Wyniki wyszukiwania - BazTech

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Modeling of heat transfer and fluid flow in a rectangular channel with an obstacle

Stryczyński Mikołaj, Majchrzak Ewa

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 2

121--132

EN

Heat transfer and fluid flow in the rectangular channel with an obstacle are considered. The problem is described by the Fourier-Kirchhoff equation, Navier-Stokes equations and continuity equation supplemented by appropriate boundary and initial conditions. To solve this system of equations the finite difference method with a staggered grid is used. The results of computations obtained using authorial computer program are compared with ANSYS Fluent simulation. Computations are carried out for obstacles of various sizes and positions, and on this basis the conclusions are formulated.

2

Numerical approaches to the heat transfer problem in modern electronic structures

Raszkowski T., Samson A.

Computer Science

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2017

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Vol. 18 (1)

71--93

EN

The main aim of this paper is to present a detailed description of the research related to the modeling of heat conduction in modern electronic structures, including special consideration for numerical aspects of analyzed algorithms. The motivation to undertake the research as well as some of the most-important results of the experiments and simulations are also included. Moreover, a numerical approximation of the problem as well as the methodology used and a sample solution of the mentioned problem are presented. In the main part, the discretization techniques, Ordinary Differential Equation algorithms, and simulation results for Runge-Kutta’s and Gear’s algorithms are analyzed and discussed. Additionally, a new effective approach to the modeling of heat transfer in electronic nanostructures is demonstrated.

3

On free convection heat transfer from vertical plate - proposition of a new model

Leble S., Lewandowski W. M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2016

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Vol. 20, No 2

249--265

EN

The free convection heat transfer from an isothermal vertical plate in open space is investigated theoretically. In contrast to conventional approaches we use neither boundary layer nor self-similarity concepts. We base on expansion of the fields of velocity and temperature in a Taylor Series in x coordinate with coefficients being functions of the vertical coordinate (y). In the minimal version of the theory we restrict ourselves by cubic approximation for both functions. The Navier-Stokes and Fourier-Kirchhoff equations that describe the phenomenon give links between coefficient functions of y that after exclusion leads to the ordinary differential equation of forth order (of the Mittag-Leffleur type). Such construction implies four boundary conditions for a solution of this equation while the links between the coefficients need two extra conditions. All the conditions are chosen on the basis of the experience usual for free convection. The choice allows us to express all the theory parameters as functions of the Rayleigh number and the temperature difference. To support the conformity of the theory we derive the Nusselt-Rayleigh numbers relation that has the traditional form. The solution in the form of velocity and temperature profiles is evaluated and illustrated for air by examples of plots of data.

4

Modelling the effect of SiC mass fraction on crystallization of magnesium metal matrix composite; AZ91/SiC

Lelitko J., Żak P., Suchy J., Krajewski W., Krawiec H., Greer. L., Shumacher P., Shirzadi A., Haber K., Darłak P.

Inżynieria Materiałowa

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2010

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Vol. 31, nr 3

703-707

EN

The aim of this work was prepare micro-macro crystallization model of AZ91/SiC composite that depends on mass fraction of SiC particles. This model base on temperature and chemical elements concentration, it also takes into account primary a-Mg phase nucleation rate. The behavior of temperature and chemical composition field can be calculated using Fourier- -Kirchhoff equation and modified second Fick's law. The nucleation rate for this alloy was calculated from log-normal Fras equation. Fitting parameters were found using experimental data. Different composites castings with different mass fraction of SiC particles were performed. The grain density and undercooling in each case were measured. Obtained data was used as test values during statistical fitting of the unknown model adjustment parameters. The simulation software on the base of prepared model was written. Experiment for the same composite as set as initial data of the simulation was performed. The simulation results were compared with an experimental data. Analysis shows good fitting of presented model with the real values.

PL

Celem niniejszej pracy było przygotowanie modelu mikro-makro krystalizacji kompozytu na bazie stopu AZ91 (tab. 1), wzmocnionego cząstkami SiC, który uwzględniałby udział masowy cząstek zbrojących. Model bazuje na równaniach opisujących rozkład pola temperatury (rownanie Fouriera- -Kirchhoffa) oraz polu stężeń pierwiastków chemicznych (zmodyfikowane prawo Ficka). Szybkość zarodkowania dla badanego materiału została opisana równaniem Frasia. Parametry dopasowania w proponowanym modelu zostały wyznaczone statystycznie na podstawie danych doświadczalnych. Aby zrealizować założony cel pracy, wykonano kilka wytopów dla rożnych kompozytów AZ91/SiC. Analiza mikrostruktury odpowiednio przygotowanych oraz wytrawionych próbek pozwoliła na wyznaczenie gęstości ziaren. Statystyczne zestawienie tych danych z wartościami przechłodzenia prowadzi do modelu zarodkowania kompozytu AZ91/SiC zależnego od przechłodzenia (14÷18) oraz od przechłodzenia i udziału masowego SiC (19). Wyniki symulacji wykazują bardzo wysokie dopasowanie w stosunku do wyników doświadczalnych (rys. 14). Analiza wyników symulacji pozwala na poznanie wielu aspektów procesów odbywających się w krzepnącym odlewie (rys. 15÷17).