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1

Numerical study of heating transfer by natural convection in an inclined elliptical cylinder charged with nanofluid

Amroune Amina, Bouras Abdelkrim, Taloub Djedid, Driss Zied

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 3

28--41

EN

In this paper, thermal transfer with natural convection in a tilted annular cylinder with a Cu-water nanofluid has been numerically studied. The hot interior and cold exterior elliptical surfaces of the enclosure were maintained at constant temperatures Th and Tc , respectively. The governing equations were solved by the stream function-vorticity approach. The finite volume approach was utilized to discretise the controlling equations. The volume fraction range of the nanoparticles and the Rayleigh number was as follows: [...] respectively. The inclination angles were γ=30°,45°,and 60°. Results were given as isotherm contours, streamlines, average and local Nusselt numbers. The results indicate that the thermal transfer ratio increases with an increase in the tilt angle, regardless of the nanoparticle size values. and the impact of the inclination angle on the heating transfer rate is more important the higher the Rayleigh number and the more convection there is.

2

Heat transfer by natural convection from a heated square inner cylinder to its elliptical outer enclosure utilizing nanofluids

Bouras Abdelkrim, Taloub Djedid, Driss Zied, Debka Siham

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 2

22--34

EN

In this paper a numerical study of natural convection of stationary laminar heat transfers in a horizontal ring between a heated square inner cylinder and a cold elliptical outer cylinder is presented. A Cu-water nanofluid flows through this annular space. Different values of the Rayleigh number and volume fraction of nanoparticles are studied. The system of equations governing the problem was solved numerically by the fluent calculation code based on the finite volume method and on the Boussinesq approximation. The interior and exterior surfaces are kept at constant temperature. The study is carried out for Rayleigh numbers ranging from 310 to 510. We have studied the effects of different Rayleigh numbers and volume fraction of nanoparticles on natural convection. The results are presented as isotherms, isocurrents, and local and mean Nusselt numbers. The aim of this study is to study the influence of the thermal Rayleigh number and volume fraction of nanoparticles on the heat transfer rate.

3

On the onset of thermal instability of a porous medium layer saturating a Jeffrey nanofluid

Rana Gian C., Gautam Poonam Kumari

Engineering Transactions

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2022

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Vol. 70, iss. 2

123--139

EN

The onset of stationary convection in thermal instability of porous layer saturating a Jeffrey nanofluid is studied. The behaviour of nanofluid is described by a Jeffrey fluid model and the porous layer is assumed to follow Darcy’s law. Due to the presence of the Jeffrey parameter and nanoparticles, the momentum-balance equation of fluid is modified. The linear stability analysis and normal modes analysis method are utilised to derive the dispersion relation for the Rayleigh number in terms of various parameters for free-free boundaries. The effects of the Jeffrey parameter, Lewis number, modified diffusivity ratio, nanoparticles’ Rayleigh number and medium porosity on the physical system are discussed analytically and graphically.

4

Effect of aspect ratio of enclosure on free convection from horizontal cylinders in Bingham plastic fluids

Baranwal Ashok Kumar, Gupta Anoop Kumar, Tiwari Anurag Kumar, Melnik Roderick

Chemical and Process Engineering

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2022

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Vol. 43, nr 2

271--277

EN

Heat transfer in steady free convection from differentially heated cylinders enclosed in a rectangular duct filled with Bingham plastic fluids has been solved numerically for the ranges of the dimensionless groups as, Rayleigh number, 102 Ra 106; Prandtl number, 10 Pr 100 and, Bingham number, 0 Bn 50 for aspect ratios AR = 05, 0.6, 0.7, 0.8, 0.9 and 2. The streamlines, isotherm contours, yield surfaces, local and average Nusselt numbers were analysed and discussed. It is found that as the aspect ratio of the enclosure increases from 0.5 to 0.9, the average Nusselt number on the surface of the hot cylinder increases as a larger amount of fluid takes part in convection. Moreover, at sufficiently large Bingham numbers, yield stress forces dominate over buoyancy causing the flow to cease and thus the Nusselt number approaches its conduction limit. Finally, the Nusselt number approaches its conduction limit once the maximum Bingham number is reached.

5

Anisotropic turbulent viscosity and large-scale motive force in thermally driven turbulence at low Prandtl number

Mizerski K. A.

Archives of Mechanics

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2022

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Vol. 74, nr 5

409-436

EN

The fully developed turbulent Boussinesq convection is known to form large-scale rolls, often termed the ‘large-scale circulation’ (LSC). It is an interesting question how such a large-scale flow is created, in particular in systems when the energy input occurs at small scales, when inverse cascade is required in order to transfer energy into the large-scale modes. Here, the small-scale driving is introduced through stochastic, randomly distributed heat source (say radiational). The mean flow equations are derived by means of simplified renormalization group technique, which can be termed a ‘weakly nonlinear renormalization procedure’ based on consideration of only the leading order terms at each step of the recursion procedure, as full renormalization in the studied anisotropic case turns out unattainable. The effective, anisotropic viscosity is obtained and it is shown that the inverse energy cascade occurs via an effective ‘motive force’ which takes the form of transient negative, vertical diffusion.

6

Effect of magnetic and temperature variation on Al2O3 nanofluid convection

Chawla Meenu, Bhardwaj Rashmi, Bangia Aashima, Das Saureesh, Goncerzewicz Jan

Mathematica Applicanda

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2020

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Vol. 48, no. 1

3--23

EN

Nonlinear dynamics of Aluminium Oxide (Al2O3) nanofluid convection under variation of the external magnetic field and temperature variation is studied using a system of partial differential equations arising from equations of conservation of momentum and energy. Applying Galerkin approximation the system of first-order ordinary differential equations is obtained. In the above system, by stability analysis, a critical condition for stability is obtained which is verified through numerical simulations. The influence of variation of magnetic field and temperature is examined through variation of Hartmann number Ha and Rayleigh number Ra As Ra increases, the system enters into a chaotic phase which can be transformed into a stable state of convection by the increase of the external magnetic field. Thus, the external magnetic field is useful in controlling the undesired chaotic state of nanofluid convection. The present study is significant in applications as nanofluids are used in medical treatment, coolants in nuclear reactors and engines, environmental engineering, industrial engineering, and many other applications in the industries.

PL

Artykuł poświęcony jest nieliniowej dynamice tlenku glinu (Al2O3). Konwekcja nanocieczy w warunkach zmienności zewnętrznego pola magnetycznego i zmian temperatury jest badana za pomocą układu równań różniczkowych cząstkowych wynikających z równań zachowania pędu i energia. Stosując przybliżenie Galerkina uzyskuje się układ równań różniczkowych zwyczajnych pierwszego rzędu. W powyższym systemie, za pomocą analizy stateczności, uzyskuje się krytyczny warunek stateczności, który jest weryfikowany za pomocą symulacji numerycznych. Wpływ zmienności pola magnetycznego i temperatury bada się na podstawie zmiany liczby Hartmanna Ha i liczby Rayleigha Ra. Wraz ze wzrostem Ra układ wchodzi w fazę chaotyczną, która może zostać przekształcona w stabilny stan konwekcji poprzez wzrost zewnętrznego pola magnetycznego. Zatem zewnętrzne pole magnetyczne jest przydatne w kontrolowaniu niepożądanego chaotycznego stanu konwekcji nanofluidu. Niniejsze badanie ma istotne znaczenie w zastosowaniach, ponieważ nanociecze są wykorzystywane w leczeniu, chłodziwach w reaktorach jądrowych i silnikach, inżynierii środowiska, inżynierii przemysłowej i wielu innych zastosowaniach przemysłowych.

7

Effect of Rayleigh number on internal eccentricity in a heated horizontal elliptical cylinder to its coaxial square enclosure

Bouras Abdelkrim, Taloub Djedid, Driss Zied

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 3

17--29

EN

This paper deals with numerical investigation of a natural convective flow in a horizontal annular space between a heated square inner cylinder and a cold elliptical outer cylinder with a Newtonian fluid. Uniform temperatures are imposed along walls of the enclosure. The governing equations of the problem were solved numerically by the commercial code Fluent, based on the finite volume method and the Boussinesq approximation. The effects of Geometry Ratio GR and Rayleigh numbers on fluid flow and heat transfer performance are investigated. The Rayleigh number is varied from 103 to 106. Throughout the study the relevant results are presented in terms of isotherms, and streamlines. From the results, we found that the increase in the Geometry Ratio B leads to an increase of the heat transfer coefficient. The heat transfer rate in the annulus is translated in terms of the average Nusselt numbers along the enclosure's sides. Tecplot 7 program was used to plot the curves which cleared these relations and isotherms and streamlines which illustrate the behavior of air through the channel and its variation with other parameters. The results for the streamlines, isotherms, local and average Nusselt numbers average Nusselt numbers are compared with previous works and show good agreement.

8

Vertical heat transport at infinite Prandtl number for micropolar fluid

Caggio M., Kalita P., Łukaszewicz G., Mizerski K. A.

Archives of Mechanics

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2020

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Vol. 72, nr 6

525--553

EN

We investigate the upper bound on the vertical heat transport in the fully 3D Rayleigh–Bénard convection problem at the infinite Prandtl number for a micropolar fluid. We obtain a bound, given by the cube root of the Rayleigh number, with a logarithmic correction. The derived bound is compared with the optimal known one for the Newtonian fluid. It follows that the (optimal) upper bound for the micropolar fluid is less than the corresponding bound for the Newtonian fluid at the same Rayleigh number. Moreover, strong microrotational diffusion effects can entirely suppress the heat transfer. In the Newtonian limit our purely analytical findings fully agree with estimates and scaling laws obtained from previous theories significantly relying on phenomenology.

9

Electro-hydrodynamic convection in a rotating dielectric micropolar fluid layer

Kaur H., Verma G. N.

International Journal of Applied Mechanics and Engineering

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2019

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Vol. 24, no. 4

106--124

EN

Thermal convection of a rotating dielectric micropolar fluid layer under the action of an electric field and temperature gradient has been investigated. The dispersion relation has been derived using normal mode analysis. The effects of the electric Rayleigh number, micropolar viscosity, Taylor number and Prandtl number on stability and over stability criteria are discussed. It is found that rotation postpones the instability in the fluid layer, while the Prandtl number and rotation both have a stabilizing effect. It is also observed that the micropolar fluid additives have a stabilizing effect, whereas the electric field has a destabilizing effect on the onset of convection stability.

10

Transient natural convection in partitioned enclosures

Zemani F., Sabeur-Bendehina A.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 4

1015--1030

EN

In this paper, the natural convection flow in a cavity heated differentially with a partition placed in the middle of the hot wall is numerically simulated. The aspect ratio of the geometry, Prandtl number are fixed at 0.24, 6.64, respectively, for different partitions lengths; however the Rayleigh number values were ranging from 106 to 3:77 x 109 in order to observe the transition regime. The fluid flow and the heat transfer described in terms of continuity, linear momentum and energy equations were predicted by using the finite volume method. To approach the physical reality experience, calculations were performed in a cavity with the same size and same priority of the fluid with an average temperature Tm imposed on the cooled wall, also another simulation with an average temperature Tm imposed on the horizontal wall. Time evolution, isotherms and mean Nusselt number are presented for all investigated values. Representative results illustrating the effects of the partition length for the heat transfer and the thermal boundary layer are also reported and discussed. The results indicate that the flow and heat transfer properties are altered by the presence of the partition, especially in the initial stage. In a certain sense, the partition blocks the flow and forces it to come off the hot wall. Since the partition parameters are critical for the transient natural convection ow in the cavity, different partition lengths on the warm wall have been studied.

11

Thermal convection in a ferromagnetic fluid layer with magnetic field dependent viscosity: a correction applied

Prakash J., Kumar R., Kumari K.

Studia Geotechnica et Mechanica

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2017

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Vol. 39, nr 3

39--46

EN

The effect of magnetic field dependent (MFD) viscosity on thermal convection in a horizontal ferromagnetic fluid layer has been investigated numerically. A correction is applied to Sunil et al. [24] which is very important in order to predict the correct behavior of MFD viscosity. Linear stability analysis has been carried out for stationary convection. The MFD viscosity parameter δ as well as the measure of nonlinearity of magnetization M3, both have a stabilizing effect on the system. Numerical results are also obtained for large values of magnetic parameter M1 and predicted graphically.

12

Analysis of components effecting free convection intensity in steel rectangular sections

Wyczółkowski R.

Archives of Thermodynamics

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2015

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Vol. 36, no. 3

105--121

EN

Free convection is one of the heat transfer modes which occurs within the heat-treated bundles of steel rectangular section. A comprehensive study of this phenomenon is necessary for optimizing the heating process of this type of charge. The free convection intensity is represented by the Rayleigh number Ra. The value of this criterion depends on the following parameters: the mean section temperature, temperature difference within the section, kinematic coefficient of viscosity, volume expansion coefficient and the Prandtl number. The paper presents the analysis of the impact of these factors on free convection in steel rectangular sections. The starting point for this analysis were the results of experimental examinations. It was found that the highest intensity of this process occurs for the temperature of 100°C. This is mainly caused by changes in the temperature difference observed in the area of sections and changes in kinematic coefficient of viscosity of air. The increase in the value of the Rayleigh number criterion at the initial stage is attributable to changes in the parameter of temperature difference within the section. After exceeding 100°C, the main effect on convection is from changes in air viscosity. Thus, with further increase in temperature, the Rayleigh number starts to decline rapidly despite further rise in the difference in temperature.

13

Analysis of the Rayleigh number in the area of steel rectangular sections in the conditions of stedy and unstedy heat flow

Wyczółkowski R.

Civil and Environmental Engineering Reports

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2014

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No. 14

107--118

EN

The paper presents the experimental measurements dedicated to the research for the Rayleigh number (Ra) in the area of rectangular steel sections. This problem is associated with the analysis of the free convection which takes place in the heating of sections bundles during the heat treatment. The study was conducted for both steady and transient heat transfer. The values of the Ra number obtained for the tested sections allow to describe the phenomenon of convection on the basis of a very simple criterial dependence. It greatly simplifies the mathematical description of the heat transfer phenomenon in the concerned charges.

PL

W artykule przedstawiono wyniki badań eksperymentalnych, których celem było określonie liczby Rayleigha (Ra) dla profili prostokątnch, nagrzewanych w warunkach ustalonej i nieustalonej wymiany ciepła. Analizie poddano trzy rodzaje profili: 40x20 mm, 60x60 mm oraz 80x80 mm. Badania dla warunków ustalonych przeprowadzono w komorze grzewczej stanowiska do pomiarów efektywnej przewodności cieplnej wsadów porowatych. Natomiast badania w warunkach nieustalonych przeprowadzono w elektrycznym piecu komorowym. Charakter zmian liczby Ra w funkcji temperatury, dla obu sposobów nagrzewania jest podobny. W każdym z przypadków, maksymalną wartość parametr Ra uzyskuje w przedziale temperatury około 100200oC. Dla profili 80x80 mm parametr ten jest około sześciokrotnie większy w porównaniu z profilami 60x60 mm. W przypadku nieustalonego przepływu ciepła, bezwzględne wartości parametru Ra są o rząd wielkości większe od wartości uzyskanych dla warunków ustalonych. Odnotowane liczby Ra nie przekroczyły wartości 107. Maksymalna wartość tego parametru wyniosła około 1,2x106. Zatem przy nagrzewaniu analizowanych profili, występujacą w ich wnętrzu konwekcję, można traktować jako intensyfikację przewodzenia w wypełniającym je powietrzu. Wyniki przedstawionych badań posłużą do analizy wpływu występującej wewnątrz profili konwekcji, na proces nagrzewania wiązek tych elementów. Ostatecznym wynikiem prowadzonych w tym zakresie analiz, będzie opracowanie modelu do wyznaczania efektywnej przewodności cieplnej tego wsadu.

14

Variable gravity effects on thermal instability of nanofluid in anisotropic porous medium

Chand R., Rana G. C., Kumar S.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 3

631--642

EN

In this paper, we study the effects of variable gravity on thermal instability in a horizontal layer of a nanofluid in an anisotropic porous medium. Darcy model been used for the porous medium. Also, it incorporates the effect of Brownian motion along with thermophoresis. The normal mode technique is used to find the confinement between two free boundaries. The expression of the Rayleigh number has been derived, and the effects of variable gravity and anisotropic parameters on the Rayleigh number have been presented graphically.

15

A Characterization of the Rivlin-Ericksen Viscoelastic Fluid in the Presence of a Magnetic Field and Rotation

Banyal A. S.

Engineering Transactions

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2012

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Vol. 60, iss. 4

355-355

EN

A layer of Rivlin-Ericksen viscoelastic fluid heated from below is considered in the presence of an uniform vertical magnetic field and rotation. Following the linearized stability theory and normal mode analysis, this paper mathematically establishes the condition for characterizing oscillatory motion, which may be neutral or unstable, for rigid boundaries at the top and bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in the configurations, are necessarily non-oscillatory in the regime TAF 2 + TA 4 + Qp2 2 1; where TA is the Taylor number, Q is the Chandrasekhar number, p2 is the magnetic Prandtl number, and F is the viscoelasticity parameter. This result is important, since it holds for all wave numbers for rigid boundaries of infinite horizontal extension at the top and bottom of the fluid, and the exact solutions of the problem investigated in closed form are not obtainable.

16

Experimental tests for the occurence of convective heat transfer within the bed of rectangular steel profiles

Wyczółkowski R., Musiał D.

Archives of Thermodynamics

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2012

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Vol. 33, no. 3

89-100

EN

The paper describes tests intended to examine the occurrence of natural convection within the space occupied by 40x20 mm rectangular steel sections. Within these tests the bed of four layers of section was heated by the electric palate heater. Depending on the manner in which the heater was positioned, the tests were divided into two series. In the case of heating from above, the heat flowing through the bed is transferred only by conduction and radiation. When heating the bed from below, in addition to conduction and radiation, also a convective heat transfer will occur. Should this be the case, it will result in the intensification of the heat exchange. The results of measurements carried out have not demonstrated that the occurrence of any possible natural convection would influence the development of a temperature field in this type of charge.

17

Influence of the method of dry convection in the atmosphere modeling on the dynamic properties of the model

Brojewski R., Jasiński J.

Journal of Technical Physics

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2003

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Vol. 44, no 2

215-233

EN

This paper presents the problem of modeling dry convection in the atmosphere based on scaling of the movement equations resulting from the assumption that convection streams are mainly generated by the Archimedes draught force. This approach leads to description of the atmosphere movement different than in the Boussinesq approximation. The simplest case of Galerkin type equations in 3D phase space was considered. The obtained equations have different dynamics than the equations of the classical Lorenz model of dry convection. Lorenz model dynamics is controlled by the configuration of 2 non-dimensional numbers, while the dynamics of the proposed model is controlled by 3 numbers. It is presented in the language of symbolic dynamics, illustrated with numerous examples - indicating its different character than in the classical Lorenz model, among others: different values of Rayleigh number for which the systems loose structural stability.

18

On thermal convection in micropolar fluids in presence of suspended particles

Mohan H., Kumar P., Anjula

Studia Geotechnica et Mechanica

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2002

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Vol. 24, nr 3-4

53--63

PL

Opisano niestabilność termiczną płynów mikropolamych w obecności cząstek zawieszonych. Sprzężenie między ruchem wirowym a strumieniami ciepła może być przyczyną nadstabilnych stanów w układzie. Zawieszone cząstki wprowadzają także drgania w układzie, a wartość liczby Rayleigha zmniejsza się ze zwiększeniem liczby cząstek zawieszonych.

EN

The thermal instability of micropolar fluids in the presence of suspended particles has been considered. The coupling between spin and heat fluxes may bring overstable modes in the system. The suspended particles also introduce oscillatory modes in the system and the Rayleigh number is found to decrease with the increase in suspended particles.

19

Onset of convection in a sparsely packed porous layer with throughflow

Shivakumara I. S., Nanjundappa C. E.

Archives of Mechanics

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2001

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Vol. 53, nr 3

219-241

EN

The onset of Rayleigh-Bénard convection in a sparsely packed porous layer with vertical throughflow is investigated using Brinkman's modification of the Darcy flow model with fluid viscosity different from effective viscosity. The critical Rayleigh numbers are obtained for free-free, rigid-rigid and rigid-free boundaries which are insulated to temperature perturbations. It is noted that an increase in the value of viscosity ratio is to delay the onset of convection. Further, it is observed that the throughflow can be used either to suppress or augment convection, depending on the nature of boundaries and also on the values of physical parameters.

20

An approximate solution of the Lorenz equations

Icha A.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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1998

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z. 7

447-452

EN

In this paper the renormalization group approach is applied to ordinary differential equations . The method is developed on the basis of the classical theory of envelope and it is used for getting asymptotic behavior of solutions in Lorenz problem. As the result , an aproximate but global solution of the Lorenz model is obtained near origin steady state (0,0,0) for a reduced Rayleigh number r ~ 1 .

PL

W pracy zastosowano metodę grupy renormalizacji w celu analizy układów równań różniczkowych zwyczajnych . Wykorzystując geometryczne sformułowanie tej metody , oparte na pojęciu obwiedni rodziny krzywych, określono asymptotyczne zachowanie się rozwiązań równań Lorenza . W rezultacie , otrzymano przybliżone , globalne rozwiązanie modelu Lorenza w otoczeniu punktu stałego (0,0,0 ) przy liczbie Rayleigha r ~ 1 .