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1
Content available Cattaneo-Vernotte bioheat transfer equation. Stability conditions of numerical algorithm based on the explicit scheme of the finite difference method
Mochnacki B., Tuzikiewicz W.
Journal of Applied Mathematics and Computational Mechanics
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2016
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Vol. 15, nr 4
137-144
EN
The Cattaneo-Vernotte (CVE) equation is considered. This equation belongs to the group of hyperbolic PDE. Supplementing this equation by two additional terms corresponding to perfusion and metabolic heat sources one can apply the CVE as a mathematical model describing the heat transfer processes proceeding in domain of the soft tissue. Such an approach is recently often preferred substituting the classical Pennes model. At the stage of numerical computations the different numerical methods of the PDE solving can be used. In this paper the problems of stability conditions for the explicit scheme of the finite difference method (FDM) are discussed. The appropriate condition limiting the admissible time step have been found using the von Neumann analysis.
2
Content available Bioheat transfer equation : the problem of FDM explicit scheme stability
Tuzikiewicz W., Duda M.
Journal of Applied Mathematics and Computational Mechanics
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2015
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Vol. 14, nr 4
139--144
EN
In the paper the problem of explicit FDM scheme stability for the bio-heat transfer equation (the Pennes equation) is discussed. To formulate the appropriate condition the von Neumann approach is applied. The first chapter contains the known derivation of FDM stability condition for the Fourier equation. In the second part, a similar condition is found for the case of the bio-heat transfer equation containing both the perfusion and metabolic heat sources.
3
Content available Wpływ włókna szklanego na właściwości mechaniczne i krystaliczność kompozytów POM i PA6
Wojciechowska M., Kwiatkowski D., Tuzikiewicz W.
Przetwórstwo Tworzyw
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2014
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[R.] 20, nr 5 (161)
462--467
PL
Artykuł został podzielony na dwie części. W pierwszej części zaprezentowano szczegółowy przegląd literatury dotyczący zagadnień związanych z właściwościami mechanicznymi kompozytów, a także zamieszczono dotychczasowe wyniki badań nad kompozytami wzmocnionymi włóknami opublikowane w kilkudziesięciu artykułach branżowych oraz w najważniejszych dostępnych na polskim rynku książkach opisujących te zagadnienia. W części drugiej podano wyniki własnych badań wpływu ilości włókna szklanego na właściwości mechaniczne oraz udział fazy krystalicznej kompozytów na osnowie poliacetalu i poliamidu 6.
EN
The article is split into two parts. The first part presents a detailed review of the literature concerning issues related to the mechanical properties of composites and the results of polymeric materials reinforced with glass fiber, and contains the results of previous studies on reinforced composites filled with fibrous, published in several professional articles available on the Polish market books. The second part gives the results of the influence of the amount of glass fiber on the mechanical properties and the participation of the crystalline phase of composites based on polyacetal and polyamide 6.
4
Content available Sensitivity of transient temperature field in the casting domain with respect to latent heat perturbations
Tuzikiewicz W.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 4
143--149
EN
The mathematical model of thermal processes in the casting domain can be formulated using the fixed domain approach. The energy equation corresponding to this model contains the parameter called a substitute thermal capacity (STC), in which the alloy latent heat appears. The aim of considerations is the application of sensitivity analysis methods for estimation of temperature field changes due to the perturbations of alloy latent heat. In this the analytical form of STC results from the consideration concerning the lever arm model and the Scheil model. The equations determining the sensitivity function are found using the so-called direct approach. At the stage of numerical modeling the finite difference method is used. In the final part of the paper the example of computations is shown.
5
Content available Sensitivity analysis of the crystallization model with respect to cooling conditions
Szopa R., Tuzikiewicz W., Siedlecki J.
Journal of Applied Mathematics and Computational Mechanics
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2013
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Vol. 12, nr 3
115--122
EN
In the paper the pure metal crystallization process is considered. The cooling conditions of the metal domain are determined by the mould dimensions and thermophysical parameters of the mould material (volumetric specific heat and thermal conductivity). The mathematical model of heat transfer processes proceeding in the system metal – mould is created by the system of heat diffusion partial differential equations corresponding to the sub-domains considered supplemented by the adequate geometrical, physical and boundary-initial conditions. The sensitivity model determining the perturbations of thermal processes due to the perturbations of cooling processes can be constructed using the direct approach (differentiation with respect to parameters analyzed) or using the differential quotients. Both approaches will be discussed in the paper presented.
6
Content available remote Substitute thermal capacity of binary alloys : review of hypotheses
Siedlecki J., Tuzikiewicz W.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 4
121-129
EN
In the paper the problems connected with the mathematical modeling of alloys solidification (macro scale) are presented. The similar lecture was delivered by the authors during the IV Conference on Mathematical Modelling in Physics and Technique, Kleszczów, 28-30 June 2012. In particular the one domain method (fixed domain approach) in which the parameter called 'a substitute thermal capacity' appears will be discussed. The one domain method bases on the Fourier equation describing the thermal processes in the whole conventionally homogeneous casting domain. The substitute thermal capacity (STC) can be defined in the different ways. The first group of definitions results from the differentiation of the function determining the local volumetric solid state fraction in the neighborhood of the point considered, while the second one is based on the direct assumption of the STC form, at the same time this function should fulfill the condition resulting from the change of alloy physical enthalpy during the phase change. The details of these approaches will be presented in the Sections 2 and 3.
7
Content available remote Influence of cryoprobe cooling/heating rate on the course of freezing process
Mochnacki B., Siedlecki J., Tuzikiewicz W.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2010
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Vol. 9, nr 2
197-202
EN
The methods of sensitivity analysis are used in order to observe the influences of changes of the cryoprobe tip cooling/heating rate on a course of biological tissue freezing process. The temperature history of tip temperature is assumed in a form of broken line. The direct variant of sensitivity analysis is here applied. At the stage of numerical modeling the control volume method is used. In the final part of the paper the examples of computations are shown.
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