This problem models heat propagation in a rod where the left end is kept at constant temperature T1, the right end is kept at temperature T2, the initial temperature is f(x) and at each point x, there is heat radiating at the rate F (x, t) at time t. Note that the PDE, the boundary conditions, and the initial condition, are nonhomogeneous. We can use the principle of superposition to decompose ...

Dual scattering channel schemes extend the transmission line matrix numerical method (Johns’ TLM algorithm) in two directions. For one point, transmission line links are replaced by abstract scattering channels in terms of paired distributions (characteristic impedances are thus neither needed, nor in general defined, e.g.). In the second place, non-trivial cell interface scattering is admitted...

In this work, an analytical solution for thermoelastic waves in a metal induced by an ultrafast laser pulse was formulated in the form of a Fourier series. The two-step heat transfer model was applied to account for the thermal nonequilibrium between electrons and the lattice during ultrafast pulsed laser heating. The coupling between the strain rate and the temperature ®eld was also considered...

AR = cavity aspect ratio a = speed of sound b = cavity half-width ~ C = dynamic compressibility c = phase speed cp = specific heat at constant pressure f = frequency H = cavity depth k = wave number m = propagation constant P = pressure Pr = Prandtl number R = reflection coefficient p = acoustic pressure pi = initial pulse amplitude Re = acoustic Reynolds number s = cavity spacing T = temperatu...

Based on low-temperature experimental data in solid dielectric crystals, we derive a model of heat conduction for rigid materials using the theory of thermodynamic internal state variables. The model is intended to admit wavelike propagation of heat below—and diffusive conduction above—a particular temperature value A rapid decay of the speed of thermal waves occurs just below this temperature,...

Based on low temperature experimental data in solid dielectric crystals, we derive a model of heat conduction for rigid materials using the theory of thermodynamic internal state variables. The model is intended to admit wavelike propagation of heat below and diffusive conduction above a particular temperature value θλ. A rapid decay of the speed of thermal waves occurs just below this temperat...

Dual scattering channel schemes extend the transmission line matrix numerical method (Johns’ TLM algorithm) in two directions. For one point, transmission line links are replaced by abstract scattering channels in terms of paired distributions (characteristic impedances are thus neither needed, nor in general defined, e.g.). In the second place, non-trivial cell interface scattering is admitted...

nonequilibrium statistical mechanics we focus on nonequilibrium corrections Δs to entropy and energy of the fluid in terms of the nonequilibrium density distribution function, f. We also evaluate coefficients of wave model of heat such as: relaxation time, propagation speed and thermal inertia. With these data a quadratic Lagrangian and a variational principle of Hamilton's type follows for a f...

Thermal effects are important considerations at the initial stage in spark plasma sintering of non-conductive Al2O3 powders. The generalized thermo-elastic theory is introduced to describe the influence of the heat transport and thermal focusing caused by thermal wave propagation within a constrained space and transient time. Simulations show that low sintering temperature can realize high loca...

The linear Cattaneo equation appears in heat transport theory to describe heat wave propagation with nite speed. It also can be seen as a generalization of a correlated random walk. If the system admits non conservative forces (or reactions) then a nonlinear Cattaneo system is obtained. Here we consider asymptotic behavior of solutions of the nonlinear Cattaneo system. Following Brayton and Mir...