Small scale thermal devices, such as micro heater, have led researchers to consider more accurate models of heat in thermal systems. Moreover, biological applications of heat transfer such as simulation of temperature field in laser surgery is another pathway which urges us to re-examine thermal systems with modern ones. Non-Fourier heat transfer overcomes some shortcomings of Fourier heat tran...

In the first part of the article we introduce C-algebras associated to self-similar groups and study their properties and relations to known algebras. The algebras are constructed as sub-algebras of the Cuntz-Pimsner algebra (and its homomorphic images) associated with the self-similarity of the group. We study such properties as nuclearity, simplicity and Morita equivalence with algebras relat...

In this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. The system is firstly, transformed into an ordinary differential equation by wave transformation. The solution of ODE is obtained by the homotopy perturbation method. To show the periodic behavior of the solution, a modification based on the Laplace transforms and...

In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the s...

In this paper we are interested in solving parabolic problems with a piecewise constant diffusion coefficient on structured Cartesian meshes. The aim of this paper is to investigate the applicability and convergence behavior of combining two non-conventional but innovative methods: the Laplace transformation method in the discretization of the time variable and the immerse finite element method...

This paper deals with magneto-thermo-elastic interaction due to thermal shock on the stress free boundary of the half-space of perfect conducting medium in the context of two-temperature generalized thermo-elasticity with energy dissipation (TEWED) (GN III model), see [1, 2, 3]. The governing equations are solved in the Laplace transformation domain using state-space approach. The inversion of ...

The interpretation of the optical Appell transformation, as previously elaborated in relation to the free-space paraxial propagation under both a rectangular and a circular cylindrical symmetry, is reviewed. Then, the caloric Appell transformation, well known in the theory of heat equation, is shown to be amenable for a similar interpretation involving the Laplace transform rather than the Four...