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Numerical solution of integral equations in the density problems

100%

Hącia L.

tom No 52

103-113

In this paper density problems are restricted to the current and the heat conduction. Analysis of the current density leads to system integral equations of the Fredholm type [4-5]. That problem in timeprovides to the mathematical model determined by the system of integro-differenti al equations [2-3] and it is extended for few conductors. The functions density for heat conduction problems are determined by Volterra-Fredholm integral equations. Presented theory is illustrated fay computational experiments.

Fredholm integral equations in the radiative heat transfer problems

63%

Hącia L. , Domke K.

tom No 52

115-123

Basic equations of radiative heat transfer have been presented, along with typical Dirichlet and Neumann boundary conditions for established stales. Possible methods of solving integral equations describing radiative heat transfer have been identified, and these have been limited to iterative and projection methods. We restrict to method of successive approximations, discretization method, Galerkin method, collocation method and method of special kernels. Moreover, quadratures and probabilistic methods frequently used in the radiosity are presented. Presented problem is illustrated by example.

Chosen aspects of FDM simulation for prediction of casting quality

51%

Hącia L. , Ignaszak Z. , Mikołajczak P.

tom Nr 46

17-24

Process of casting solidification leads to the initial boundary values of parabolic equations. The finite difference method is applied. The study deals with the influence of spatial discretization cast-mould for solidification time and gradient parameters. The presented method is illustrated by numerical examples.

Proces krzepnięcia odlewa opisany równaniami parabolicznymi rozwiązano metodą różnic skończonych. Przebadano wpływ dyskretyzacji przestrzeni układu odlew-forma na czas krzepnięcia i parametry gradientowe. Zastosowaną metodę przedstawiono na przykładzie obliczeń numerycznych.