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1
Content available Numerical analysis of the heating of a die for the extrusion of aluminium alloy profiles in terms of thermochemical treatment
Joachimiak Damian, Judt Wojciech, Joachimiak Magda
Archives of Thermodynamics
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2023
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Vol. 44, no 2
159--175
EN
Thermochemical treatment processes are used to produce a surface layer of the workpiece with improved mechanical properties. One of the important parameters during the gas nitriding processes is the temperature of the surface. In thermochemical treatment processes, there is a problem in precisely determining the surface temperature of heat-treated massive components with complex geometries. This paper presents a simulation of the heating process of a die used to extrude aluminium profiles. The maximum temperature differences calculated in the die volume, on the surface and at the most mechanically stressed edge during the extrusion of the aluminum profiles were analysed. The heating of the die was simulated using commercial transient thermal analysis software. The numerical calculations of the die assumed a boundary condition in the form of the heat transfer coefficient obtained from experimental studies in a thermochemical treatment furnace and the solution of the nonstationary and non-linear inverse problem for the heat conduction equation in the cylinder. The die heating analysis was performed for various heating rates and fan settings. Major differences in the surface temperature and in the volume of the heated die were obtained. Possible ways to improve the productivity and control of thermochemical treatment processes were identified. The paper investigates the heating of a die, which is a massive component with complex geometry. This paper indicates a new way to develop methods for the control of thermochemical processing of massive components with complex geometries.
2
Content available Identification of the average and local boundary condition of heat transfer during cooling with a water spray under surface boiling
Jasiewicz Elżbieta, Hadała Beata, Malinowski Andrzej
Computer Methods in Materials Science
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2020
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Vol. 20, No. 4
147--155
EN
The study determined the local and average heat transfer coefficient and the heat flux on the surface of a cylinder cooled with a water nozzle. The inverse method was used to identify the heat transfer coefficient. An objective function was defined to determine the distance between the measured and calculated temperatures. Two models describing the heat transfer coefficient on the cooled surface were considered. The first model described changes in the heat transfer coefficient as a function of the sample radius and cooling time, and the second one assumed the dependence of the heat transfer coefficient solely on time. Numerical simulations showed significant differences in the determined heat transfer coefficients depending on the adopted model of the boundary condition. The performed tests included experimental temperature measurements at selected points of the sensor, numerical simulations of temperature changes, and the inverse solution.
3
Analiza wpływu błędu danych wejściowych na wynik identyfikacji współczynnika wymiany ciepła
Jasiewicz Elżbieta, Jasiewicz Kamil, Sosik Marcin, Cebo-Rudnicka Agnieszka, Hadała Beata
Przegląd Mechaniczny
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2019
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nr 6
41--44
PL
W artykule przedstawiono analizę wpływu błędu danych wejściowych związanych z pomiarem temperatury na współczynnik wymiany ciepła wyznaczony z rozwiązania zagadnienia odwrotnego dla równania przewodzenia ciepła. Do obliczenia współczynnika wymiany ciepła użyto programu komputerowego wykorzystującego metodę elementów skończonych.
EN
The article presents an analysis of the imput data error related to temperature measurement on the heat transfer coefficient determined from the solution of the inverse problem for the heat conduction equation. The computer program utilizing the finite element method has been used to calculate the heat transfer coefficient.
4
Content available Identification of the Thermal Conductivity Coefficient in the Heat Conduction Model with Fractional Derivative
Brociek R., Słota D.
Archives of Foundry Engineering
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2019
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iss. 3
38--42
EN
Main goal of the paper is to present the algorithm serving to solve the heat conduction inverse problem. Authors consider the heat conduction equation with the Riemann-Liouville fractional derivative and with the second and third kind boundary conditions. This type of model with fractional derivative can be used for modelling the heat conduction in porous media. Authors deal with the heat conduction inverse problem, which, in this case, consists in identifying an unknown thermal conductivity coefficient. Measurements of temperature, in selected point of the region, are the input data for investigated inverse problem. Basing on this information, a functional describing the error of approximate solution is created. Minimizing of this functional is necessary to solve the inverse problem. In the presented approach the Ant Colony Optimization (ACO) algorithm is used for minimization.
5
Content available remote Uproszczona metoda analizy pola termicznego w izolacji przewodu przy wykorzystaniu funkcji Greena
Zaręba M.
Przegląd Elektrotechniczny
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2018
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R. 94, nr 11
155--158
PL
W pracy przedstawiono uproszczoną metodę analizy pola termicznego w izolacji przewodu przy wykorzystaniu funkcji Greena. Podstawą metody jest dekompozycja obszarów przewodu. Żyłę przewodu modelowano jako element skupiony, zaś izolację analizowano jako element o parametrach rozłożonych. W rezultacie, w pracy wyznaczono krzywe rozgrzewu oraz termiczne stałe czasowe w izolacji przewodu przy stałej (uśrednionej) i zmiennej rezystywności żyły przewodu. Wyniki pozytywnie zweryfikowano metodą elementów skończonych.
EN
In the paper a simplified method of determination of the thermal field in wire insulation was presented by using the Green’s function. The basic of the method is the decomposition of the regions of the wire. The core of the insulation was modeled as a inert element of the first order, and the insulation was analyzed as the distributed parameter. As a result, heating up curves and time constant in the insulation of the wire were determined for the constant (averaged) and variable resistivity. The result was positively verified using the finite element method.
6
Content available Analytical and numerical solution of the heat conduction problem in the rod
Węgrzyn-Skrzypczak E., Skrzypczak T.
Journal of Applied Mathematics and Computational Mechanics
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2017
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Vol. 16, nr 4
79--86
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 addition, to check the compatibility of both solutions, distributions of the temperature for selected time moments are compared and discussed.
7
Content available The temperature of a brake disc during frictional heating with linear distribution of the contact pressure
Topczewska K.
Technical Issues
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2016
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nr 3
113--119
EN
In this paper the analytical solution of the boundary–value heat conduction problem for a brake rotor was developed. A solid brake disc is heated by frictional heat flux during braking with constant deceleration. Intensity of the heat flux affecting friction surface of the disc is proportional to the specific power of friction. It was assumed that contact pressure between the pad and the disc increases linearly, from zero in the initial moment of the braking process to the maximum value in standstill. Calculations were carried out on variables and parameters in the dimensionless form. The obtained results were compared with adequate resultsduring braking with constant deceleration, with an assumption of pressure constant in time.
8
Content available Implicit finite difference method for the space fractional heat conduction equation with the mixed boundary condition
Brociek R., Słota D.
Silesian Journal of Pure and Applied Mathematics
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2016
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Vol. 6, iss. 1
125--136
EN
This paper presents the numerical solution of the space fractional heat conduction equation with Neumann and Robin boundary conditions. In described equation the Riemann-Liouville fractional derivative is used. Considered model is solved by using the implicit finite difference method. The paper also presents the numerical examples to illustrate the accuracy and stability of described method.
9
Content available Harmonic impact on the surface of a half-plane in the framework of Time-Fractional Heat Conduction
Povstenko Y.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2016
|
Vol. 21
85--92
EN
The time-fractional heat conduction equation with the Caputo derivative is considered in a half-plane. The boundary value of temperature varies harmonically in time. The integral transform technique is used; the solution is obtained in terms of integral with integrand being the Mittag-Leffler functions. The particular case of solution corresponding to the classical heat conduction equation is discussed in details.
10
Content available remote Cooling of hot water with non-uniform initial temperature
Neupauer K., Komorowicz T., Kupiec K.
Czasopismo Techniczne. Chemia
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2016
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Y. 113, iss. 1-Ch
101--110
EN
A mathematical model of water cooling in a vertical tank with non-uniform initial temperature has been presented in this paper. This kind of process is important in solar installations. Calculation results for various cases comprising, among others, two or three layers of water with different initial process temperatures as well as various combinations of heat resistance of the side wall, the tank bottom and the tank cover, have been given as well.
PL
Przedstawiono model matematyczny chłodzenia wody o niejednorodnej temperaturze początkowej w zbiorniku o osi pionowej. Taki proces ma praktycznie znaczenie w instalacjach solarnych. Przedstawiono wyniki obliczeń dla różnych przypadków obejmujących m.in. dwie lub trzy warstwy wody o różnych temperaturach na początku procesu oraz rozmaite kombinacje pomiędzy wielkościami oporów cieplnych ściany bocznej oraz dna i pokrywy zbiornika.
11
Content available Zapłon stałych paliw rakietowych – wybór z prac własnych i analiza literaturowa
Wolszakiewicz T.
Chemik
|
2016
|
Vol. 70, nr 1
27--32
PL
W pracy przedstawiono wyniki badań progu zapłonu stałych paliw rakietowych dla wybranych mieszanin pirogenicznych. Opisano aktualny stan literatury i przeprowadzono obliczenia numeryczne metodą Monte Carlo. Opisano zasady wyznaczenia energii emitowanej przez tabletki pirogeniczne przy zastosowaniu bardzo czułych czujników temperatury i rozwiązaniu równań przewodnictwa ciepła.
EN
The paper presents the results of research for the ignition threshold of solid rocket fuels for the selected pyrogenic mixtures. Also the current state of the literature was described and numerical calculations using Monte Carlo method were performed. The principles to determine the energy emitted by the pyrogenic tablets were described using very sensitive temperature sensors and solving equations of heat conduction.
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