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1
Content available Thermal convection in a ferromagnetic fluid layer with magnetic field dependent viscosity: a correction applied
100%
Prakash J. , Kumar R. , Kumari K.
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tom 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.
2
Content available remote Practical Kedem-Katchalsky equations and their modification
88%
Jarzyńska M.
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nr 4
586-598
EN
The research problem presented in this work concerns modification of the Kedem-Katchalsky (K-K) equation for volume flow (J v) through system (h|M|l), consisting of a membrane M and boundary layers h and l. Such boundary layers appear in the vicinity of the membrane on both sides due to the lack of mixing of solutions. This paper also includes the derivation of the equation for volume flow (J vr) dissipated on concentration boundary layers h and l. The derivation of these equations concerns the case in which the substance transport through the membrane is generated by the osmotic pressure gradient $$\Delta \dot \prod $$ . On the basis of the equations for the volume flows (J v) and (J vr), some calculations for a nephrophane membrane, used in medicine, and for aqueous glucose solutions have been carried out. In order to test the equations for (J v) and (J vr), we have also carried out calculations for the volume flow (J′ v) that is transferred through the membrane in the case of mixed solutions on both sides of the membrane. This volume flux has been calculated on the basis of the original (K-K) equation. The results are presented in Fig. 2.
3
Content available Anisotropic turbulent viscosity and large-scale motive force in thermally driven turbulence at low Prandtl number
88%
Mizerski K. A.
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tom 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.
4
An approximate solution of the Lorenz equations
75%
Icha A.
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tom 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 .
5
Content available Analysis of components effecting free convection intensity in steel rectangular sections
75%
Wyczółkowski R.
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6
Content available Variable gravity effects on thermal instability of nanofluid in anisotropic porous medium
75%
Chand R. , Rana G. C. , Kumar S.
International Journal of Applied Mechanics and Engineering
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2013
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tom 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.
7
Content available Numerical study of heating transfer by natural convection in an inclined elliptical cylinder charged with nanofluid
63%
Amroune A. , Bouras A. , Taloub D. , Driss Z.
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tom 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.
8
Content available Electro-hydrodynamic convection in a rotating dielectric micropolar fluid layer
63%
Kaur H. , Verma G. N.
International Journal of Applied Mechanics and Engineering
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2019
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tom 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.
9
Content available Effect of aspect ratio of enclosure on free convection from horizontal cylinders in Bingham plastic fluids
63%
Baranwal A. K. , Gupta A. K. , Tiwari A. K. , Melnik R.
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tom 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.
10
Content available Analysis of the Rayleigh number in the area of steel rectangular sections in the conditions of stedy and unstedy heat flow
63%
Wyczółkowski R.
Civil and Environmental Engineering Reports
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2014
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tom 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.
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