In this paper, the non-Fourier heat conduction in a semi-infinite body was examined. The heat wave non-Fourier heat conduction model was used for thermal analysis. Thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The heat source was also considered temperature-dependent which resulted in a non-homogeneous equation. The Mac-Cormack predictor-correct...

We classify from Lie symmetry standpoint the hyperbolic heat equation with temperature-dependent medium properties. We prove that the hyperbolic heat equation may admit a two-, three-, fouror infinitedimensional symmetry Lie algebra depending on the functional form of density, thermal conductivity, and specific heat. The last possibility corresponds to exactly linearizable hyperbolic heat equat...

numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...

We investigate the inverse problem associated with the heat equation involving recovery of initial temperature distribution in a two-layer cylinder with perfect thermal contact at the interface. The heat equation is solved backward in time to obtain a relationship between the final temperature distribution and the initial temperature profile. An integral representation for the problem is found,...

In this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type. In particular we obtain a complete theory for the 22 systems of genuinely nonlinear hyperbolic balance laws in 1-D with a strong dissipative term. A diierent method, which combines the div-curl lemma with accretive ope...

Nonlocal problems is a major research area in many branches of modern physics, biotechnology, chemistry and engineering, which arises when it is impossible to determine the boundary values of unknown function and its derivatives. Increasingly often, there arise problems with nonlocal integral boundary conditions, especially in particle diffusion [1] and heat conduction [2, 3]. Partial different...

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

In this Letter, we revisit the Maxwell-Cattaneo law of finite-speed heat conduction. We point out that the usual form of this law, which involves a partial time derivative, leads to a paradoxical result if the body is in motion. We then show that by using the material derivative of the thermal flux, in lieu of the local one, the paradox is completely resolved. Specifically, that using the mater...