In this paper, the three-dimensional hyperbolic effect subjected to a cosine heat flux boundary condition is carried out. Equations in rectangular coordinates are solved. Analytical solution with method of separation of variables is derived. The main aim of this paper is to obtain some possibly explicit analytical solution of the (1+3)-dimensional hyperbolic heat conduction equation for given i...

Rapid transient heat conduction in multilayer materials under pulsed heating is solved numerically based on a hyperbolic heat conduction equation and taking into consideration the non-Fourier heat conduction effects. An implicit difference scheme is presented and a stability analysis conducted, which shows that the implicit scheme for the hyperbolic equation is stable. The code is validated by ...

Lagging models of heat conduction, such as the Dual-Phase-Lag or the Single-Phase-Lag models, lead to heat conduction equations in the form of partial differential equations with delays or to partial differential equations of hyperbolic type, and have been considered to model microscale heat transfer in engineering problems or bio-heat transfer in medical treatments. In this work we obtain expl...

To realize the lagging behavior in heat conduction observed in these two decades, this paper firstly theoretically excludes the possibility that the underlying thermal inertia is a result of the time delay in heat diffusion. Instead, we verify in experiments the electro-thermal analogy, wherein the thermal inertial is parameterized by thermal inductance that formulates hyperbolic heat-conductio...

In this paper, we consider a non-isothermal, non-Newtonian injection process. This leads to the study of a novel elliptic–hyperbolic system. The hyperbolic nature of the system arises because we replace the infinite speed of propagation from classical, thermal elasticity by a finite propagation velocity. We present a formal derivation of the elliptic–hyperbolic system starting from conservation...

In this paper, we investigate the system of compressible Navier-Stokes equations with hyperbolic heat conduction, i.e., replacing the Fourier’s law by Cattaneo’s law. First, by using Kawashima’s condition on general hyperbolic parabolic systems, we show that for small relaxation time τ , global smooth solution exists for small initial data. Moreover, as τ goes to zero, we obtain the uniform con...

In this paper, a non-Fourier heat conduction problem is analyzed by employing newly developed theory. Application of conventional numerical schemes leads to strong oscillations of the results around discontinuities in solution domain. To overcome this difficulty the variational formulation of the Laplace-transformed hyperbolic heat conduction equation is developed. The results were used for eva...