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2 2008

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Heat transfer in domain of metal superficial layer subjected to a strong external heat flux

Majchrzak E., Mochnacki B., Suchy J. S.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2008

Vol. 7, nr 1

121-128

In the paper the thermal processes proceeding in a superficial layer of metal subjectedto a strong external heat flux are analyzed. The different mathematical models of heat conduction in domain considered are taken into account. The first bases on the dual-phase-lagequation describing a micro-scale heat transfer. DPLE contains the parameters corresponding to relaxation time τ q and the normalization time τ T . The second model considered here results from the assumption that τ T = 0 and then DPLE reduces to the Cattaneo equation. The last one (τ q = τ T = 0) corresponds to the well known Fourier equation. Using the implicit scheme of FDM algorithm the numerical simulations have been done and the conclusions resulting from the results obtained have been formulated.

Evaporation effect in domain of tissue subjected to a strong external heat source

Mochnacki B., Dziewoński M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2008

Vol. 7, nr 1

149-154

Thermal processes proceeding in domain of biological tissue subjected to a strong external heat flux can cause the water evaporation effect (the concentration of liquid in the tissue is taken to be 79%). The phase change is assumed to occur between 98 and 102°C. This rather artificial range results from the mathematical model basing on a concept of fixed domain approach which is used in this paper. The high temperature of tissue can be an effect of accidental burns or conscious activities connected with the hyperthermia treatments. From the mathematical point of view the problem is described by the well known Pennes equation with additional term controlling the evaporation process and a set of boundary-initial conditions. On a stage of numerical simulation the finite difference method is used. The examples of computations are also presented.