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In this article, we utilize the finite Sine-Fourier transform and the Laplace transform for solving fractional partial differential equations with regularized Hilfer-Prabhakar derivative. These transforms are used to get analytical solutions for the time fractional heat conduction equation (TFHCE) with the regularized Hilfer-Prabhakar derivative associated with heat absorption in spherical coordinates...
In this paper, a solution of the single-phase lag heat conduction problem is presented. The research concerns the generalized 1D Cattaneo equation in a whole-space domain, where a second order time derivative is replaced by the fractional Caputo derivative. The Fourier-Laplace transform technique is used to determine a solution of the considered problem. The numerical inversion of the Laplace transforms...
This paper presents the concept and three practical examples of using complex thermal impedance for characterisation different thermal objects. The first problem describes estimation time shift between power and temperature in electric distribution systems with non-sinusoidal currents. The second example discussed here, shows the estimation of power losses distribution in the magnetic punched ferromagnetic...
An exact solution to the problem of an unsteady two dimensional free convection flow past an infinite vertical porous plate, which moves with a constant velocity in a viscous and incompressible fluid in the presence of thermal radiation is presented. The Laplace transform technique is used. The fluid is a gray fluid, absorbing-emitting radiation but a non scattering medium.
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