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Estimation of dual phase lag model parameters using the evolutionary algorithms

Mochnacki B., Paruch M.

Archives of Foundry Engineering

2011

Vol. 11, iss. 3 spec.

277--281

Generalization of Fourier law, in particular the introduction of two ‘delay times’ (relaxation time τq and thermalization time τT) leads to the new form of energy equation called the dual-phase-lag model (DPLM). This equation should be applied in a case of microscale heat transfer modeling. In particular, DPLM constitutes a good approximation of thermal processes which are characterized by extremely short duration (e.g. ultrafast laser pulse), extreme temperature gradients and geometrical features of domain considered (e.g. thin metal film). The aim of considerations presented in this paper is the identification of two above mentioned positive constants τq, τT. They correspond to the relaxation time, which is the mean time for electrons to change their energy states and the thermalization time, which is the mean time required for electrons and lattice to reach equilibrium. In this paper the DPLM equation is applied for analysis of thermal processes proceeding in a thin metal film subjected to a laser beam. At the stage of computations connected with the identification problem solution the evolutionary algorithms are used. To solve the problem the additional information concerning the transient temperature distribution on a metal film surface is assumed to be known.

Laminar, transitional, turbulent liquid flow in smooth capillary pipes

Szewczyk H.

Chemical and Process Engineering

2008

Vol. 29, z. 4

955-977

Hydraulic characteristics smooth capillaries of 280.6 and 327.8 [mi]m in diameters in the range of ]550, 6600[ Re were determined experimentally. The critical Reynolds number ReCR 2100 (concerns capillaries with sharp-edged inlets, since ReCR increases, when the edge is rounded off), whereas the flow is turbulent, if Re 2800. The laminar-turbulent transition occurs in the range of ]2100, 2800[ Re, and the characteristic curves cease to run unequivocally, however, they are contained in the area with a determined envelope (not given in the literature). It was confirmed, based on 1420 author.s results (6 capillaries 281.1270 [mi]m, Re]180, 5800[), that the Hagen-Poiseuille law and the Blasius formula are also related to microscale flows.

Wyznaczono doświadczalnie charakterystyki hydrauliczne gładkich kapilar o średnicach 280,6 [mi]m 327,8 [mi]m w przedziale ]550, 6600[ Re. Krytyczna liczba Reynoldsa ReCr wynosi ok. 2100 (dotyczy to kapilar z ostrokrawędziowym wlotem, gdyż po zaokrągleniu tej krawędzi ReCR wzrasta), natomiast jeśli Re 2800, to ruch jest turbulentny. W przedziale ]2100, 2800[ Re następuje przejście laminarno-turbulentne i tu charakterystyki nie są jednoznaczne, ale mieszczą się w polu, którego obwiednię wyznaczono (nie podaje jej literatura), Na podstawie 1420 własnych wyników (6 kapilar 281.1270 [mi]m, Re]180, 5800[) autor potwierdził, że prawo Hagena-Poiseuille'a oraz formuła Blasiusa dotyczą także przepływów mikroskalowych.