Bohdan Mochnacki

Identification of Thermal Properties of the System Casting-Mould

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.

Numerical modelling of bioheat transfer in multi-layer skin tissue domain subjected to a flash fire

Publisher Summary This chapter reviews the numerical analysis of thermal processes proceeding in the multilayer domain of skin tissue subjected to an external heat source. Heat transfer in the skin tissue was assumed to be transient and2D. The bio-heat transfer in the domain considered is described by the system of the Pennes equations.On the assumed part of skin surface the Neumann condition determining the value of external heat flux is given, on the conventionally assumed internal surfaces of the tissue–the no-flux condition is accepted. For time t= 0 the initial distribution of temperature is known. The main subject of the chapter is the sensitivity analysis of temperature field with respect to the skin tissue parameters. On the stage of numerical computations the boundary element method has been used. The skin has been assumed to be the homogeneous domain characterized .by mean parameters of successive layers

Numerical Modelling of Hyperthermia and Hypothermia Processes

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.

Boundary element model of coupled heat and mass transfer in solidifying castings

The solidification and cooling processes taking place in the casting domain can be described by the system of partial differential equations and adequate boundary, geometrical, physical and initial conditions. From the mathematical point of view, the so-called moving boundary problem should be considered and the task can be effectively solved using numerical methods. In this paper, the alloys solidification is considered. In differential equations describing the solidification process, the parameter called a substitute thermal capacity is introduced; in other words, the one domain approach is applied. The heat transfer model is coupled with the macrosegregation model, because the temperatures limiting the mushy zone sub-domain are a function of the alloy components concentration (a binary alloy is taken into account). Two macrosegregation models are constructed on the basis of the lever-arm law and Scheils equation, respectively. In terms of numerical computation, the boundary element method (heat transfer model) and the control volume method (macrosegregation) are applied. The typical numerical solutions presented in the literature do not take into account the relationships between heat transfer and macrosegregation processes or the models proposed are very complex and not effective. The solution presented in this paper seems to be sufficiently exact and very simple for numerical realisation.

Computer simulation of heat transfer between the particles and metal matrix during the solidification of a cast composite

In this paper, the thermal interactions between a single particle of lead and a metal matrix (Al-Si alloy) are analysed. From the mathematical point of view, this task belongs in the field of moving boundary problems. The problem has been solved using the finite element method for spherical domains. The course of particle melting (pure metal) has been modelled on the basis of the procedure called the temperature recovery method, and the solidification of metal matrix (alloy) on the basis of the fixed domain approach. The results of numerical computations are presented in the final section of the paper.

Application of the boundary element method for the numerical modelling of the solidification of cylindrical and spherical castings

Abstract From the mathematical point of view the solidification process proceeding in the domain casting–mould is described by the system of partial differential equations and boundary/initial conditions. It should be pointed out that taking into account the complex form of the governing equations and the physical, geometrical, boundary and initial conditions an effective solution can be obtained only using numerical methods. In this paper the combined variant of the boundary element method called the BEM using discretization in time is applied. In particular the well-known numerical algorithm for domains oriented in the cartesian co-ordinate system is considered. In order to adapt the method for numerical simulation of the heat-transfer processes proceeding in domains oriented in other co-ordinate systems a certain algorithm consisting in the introduction of an artificial source is used.

Numerical model of macro-segregation during directional crystallization process

Abstract In the paper the mathematical model of macro-segregation proceeding during the directional crystallization process is presented. The boundary-initial problem considered is discussed. Next the numerical approximation constructed on the basis of the boundary element method supplemented by a procedure called the artificial heat source method is described. The boundary condition on the solidification front resulting from the alloy component balance is introduced, while in finally the practical aspects of computations concerning the course of the process are discussed.

Application of Control Volume Method Using the Voronoi Tessellation in Numerical Modelling of Solidification Process

The paper presents the method to analyse the thermal processes occurring in the cast composite solidification. The cast is formed by a bundle of parallel fibres randomly immersed in a host metal matrix. The heat is transferred from the metal matrix and absorbed by the fibres. The objective of this paper is to evaluate the volumetric fraction of the fibres for which the solidification of the metal matrix occurs only due to the presence of fibres playing a role of internal chills. Our method is to compute Voronoi diagrams with Voronoi regions representing the geometric location of the fibres in the metal matrix and to use these regions as control volumes within a variant of the Control Volume Method.

Application of the Shape Sensitivity Analysis in Numerical Modelling of Solidification Process

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.

Numerical Model of Thermal Processes in Domain of Thin Film Subjected to a Cyclic External Heat Flux

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.