Semianalytical Solution to Heat Transfer Problems Using Fourier Transform Technique, Radial Basis Functions, and the Method of Fundamental Solutions
Document Type
Article
Publication Date
1-1-2007
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
An analytically based approach for solving a transient heat transfer equation in a bounded two dimensional domain is proposed. The major features of the method are time-Fourier transformation of the problem, analytical derivation of an elementary particular solution for a localized radial basis delta-like source using the space-Fourier transform, expansion of the total particular solution in terms of those elementary particular solutions, approximation of the homogeneous solution using the method of fundamental solution, and inversion into the time domain using fast Fourier transform. The prime distinction of this scheme from the closest analogs lies in the construction of the particular solution.
Publication Title
Numerical Heat Transfer Part B-Fundamentals
Volume
52
Issue
5
First Page
409
Last Page
427
Recommended Citation
Glushkov, E.,
Glushkova, N.,
Chen, C.
(2007). Semianalytical Solution to Heat Transfer Problems Using Fourier Transform Technique, Radial Basis Functions, and the Method of Fundamental Solutions. Numerical Heat Transfer Part B-Fundamentals, 52(5), 409-427.
Available at: https://aquila.usm.edu/fac_pubs/2125