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Archiwum Odlewnictwa
2004 R. 4, nr 14 538-543
PL W pracy przedstawiono sposób modelowania procesu krzepnięcia z uwzględnieniem ruchów konwekcyjnych, powstałych w strefie ciekłej oraz stało-ciekłej. Strefa stałociekła traktowana jest jako ośrodek porowaty, w którym uwzględniono ruch cieczy wywołany konwekcją swobodną. Rozpisano równania przewodnict[...]
EN Modeling of solidification process with convection in liquid and mushy zone is described in this paper. Mushy zone is considered as a porous medium. Heat transfer and Navier-Stokes equations are described. Finite eIements method (FEM) was used to solve them.
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Archives of Foundry Engineering
EN Presented paper is focused on numerical modeling of binary alloy solidification process with connection to shrinkage cavity formation phenomenon. Appropriate matching of cooling parameters during solidification process of the cast with raiser is essential to obtain suitable properties of the manufac[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN The paper deals with numerical model of thermal phenomena and phase transformation in solid state with tempering. To modeling the process heat transfer equation and macroscopic model of phase change based on CCT and CHT diagrams are used. The numerical solution of heat conductivity equation is intro[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
2006 Vol. 5, nr 1 185-190
EN The paper deals with numerical modeling of binary alloys solidification process with motion of the fluid in the liquid and mushy zone. The mathematical model of the phenomenon is presented. Finite Element Method is used for modeling process. The results of the numerical simulation in the 2D region a[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
2002 Vol. 1, nr 1 227--233
PL W pracy zajęto się jednym z aspektów rozwiązania równań Naviera-Stokesa. Jak wiadomo, rozwiązanie numeryczne tych równań stwarza wiele problemów związanych ze stabilnością procesu obliczeniowego. W celu pokonania tych trudności zastosowano metodę elementów skończonych z wykorzystaniem elementów Tayl[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
2007 Vol. 6, nr 1 261-267
EN In the paper mathematical and numerical model of binary alloy solidification process is proposed. The metal alloy is viewed as mixture of basic component and solute. The approach basing on moving, sharp phase interface between liquid and solid region isintroduced. Constitutional undercooling phenome[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
2009 Vol. 8, nr 1 185-191
EN In the paper mathematical and numerical model of air convection in 3D region is considered. Governing equations of the model are presented. Main assumptions of numerical approach are discussed. Finite Element Method (FEM) with Characteristic Based Split (CBS) scheme is used to solve the problem. Tw[...]
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Archives of Foundry Engineering
PL W pracy przedstawiono model matematyczny i numeryczny procesu krzepnięcia z uwzględnieniem ruchów konwekcyjnych fazy ciekłej, generowanych zarówno w strefie ciekłej jak i stało-ciekłej. Strefa przejściowa pomiędzy obszarem cieczy i ciała stałego traktowana jest jako ośrodek porowaty, w którym uwzglę[...]
EN The paper presents numerical modeling of solidification process with convective motion of the liquid phase, generated both in the liquid and mushy zones. The transition region between the areas filled with liquid and solid is treated as a porous medium, which incorporates the suppression of fluid mo[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN In this paper a two-dimensional double diffusive natural convection system is considered. A mathematical model of heat and moisture transport driven by combined thermal- and solutal-induced buoyancy forces is described. A numerical model based on the Finite Element Method (FEM) is proposed. The resu[...]
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Archives of Foundry Engineering
EN The paper deals with comparison of numerical analysis results obtained for binary alloys solidification process in the sand and permanent mould with motion of the fluid in the liquid and mushy zone. The partial differential equations describing mathematical model of the phenomena are presented. Fini[...]
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Journal of Applied Mathematics and Computational Mechanics
2015 Vol. 14, nr 4 145--152
EN In the paper the mathematical and numerical descriptions of the general case of thermal contact between two flat bodies are presented. The numerical model of the problem is based on the Finite Element Method (FEM). Variable width of the contact gap between interacting bodies is considered. The model[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
2008 Vol. 7, nr 1 193-197
EN Presented paper is focused on results of numerical solution of transient heat conductivity equation in two-dimensional region. Convection term is neglected in mathematical model of the phenomenon. Solutions based on classical Galerkin finite element formulation obtained for girds of different qualit[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
2010 Vol. 9, nr 2 235-242
EN In the paper mathematical description of Discontinuous Galerkin Method (DGM) used in the theory of thermoelasticity is presented. Displacement form of governing equations is introduced as the base of mathematical model. Space discretization methodology for discontinuous finite element method is show[...]
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Journal of Applied Mathematics and Computational Mechanics
EN In this paper, the results of analytical and numerical solution of the problem of heat transport in the rod of finite length are presented. The analytical solution is obtained with the use of the Fourier series. The numerical model of the problem is based on the Finite Element Method (FEM). In addit[...]
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Archives of Foundry Engineering
EN The paper focuses on modeling of binary alloy solidification process with using Finite Element Method (FEM). The process is characterized by liquidus and solidus temperatures which are constant because solutal segregation is neglected. Analysed region is threedimensional and consists of casting and [...]
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Journal of Applied Mathematics and Computational Mechanics
2014 Vol. 13, nr 2 135--140
EN The presented work is focused on the basis of mathematical and numerical descriptions of the binary alloy solidification problem. The mathematical formulation is based on the so-called substitute thermal capacity, which implies a change in the specific heat of solidifying material. In the literature[...]
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Journal of Applied Mathematics and Computational Mechanics
2014 Vol. 13, nr 2 141--147
EN In this paper, the results obtained from five models of the solidification with substitute thermal capacity were compared. The calculations were carried out for steel containing 0.35% carbon with using an in-home solver based on the finite element method (FEM). A comparison was made on the base of a[...]
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Archives of Foundry Engineering
EN The paper presents a method of mathematical and numerical modelling of directional solidification process of pure metal in the two-dimensional region. In this case, the thermal conditions associated with the process favours the occurrence of sharp solidification front. The mathematical description o[...]
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Journal of Applied Mathematics and Computational Mechanics
2013 Vol. 12, nr 2 111--116
EN In this paper a simple and effective method for tracking interfaces in two-dimensional area is described. The presented approach is very attractive in solving Stefan problems where moving internal boundaries occur. It is based on the level set method (LSM) and uses the so-called distance function. A[...]
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Journal of Applied Mathematics and Computational Mechanics
2013 Vol. 12, nr 2 105--110
EN In this paper accuracy of a simple and effective method for tracking interfaces in two-dimensional area is investigated. The method is based on the level set method (LSM) with "brute force" reinitialization algorithm. A comparison of numerical solution with an analytical solution is presented and di[...]
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