization of the mean-squared error defined by the domain parabolic equation. The concept of a variable exponent results in simple relationships involving the LambertW function and the initial values defined through the profile calibration at x= 0. Two simple 1-D problems with classic solutions are developed to demonstrate the method. © 2012 Académie des sciences.