Papers by Author: Bohdan Mochnacki

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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: Bohdan Mochnacki, Mariusz Ciesielski
Abstract: Thermal processes in a thin metal film subjected to a cyclic external short-pulse heating are considered (axially-symmetrical 3D problem). The heat transfer proceeding in domain analyzed is here described by the dual phase lag model (DPLM). According to the newest opinions the DPLM constitutes a very good description of real heat transfer processes proceeding in the micro-scale domains subjected to the strong external heat flux. The base of DPLM formulation is a generalized form of Fourier law (GFL) in which two times τq, τT appear (the relaxation time and thermalization one, respectively). The acceptation of GFL leads to DPLM equation [1, 2]. Thermal processes proceeding in a thin metal film subjected to a cyclic external short-pulse heating are considered (axially symmetrical 3D problem). In the paper the thermal interactions between cyclic external heat source qb and cylindrical micro-domain are analyzed. The external heat source is the function dependent on spatial co-ordinates and time. On the remaining parts of the boundary the no-flux conditions are assumed. It should be pointed out that the DPL model requires the adequate transformation of boundary conditions which appear in the typical macro heat conduction models. The initial conditions are also known (initial temperature of domain and initial heating rate). Numerical model of the process discussed bases on a certain variant of finite differences method and in the final part of the paper the examples of computations are shown.
1460
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
Authors: Bohdan Mochnacki, R. Szopa
Abstract: Mathematical description of alloys solidification on the macro scale can be formulated using the one domain method (fixed domain approach). The energy equation corresponding to this model contains the parameter called the substitute thermal capacity (STC). The analytical form of STC results from the assumption concerning the course of the function fS = fS (T) describing the changes of solid state volumetric fraction and the temperature at the point considered. Between border temperatures TS , TL the function fS changes from 1 to 0. In this paper the volumetric fraction fS (more precisely fL = 1- fS ) is found using the simple models of macrosegregation (the lever arm rule, the Scheil model). In this way one obtains the formulas determining the course of STC resulting from the certain physical considerations and this approach seems to be closer to the real course of thermal processes proceeding in domain of solidifying alloy.
33
Authors: E. Majchrzak, Bohdan Mochnacki, M. Dziewoński, M. Jasiński
Abstract: In the paper the results of different numerical solutions of bioheat transfer problems are presented. The base of numerical algorithms constitute the models containing the bioheat transfer equation (or equations) and the adequate geometrical, physical, boundary and initial conditions. In the first part of the paper the solutions concerning the transient temperature field in the biological tissue subjected to the strong external heat sources (freezing, burns) are presented. Next, the examples of sensitivity analysis application in the range of bioheat transfer are discussed. In the final part of the paper the inverse problems are formulated and the example concerning the identification of thermal parameters is shown.
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