Numerical analysis of tissue heating using the generalized dual phase lag model

1D generalized dual-phase lag equation. Sensitivity analysis with respect to the porosity

“…The presented approach can be extended for 3D problems and two-temperature models [12,14,22] in which the blood temperature is determined from the additional equation coupled with the generalized dual-phase lag equation.…”

“…The parameter τ q is the phase lag of the heat flux and parameter τ T is the phase lag of the temperature gradient. Extension of this model is the generalized dual-phase lag equation [12][13][14][15]. In this equation the phase lag times τ q and τ T are expressed in terms of the blood and tissue properties, the interphase convective heat transfer coefficient and the blood perfusion rate.…”

“…In this case the mathematical model consists of the basic problem (GDPLE supplemented by appropriate boundary and initial conditions) and the G. Kałuża, E. Majchrzak, Ł. Turchan 50 additional problem resulting from the differentiation of governing equations. These problems are solved using the explicit scheme of the finite difference method for hyperbolic equations [14,15]. In the final part of the paper the example of computations and conclusions are presented.…”

Modeling of Phase Changes in Micro-Domain Induced by an Ultrashort Laser Pulse

“…are the thermal resistances between adjacent nodes [18,19] and In Figure 5 the electrons and phonons temperature distribution after 150 ps for laser intensity I0 =8•10 5 J/m 2 is shown. …”

“…To solve the problem formulated in the chapter 3, the finite difference method is used [18,19]. The geometrical mesh with dimensions nn is introduced and the temperatures for time t f = f Δt (f ≥ 2, Δt is the constant time step) at the node (i, j) are denoted as The following approximation of equation (23) is proposed…”