Authors: Bohdan Mochnacki, Ewa Majchrzak

Abstract: The methods of sensitivity analysis allow to estimate the influence of parameters
determining the geometrical, physical, boundary and initial conditions on the course of thermal
processes in the system considered. In this paper the possibilities of shape sensitivity analysis
application (SSA) in the thermal theory of foundry processes are discussed. In particular, the direct
approach is presented because it seems that for practical applications this variant of sensitivity analysis
is more effective. The theoretical base of SSA is presented in chapters 1 and 2, next the practical
aspects of the method are discussed. In the final part of the paper the examples of computations can be
found.

2524

Authors: Ewa Majchrzak, Bohdan Mochnacki

Abstract: In the paper the problem of casting and mould thermophysical parameters identification
is discussed. So, it is assumed that in the mathematical model describing the thermal processes in
the system considered the selected parameter (or parameters) is unknown. On the basis of additional
information concerning the cooling (heating) curves at the selected set of points the unknown
parameter can be found. The inverse problem is solved using the least squares criterion in which the
sensitivity coefficients are applied. On the stage of numerical simulation the boundary element
method is used. In the final part of the paper the examples of computations are shown.

2491

Authors: Ewa Majchrzak, Marek Jasiński, Łukasz Turchan

Abstract: Thermal processes occurring in soft tissues are subjected to laser irradiation are analyzed. The transient bioheat transfer is described by the generalized dual-phase lag model. This model consists of two coupled equations concerning the tissue and blood temperatures supplemented by the appropriate boundary and initial conditions. The efficiency of the internal heat source connected to the laser irradiation results from the solution of the diffusion equation. This approach is acceptable when the scattering dominates over the absorption for wavelengths between 650 and 1300 nm, and just such a situation occurs in the case of soft tissues. Sensitivity analysis with respect to the parameters occurring in the mathematical model is done using the direct approach (differentiation of the basic equations and the boundary-initial conditions with respect to the parameter considered), especially the absorption coefficient and scattering coefficient of the soft tissue are considered. At the stage of numerical modeling the basic problem and additional problems connected with the sensitivity functions are solved using the finite difference method. In the final part the conclusions and examples of computations are presented.

108

Authors: Bohdan Mochnacki, Ewa Majchrzak

Abstract: The system casting-mould is considered. The thermal processes proceeding in a casting sub-domain are described using the one domain approach. The model of solidification process is supplemented by the energy equation concerning the mould sub-domain, the continuity conditions given on the contact surface between casting and mould, boundary conditions on the outer surface of the system and the initial ones.
To solve the problem the generalized variant of finite difference method (GFDM) is used. Temporary and local values of temperature can be found at the optional set of collocation points from the domain considered. This essential advantage of GFDM allows to locate and thicken nodes at the regions for which the temperature gradients and cooling (heating) rates are considerable. In the final part of the paper, the example of numerical simulation is shown.

2676

Abstract: The paper deals with the microscale heat transfer problems. In particular, the ultrafast laser heating of thin metal film is considered. The problem is described by so-called two-temperature models consisting of two equations concerning the electron and lattice temperatures. Energy equations are supplemented by two additional ones determining the dependencies between electrons (phonons) heat flux and electrons (phonons) temperature gradient. According to the form of above dependencies one obtains the parabolic or hyperbolic heat transfer models discussed here. The problems have been solved using the finite difference method. In the final part of the paper the results of computations and the comparison of solutions obtained are presented.

1454

Authors: Ewa Majchrzak, Jolanta Dziatkiewicz, Łukasz Turchan

Abstract: In the paper the selected problems related to the modeling of microscale heat transfer are presented. In particular, thermal processes occurring in thin metal films exposed to short-pulse laser are described by two-temperature hyperbolic model supplemented by appropriate boundary and initial conditions. Sensitivity analysis of electrons and phonons temperatures with respect to the microscopic parameters is discussed and also the inverse problems connected with the identification of relaxation times and coupling factor are presented. In the final part of the paper the examples of computations are shown.

209

Authors: Ewa Majchrzak, Jerzy Mendakiewicz

Abstract: The paper deals with the inverse problems appearing in the thermal theory of foundry processes. In particular, the problems connected with identification of casting and mould thermophysical parameters can be considered. To estimate the parameters determining heat transfer processes in the system casting-mould, the additional information concerning the changes of temperature at the points selected from the domain considered is necessary. The localization of sensors should assure the best conditions of identification process. Generally speaking, the sensor should be located at the point for which the sensitivity of temperature field with respect to parameter estimated achieves maximum. In the case of simultaneous identification of several parameters, the proper choice of sensors localization is more complicated. The main goal of the paper is to discuss a theoretical base connected with the problem formulated, to present the possibilities of numerical methods application, to solve the problem, and finally to show the examples of inverse problems solutions (in particular, the latent heat of binary alloy will be estimated).

2640

Authors: Bohdan Mochnacki, Ewa Majchrzak

Abstract: The aim of considerations is the numerical modeling of thermal processes proceeding in the system external heat source - protective clothing - air gap - human skin and next the application of sensitivity analysis methods to study the impact of clothing parameters on the transient temperature field in domain of skin tissue. From the mathematical point of view the problem is described by the system of Fourier and Pennes equations determining the transient temperature field in the successive sub-domains. This system is supplemented by the appropriate boundary and initial conditions. Taking into account the geometrical properties of the domain considered, the 1D solution seems to be sufficiently exact (e.g. chest or back). The sensitivity model is constructed on the basis of the so-called direct approach. The equations creating the mathematical model of the process considered are differentiated with respect to selected parameter. At the stage of numerical modeling the 1^{st} scheme of the boundary element method for parabolic equations has been used.

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