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1
Content available Thermo-diffusion MHD convection in enclosure using heat and mass lines visualization techniques
Kushawaha Durgesh, Yadav Sushil, Singh Dwesh K., Behera Pravata Kumar
Journal of Applied Mathematics and Computational Mechanics
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2022
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Vol. 21, nr 2
63--76
EN
The numerical study of two-dimensional laminar thermo-diffusion natural convection in an exponentially heated and concentrated square enclosure of unit length in the presence of a uniform horizontal magnetic field is presented in this paper. The left and right vertical walls are assumed to have higher and lower temperatures and concentrations, respectively, and are governed by exponential functions, whereas the horizontal walls are assumed to be adiabatic and non-diffusive. The mathematical formulation of heat and mass functions has been completed, and heat and mass line contours have been drawn based on these functions to investigate the behavior of heat and mass in the cavity. The flow governing equations were solved using a finite difference method in conjunction with the Successive Over-Relaxation (SOR) technique and then converted to a vorticity-stream function form. A detailed comparison of isotherms with heatlines and isosolutes with masslines has been performed. Furthermore, the reduction for lower Rayleigh numbers Ra surpassing the reduction for higher values of Ra. The maximum reduction in overall heat and mass transfer has been observed for higher Hartmann (Ha = 8).
2
Content available remote Więzy termomechaniczne w teorii gradientowej
Kubik J.
Roczniki Inżynierii Budowlanej
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2013
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z. 13
111--114
EN
The theory of thermomechanical constraints is used in the work in order to derive particular forms of equations for the theory of gradient thermodiffusion. The constraints are considered for the material medium in which the gradient components of the equations do not cause additional energy dissipation.
3
Content available remote Odpowiedniość równań mikropolarnej teorii mieszanin i termodyfuzji
Kubik J.
Roczniki Inżynierii Budowlanej
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2012
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z. 12
21--24
EN
The mass and momentum balances in micropolar mixture theory and thermodiffusion is analysed. One can conclude that not only local and global mass balances should be fulfilled but also local and global inertia moment should be considered. As the consequence we should make similar generalization in reminding balance.
4
Content available Wybrane problemy wzbogacania chromem stali S235JR i S355J2 przy zastosowaniu lasera CO₂
Górka A., Kocańda D.
Biuletyn Wojskowej Akademii Technicznej
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2012
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Vol. 61, nr 2
297-310
PL
Zagadnieniem rozważanym w pracy jest wzbogacanie warstwy wierzchniej stali kadłubowych S235JR i S355J2 chromem w celu zwiększenia ich odporności na działania korozyjne wody morskiej. Podjęto próbę wyjaśnienia mechanizmu tworzenia stabilnych struktur w głębi warstw dyfuzyjnych przy domieszkowaniu stali chromem. Jako modelowego aktywatora termodynamicznych zjawisk, zachodzących podczas tego procesu z zastosowaniem zmodyfikowanej metody zgrzewania tarciowego FSP (Friction Stir Processing), użyto wiązki promieniowania laserowego. Analizowano dyfuzyjny transport masy, który jest pierwotnym i dominującym zjawiskiem w przemianach fazowych zachodzących w mikroobszarach o znacznym gradiencie temperatury w procesie tworzenia cienkich warstw antykorozyjnych. Przedstawiono rozkłady stężenia chromu w warstwie dyfuzyjnej stali, wynikające ze wzorów analitycznych podanych w pracy i z własnych pomiarów doświadczalnych, otrzymanych przy wydłużonym i skróconym czasie nagrzewania wiązką laserową powłoki galwanicznego chromu osadzonej na podłożu stalowym.
EN
The paper deals with the problem of the S235JR and S355J2 hull steels enriching with chromium in order to improve their corrosive resistance against sea water. The attempts were undertaken to explain the mechanism of formation of durable layers inside the diffusion zone while the steel alloying process is providing. In the research to model the process of surface layer steel modification by means of modified friction stir processing (FSP), a continuous wave CO₂ laser beam was served as a model activator of thermodynamical phenomena appearing there. Mainly, diffusive mass transport was considered in the work as it being the original and basic phenomenon affected in the phase transformations. The theoretical and experimental concentration distributions of chromium inside the diffusive layers being diffused from galvanic coating of steel matrix were performed in the paper for short and long laser exposition time. Thanks determining in the work the conditions for collaboration of the concentration diffusion component as well the complex thermodiffusive mass transport, it is possible to design the structure and the thickness of diffusive layers in the matrix.
5
Content available Model formowania warstwy dyfuzyjnej typu Fe-Cr w polu temperatury
Górka A., Kocańda D.
Biuletyn Wojskowej Akademii Technicznej
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2012
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Vol. 61, nr 2
233-244
PL
W artykule przedstawiono model tworzenia warstw dyfuzyjnych na przykładzie chromu, jako elementu nasycającego, i żelaza jako elementu nasycanego w polu laserowej inicjacji cieplnej z zastosowaniem lasera CO₂ emitującego wiązkę o normalnym rozkładzie gęstości mocy w trybie pracy ciągłej. Zamieszczone w pracy wyniki badań weryfikacyjnych dokumentują istnienie termodyfuzyjnego strumienia masy w strefie nagrzewanego materiału. Proces ten jest dominujący w pierwszym, wyodrębnionym w tym modelu etapie tworzenia warstwy, to jest w czasie nagrzewania materiału. Obserwowane efekty oddziaływania tego strumienia na strukturę w modyfikowanej warstwie uzależnione były w pierwszym rzędzie od czasu realizacji procesu oraz od parametrów cieplno-geometrycznych obszaru wpływu ciepła, takich jak: głębokość przetopienia i grubość zastosowanej powłoki chromu nałożonego galwanicznie. Przy spełnieniu odpowiednich warunków relacji pomiędzy wymienionymi parametrami, rozkłady stężenia chromu posiadały maksima w głębi warstw, a nie na powierzchni, jak ma to miejsce w konwencjonalnych procesach dyfuzyjnych realizowanych przy stałej temperaturze.
EN
In the paper, the model of formation of the Fe-Cr diffusion layer on a carbon steel substrate in the thermal field produced by continuous laser beam with normal power density distribution is presented. Here, the enclosed results of verification investigations prove that thermodifusional mass transport is a dominant phenomenon in the first stage of the diffusion layer formation process when the chromium galvanic surface layer is under heating. The effect of the thermodiffusion flux action depends on the heating period as well as on thermo-geometrical parameters of the heat affected zone such as melting depth and the thickness of the chemical chromium layer coating on the steel substrate. While the particular relations between the above mentioned parameters of heat affected zone are satisfied then the maximum values of chromium concentration distribution can be found in the depth of diffusion layer. It seems to be on contrary to the conventional diffusion process running under constant temperature whereas the maximum concentration of chromium metal is found on the surface of diffusion layer.
6
Content available remote Analogie równań opisujących proces termodyfuzji w ośrodku ciągłym i mikropolarnym
Wieczorek B.
Roczniki Inżynierii Budowlanej
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2008
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z. 8
93--96
EN
In the paper are presented the formulation thermodiffusion problems in viscoelastic solid with multicomponent body. There is analysed the model of the continuous medium and the micropolar medium. The balance of mass, momentum, angular momentum, energy and entropy in a solid are proposed for each of the ingredients. Next, the balance equations are obtained for the body. The physical equations of the process are obtained assuming the thermodynamic potentials. Next, the final systems of equations are obtained which describe a character of mutual reaction of heat, diffusion and stress fields.
7
Content available remote Sprzężenie przepływu cieplno-dyfuzyjnego w ujęciu numerycznym
Pilśniak J., Wieczorek B.
Roczniki Inżynierii Budowlanej
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2007
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z. 7
87--90
EN
The paper is gone on the scientific research which apply to phase transition in the thermodiffusion processes. They proceed under the influence of action external agents. There was presented results of phase transition solid body to liquid body. The process is described by the system equations, which allow for mutually coupled heat and diffusion flows. The numerical solution of these equations were obtained by finite difference method of numerical analysis. The computer program was written Visual C++. The program enables the simulation of the mutually process for different boundary and initial conditions and changeable source, which generate transitions. Moreover there was made an analysis of convergence of applied computational method.
8
Content available remote Rozwiązanie fundamentalne zagadnienia quasi-statycznego stacjonarnej termodyfuzji w ośrodku sprężystym o właściwościach mikropolarnych
Wieczorek B.
Roczniki Inżynierii Budowlanej
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2007
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z. 7
129--134
EN
In a paper the problem of displacement evaluation coupled with the flow of mass and heat consideration is analysed in the elastic solid with micropolar structure. The problem of quasi-static and stationary process is described diffusion and conductivity equations and systems of motion equations for displacements and rotations. The system of equations has eight partial differential equations of the second order. The searched quantities in the problem are: the temperature T, the concentration C, the displacement field ui and rotation field ϕi. There is presented the method of the solution for the equations’ system. The transformation methods are used in the construction of fundamental solutions of the system of equations. A fundamental solution of that system is built on the basis of Fourier’s transformation, its properties and theory of distribution. On their basis are obtained the solution of the initial system. The fundamental solutions and the reciprocity theorem is applied to find the solution of the analyzed initial-boundary problem.
9
Content available remote Zależności między współczynnikami sprzęgającymi w procesie termodyfuzji w ośrodku o własnościach mikropolarnych
Wieczorek B.
Roczniki Inżynierii Budowlanej
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2006
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z. 6
149--152
EN
The problem of quasi-statical convoluted elastic thermodiffusion in described with the system of eight partial differential equations of the second order, describing character of mutual reaction of the heat, diffusion and stress fields. There were different forms of these equations systems, resulted of the way of fields reactions. They were derived from the different thermodynamic formulations of problem and from the way of interaction of fields for the considered problem. The thermodynamic potentials and the dependences between them, also the constitutive equations were used to specify interdependence between the coefficients, which are in the system of these equations. If there are known the experimental constants for one of the formulation thermodiffusion than the relations allow to determine the constants for the others of the formulation process. It is very importance, because there isn’t possible to carry out an experiment and obtain the applicable conjugates.
10
Content available remote O termodyfuzji w polu elektrycznym
Jędrzejczyk-Kubik J.
Roczniki Inżynierii Budowlanej
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2006
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z. 6
41--45
EN
An n-th component mixture placed in electric field is analysed. It is assumed that there exists a component which has a much greater density than those of the other components. Such an assumption validates the determination of the thermodiffusion equations in the electric field. In the final step, the constitutive equations for viscoelastic thermodiffusion concerning the electric field are formulated.
11
Content available remote Global solution to the initial value problem for nonlinear system of equations of thermodiffusion without displacements
Łazuka J.
Demonstratio Mathematica
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2004
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Vol. 37, nr 3
557--570
EN
In the paper we shall present the proof of global-in-time solution to the initial value problem for nonlinear partial differential equations describing physical proc-cesses of thermodiffusion without displacements. Time decay of global solution will be also shown.
12
On diffusion and thermodiffusion in a gravity field
Piekarski S.
Journal of Technical Physics
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2003
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Vol. 44, no 3
329-337
EN
The modified Fick law has been introduced in the paper: S. Piekarski, On the modified Fick law and its potential applications (J. Tech. Phys., 44, 2, 125-131, 2003). The first purpose of the present paper is to give a simpler "derivation" of the modified Fick law than that originally presented. Namely, it can be introduced as a particular case of the Wojnar equation (R. Wojnar, "Nonlinear heat equation and thermodiffusion", p. 296, Eq. (2.1), Rep. on Math. Phys., No 1/2, Vol. 46, 2000). The third equation discussed is the Einstein-Smoluchowski equation. All equations mentioned above, contain a potential for the force, acting on the diffusing matter. The important fact is that, for isothermal conditions, all the equations mentioned above are identical. In this article we try to describe the effects of the constant gravitational field on the diffusion processes. We propose an explicit form of the potential for which the equilibrium concentration profiles are consistent with the experimental results. We compare shortly our results with two models of the diffusion processes in a gravitational field described in Huang's book [8] as well as with other opinions concerning this subject. As an example of technological application of the presented theory, the diffusion of the atomic hydrogen in fluid iron is proposed.
13
Content available Thermodiffusion in periodically layered elastic composites
Kaczyński A., Matysiak S. J.
Journal of Theoretical and Applied Mechanics
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2002
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Vol. 40 nr 1
85-100
EN
The paper deals with modelling of thermodiffusion processes in periodically layered elastic composites. The study is based on the homogenized procedure with microlocal parameters and on the relations of the linear coupled theory of diffusion in thermoelastic homogeneous bodies. A useful homogenized model with microlocal parameters accounting for certain local effects of heat and diffusion fluxes, as well as stresses is derived. The equations of the homogenized model are given in terms of unknown macroconcentration, macrotemperature and macrodisplacements and extra unknowns called the microlocal parameters. An illustrating example of the application of the presented model is solved.
PL
W pracy rozważano zagadnienie modelowania procesu dyfuzji w periodycznie warstwowych sprężystych kompozytach. Rozważania oparto na procedurze homogenizacyjnej z parametrami mikrolokalnymi i na liniowej teorii dyfuzji dla jednorodnych ciał termosprężystych. Wyprowadzony został zhomogenizowany model z parametrami mikrolokalnymi uwzględniający pewne lokalne efekty dla strumieni dyfuzji i ciepła oraz naprężeń. Rozwiązano również przykład ilustrujący zastosowania wyprowadzonego modelu.
14
Content available remote Termodyfuzja w periodycznie warstwowych sprężystych kompozytach
Kaczyński A., Matysiak S. J.
Vibrations in Physical Systems
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2000
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Vol. 19
148--149
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