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Reduced differential transform method for thermoelastic problem in hyperbolic heat conduction domain

Chaudhari K. K., Sutar C. S.

International Journal of Applied Mechanics and Engineering

2021

Vol. 26, no. 1

76--87

In the present study, we have applied the reduced differential transform method to solve the thermoelastic problem which reduces the computational efforts. In the study, the temperature distribution in a two-dimensional rectangular plate follows the hyperbolic law of heat conduction. We have obtained the generalized solution for thermoelastic field and temperature field by considering non-homogeneous boundary conditions in the x and y direction. Using this method one can obtain a solution in series form. The special case is considered to show the effectiveness of the present method. And also, the results are shown numerically and graphically. The study shows that this method provides an analytical approximate solution in very easy steps and requires little computational work.

Investigation of non-Fourier thermal waves interaction in a solid material

Lenarczyk Marcin, Domański Roman

Archives of Thermodynamics

2019

Vol. 40, no 1

115--126

In this paper, effects of non-Fourier thermal wave interactions in a thin film have been investigated. The non-Fourier, hyperbolic heat conduction equation is solved, using finite difference method with an implicit scheme. Calculations have been carried out for three geometrical configurations with various film thicknesses. The boundary condition of a symmetrical temperature step-change on both sides has been used. Time history for the temperature distribution for each investigated case is presented. Processes of thermal wave propagation, temperature peak build-up and reverse wave front creation have been described. It has been shown that (i) significant temperature overshoot can appear in the film subjected to symmetric thermal load (which can be potentially dangerous for reallife application), and (ii) effect of temperature amplification decreases with increased film thickness.

On the tolerance wave-type solutions to the hyperbolic heat conduction in microperiodic composites

Łacińska L., Wierzbicki E.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2008

Vol. 7, nr 1

93-97

In the note wave-type solutions to the hyperbolic heat conduction in the microperiodic composites are investigated. The considerations are related to the tolerance averaged model of the hyperbolic heat transfer problems in microperiodic composites. The Lapunov exponent notation is applied. The open form of these solutions are formulated in one shape function case.