Numerical analysis of biological tissue heating using the dual-phase lag equation with temperature – dependent parameters

Majchrzak, Ewa; Stryczyński, Mikołaj

doi:10.17512/jamcm.2022.3.07

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…The dimensions of the domain are large enough to assume the adiabatic conditions on the external boundary. The adiabatic Neumann boundary condition in the case of DPLE (see: [22]) is of the form ( , , ) λ ( ) grad ( , , ) τ grad 0…”

Section: Mathematical Description Of the Processmentioning

confidence: 99%

“…In recent years, the several papers [1,21,22] concerning the more general form of DPLE for variable, temperature-dependent thermophysical parameters (volumetric specific heat and thermal conductivity) have been presented. In [21], the variability of the thermal conductivity coefficient is taken into account, while refs.…”

Section: Introductionmentioning

confidence: 99%

“…In [21], the variability of the thermal conductivity coefficient is taken into account, while refs. [1,22] discuss the variability of both coefficients. This form of the DPLE is also considered in the presented article.…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity of a Process for Heating Thin Metal Film Described by the Dual-Phase Lag Equation with Temperature-Dependent Thermophysical Parameters to Perturbations of Lag Times

Majchrzak,

Mochnacki

2024

Energies

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In the paper, an equation with two delay times (dual-phase lag Equation (DPLE)) in a version that takes into account the dependence of thermophysical parameters (volumetric specific heat and thermal conductivity) on temperature is considered. In particular, an analysis of the sensitivity of transient temperature field in relation to disturbances in delay times (the relaxation and thermalization times) is performed. The sensitivity model concerns the process of heating an ultrathin metal layer with a laser beam. First, the equation with two delay times in the case of temperature-dependent thermophysical parameters is presented. Next, the sensitivity equations with respect to delay times are derived using the direct method. The algorithms for solving the basic and sensitivity tasks are also briefly presented. At the stage of computations, an authorial program based on the implicit scheme of a finite-difference method is developed. In the final part of the paper, examples of numerical solutions (for layers made from gold and nickel) are presented. The research conducted here shows that disturbances in the temperature field are clearly visible and depend, on the one hand, on the thermophysical parameters of the material, and on the other hand, on the intensity of heating with an external heat source.

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Section: Mathematical Description Of the Processmentioning

confidence: 99%