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1
Content available Anisotropic turbulent viscosity and large-scale motive force in thermally driven turbulence at low Prandtl number
Mizerski K. A.
Archives of Mechanics
|
2022
|
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.
2
Content available Boundary effects on electrothermal convection in a dielectric fluid layer
Ravisha M., Raghunatha K. R., Mamatha A. L., Shivakumara I. S.
Archives of Thermodynamics
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2019
|
Vol. 40, no 1
3--19
EN
The instability characteristics of a dielectric fluid layer heated from below under the influence of a uniform vertical alternating current (AC) electric field is analyzed for different types of electric potential (constant electric potential/ electric current), velocity (rigid/free) and temperature boundary conditions (constant temperature/heat flux or a mixed condition at the upper boundary). The resulting eigenvalue problem is solved numerically using the shooting method for various boundary conditions and the solution is also found in a simple closed form when the perturbation heat flux is zero at the boundaries. The possibility of a more precise control of electrothermal convection (ETC) through various boundary conditions is emphasized. The effect of increasing AC electric Rayleigh number is to hasten while that of Biot number is to delay the onset of ETC. The system is more stable for rigid-rigid boundaries when compared to rigid-free and least stable for free-free boundaries. The change of electric potential boundary condition at the upper boundary from constant electric potential to constant electric current is found to instill more stability on the system.
3
Content available Compressible analysis of Bénard convection of magneto rotatory couple-stress fluid
Mehta C. B., Singh M.
International Journal of Applied Mechanics and Engineering
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2018
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Vol. 23, no. 1
91--105
EN
Thermal Instability (Benard’s Convection) in the presence of uniform rotation and uniform magnetic field (separately) is studied. Using the linearized stability theory and normal mode analyses the dispersion relation is obtained in each case. In the case of rotatory Benard’s stationary convection compressibility and rotation postpone the onset of convection whereas the couple-stress have duel character onset of convection depending on rotation parameter. While in the absence of rotation couple-stress always postpones the onset of convection. On the other hand, magnetic field on thermal instability problem on couple-stress fluid for stationary convection couple-stress parameter and magnetic field postpones the onset of convection. The effect of compressibility also postpones the onset of convection in both cases as rotation and magnetic field. Graphs have been plotted by giving numerical values to the parameters to depict the stationary characteristics. Further, the magnetic field and rotation are found to introduce oscillatory modes which were non-existent in their absence and then the principle of exchange of stability is valid. The sufficient conditions for non-existence of overstability are also obtained.
4
Content available On thermal instability of Kuvshiniski fluid with suspended particles saturated in a porous medium in the presence of a magnetic field
Singh M.
International Journal of Applied Mechanics and Engineering
|
2017
|
Vol. 22, no. 4
981--994
EN
The thermal instability of a Kuvshiniski viscoelastic fluid is considered to include the effects of a uniform horizontal magnetic field, suspended particles saturated in a porous medium. The analysis is carried out within the framework of the linear stability theory and normal mode technique. For the case of stationary convection, the Kuvshiniski viscoelastic fluid behaves like a Newtonian fluid and the magnetic field has a stabilizing effect, whereas medium permeability and suspended particles are found to have a destabilizing effect on the system, oscillatory modes are introduced in the system, in the absence of these the principle of exchange of stabilities is valid. Graphs in each case have been plotted by giving numerical values to the parameters, depicting the stability characteristics. Sufficient conditions for the avoidance of overstability are also obtained.
5
Content available Magneto-rotatory compressible couple-stress fluid heated from below in porous medium
Mehta C. B.
Studia Geotechnica et Mechanica
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2016
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Vol. 38, nr 1
55--63
EN
The study is aimed at analysing thermal convection in a compressible couple stress fluid in a porous medium in the presence of rotation and magnetic field. After linearizing the relevant equations, the perturbation equations are analysed in terms of normal modes. A dispersion relation governing the effects of rotation, magnetic field, couple stress parameter and medium permeability have been examined. For a stationary convection, the rotation postpones the onset of convection in a couple stress fluid heated from below in a porous medium in the presence of a magnetic field. Whereas, the magnetic field and couple stress postpones and hastens the onset of convection in the presence of rotation and the medium permeability hastens and postpones the onset of convection with conditions on Taylor number. Further the oscillatory modes are introduced due to the presence of rotation and the magnetic field which were non-existent in their absence, and hence the principle of exchange stands valid. The sufficient conditions for nonexistence of over stability are also obtained.
6
Content available A dynamically adaptive lattice Boltzmann method for thermal convection problems
Feldhusen K., Deiterding R., Wagner C.
International Journal of Applied Mathematics and Computer Science
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2016
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Vol. 26, no. 4
735--747
EN
Utilizing the Boussinesq approximation, a double-population incompressible thermal lattice Boltzmann method (LBM) for forced and natural convection in two and three space dimensions is developed and validated. A block-structured dynamic adaptive mesh refinement (AMR) procedure tailored for the LBM is applied to enable computationally efficient simulations of moderate to high Rayleigh number flows which are characterized by a large scale disparity in boundary layers and free stream flow. As test cases, the analytically accessible problem of a two-dimensional (2D) forced convection flow through two porous plates and the non-Cartesian configuration of a heated rotating cylinder are considered. The objective of the latter is to advance the boundary conditions for an accurate treatment of curved boundaries and to demonstrate the effect on the solution. The effectiveness of the overall approach is demonstrated for the natural convection benchmark of a 2D cavity with differentially heated walls at Rayleigh numbers from 103 up to 108. To demonstrate the benefit of the employed AMR procedure for three-dimensional (3D) problems, results from the natural convection in a cubic cavity at Rayleigh numbers from 103 up to 105 are compared with benchmark results.
7
Content available The onset of thermal convection in couple-stress fluid in hydromagnetics saturating a porous medium
Rana G. C.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2014
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Vol. 62, nr 2
357--362
EN
In this paper, the effect of magnetic field on thermal convection in couple-stress fluid saturating a porous medium is considered. By applying linear stability theory and the normal mode analysis method, a mathematical theorem is derived which states that the viscoelastic thermal convection at marginal state, cannot manifest as stationary convection if the thermal Rayleigh number R, the medium permeability parameter Pι the couple-stress parameter F and the Chandrasekher number Q, satisfy the inequality R ≤4π2/Pl (1 + 2π2F + PlQ/2ε) the result clearly establishes the stabilizing character of couple-stress parameter and magnetic field whereas destabilizing character of medium permeability.
8
Content available Global stability for thermal convection in a couple-stress fluid with temperature and pressure dependent viscosity
Choudhary S. S., Bharti P. K.
Studia Geotechnica et Mechanica
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2013
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Vol. 35, nr 3
85--102
EN
We show that the global nonlinear stability threshold for convection in a couple-stress fluid with temperature and pressure dependent viscosity is exactly the same as the linear instability boundary. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It has also been found that the couplestress fluid is more stable than the ordinary viscous fluid and then the effect of couple-stress parameter (F) and variable dependent viscosity (Γ) on the onset of convection is also analyzed.
9
Content available Triple- diffusive convection in a micropolar ferrofluid in the presence of rotation
Chand S.
International Journal of Applied Mechanics and Engineering
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2013
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Vol. 18, no. 2
307--327
EN
This paper deals with the theoretical investigation of the triple-diffusive convection in a micropolar ferrofluid layer heated and soluted below subjected to a transverse uniform magnetic field in the presence of uniform vertical rotation. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been employed to study the onset convection. The influence of various parameters like rotation, solute gradients, and micropolar parameters (i.e., the coupling parameter, spin diffusion parameter and micropolar heat conduction parameter) on the onset of stationary convection has been analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically for sufficiently large value of the buoyancy magnetization parameter M1 (ratio of the magnetic to gravitational forces). The principle of exchange of stabilities is found to hold true for the micropolar fluid heated from below in the absence of micropolar viscous effect, microinertia, solute gradient and rotation. The oscillatory modes are introduced due to the presence of the micropolar viscous effect, microinertia , solute gradient and rotation, which were non-existent in their absence. In this paper, an attempt is also made to obtain the sufficient conditions for the non-existence of overstability.
10
Content available remote 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.
11
Content available remote Thermal convection in a compressible Walters' (model b') elastico-viscous dusty fluid with hall currents
Vikrant, Kumar V., Jaimala
International Journal of Applied Mechanics and Engineering
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2011
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Vol. 16, no 4
1189-1203
EN
A compressible Walters' (Model B') elastico-viscous dusty fluid layer heated from below in the presence of a vertical magnetic field to include the effect of Hall currents is considered. For the case of stationary convection, Walters' (Model B') elastico-viscous fluid behaves like an ordinary Newtonian fluid. The Hall currents and dust particles are found to have a destabilizing effect on the thermal convection, whereas compressibility and the magnetic field are found to have a stabilizing effect on the thermal convection. The viscoelasticity and magnetic field (and hence the Hall currents) introduce oscillatory modes in the system, which were non-existent in their absence. Graphs are also plotted for the critical Rayleigh number and various parameters by giving some numerical values to the parameters
12
Content available remote Thermal convection in a Walters' (model B') elastico-viscous dusty fluid in hydromagnetics with the effect of compressibility and rotation
Kumar V., Aggarwal A. K., Kumar S.
International Journal of Applied Mechanics and Engineering
|
2010
|
Vol. 15, no 1
51-62
EN
A compressible, electrically conducting Walters'B' elastico-viscous fluid heated from below in the presence of a magnetic field and rotation is considered. At stationary convection, Walters' (Model B') elastico-viscous fluid behaves like a Newtonian fluid and compressibility, rotation are found to have a stabilizing effect whereas the suspended particles have a destabilizing effect on the thermal convection and magnetic field has a stabilizing effect under certain conditions. The presence of magnetic field and rotation introduces oscillatory modes in the system which were non-existent in their absence. Graphs have also been plotted by giving some numerical values to the parameters.
13
Content available remote Zjawiska cieplne w liniowych silnikach synchronicznych o magnesach trwałych
Mikołajewicz J.
Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych Politechniki Wrocławskiej. Studia i Materiały
|
2008
|
Vol. 62, nr 28
301-306
PL
W artykule przedstawiono krótki i zwięzły model matematyczny zjawisk termicznych występujących w szeregu przetworników elektromagnetycznych i elektromechanicznych. Na podstawie tego modelu opracowano algorytm numerycznego wyznaczenia i wizualizacji rozkładu temperatury w tego typu przetwornikach. Opracowany algorytm zastosowano do analizy procesu nagrzewania w liniowym silniku synchronicznym o magnesach trwałych. Rozkład pola temperaturowego wyznaczono przy wykorzystaniu metody elementów skończonych (MES) [1]. Wyniki obliczeń symulacyjnych porównano z wynikami uzyskanymi w programie komercyjnym Comsol Multiphysics 3.3. Zbieżność otrzymanych wyników jest bardzo dobra, co jest świadectwem poprawności zarówno modelu matematycznego, jak i jego implementacji. Opracowane oprogramowanie, dzięki możliwości zmian parametrów geometryczno-materiałowych, pozwala na analizę procesu nagrzewania wielu odmian i wariantów konstrukcyjnych silników liniowych.
EN
Presentation of the mathematical model and software for determination and visualization of temperature distribution in permanent magnet linear synchronous motor was the aim of the paper. The results which were obtained with the use of this software may be compared with results obtained in commercial software Comsol Multiphysics 3.3, which also uses FEM to calculate heat transfer. The comparison proves that the author's software work correctly and can be used to make simulations. There is a possibility of comparing the results of calculation for many different machine structures thanks to the introduction of different dimensions of linear motor and parameters for materials used in this machine.
14
Simulation of thermal convection depending on the angle between gravity force and temperature gradient
Jopek H.
Systems : journal of transdisciplinary systems science
|
2006
|
Vol. 11, nr 1
29-34
EN
In this papers the influence of the angle between the gravity force and the temperature gradient on the convection process is studied and simulated. Free convection is the kind of heat transfer in which the fluid's motion is caused by the volume forces, usually by the gravity force but also due to centrifugal forces or magnetic field's forces. The differences of temperature around the body are connected to differences of density and consequently buoyant force appears. For that reason, in the equations of motion the volume force is substituted by the expression representing the difference in specific weight and bouyancy which is proportional to the difference of density. It is a very common phenomenon that the convection appears in the film of fluid between the surfaces of two different temperatures
15
Content available remote Effect of compressibility and suspended particles on thermal convection in a Walters' B' elastico-viscous fluid in hydromagnetics
Sharma R. C., Aggarwal A. K.
International Journal of Applied Mechanics and Engineering
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2006
|
Vol. 11, no 2
391-399
EN
A layer of a compressible, electrically conducting Walters' B' elastico-viscous fluid permeated with suspended particles heated from below in the presence of a magnetic field is considered. For the case of stationary convection, the Walters'(model B') elastico-viscous fluid behaves like a Newtonian fluid and the compressibility, magnetic field are found to have stabilizing effects, whereas the suspended particles have a destabilizing effect on the thermal convection. The presence of each - viscoelasticity, magnetic field and suspended particles introduces oscillatory modes in the system which were non-existent in their absence.
16
Thermal convection in polymer solutions numerical experiment
Stręk T.
Zeszyty Naukowe Politechniki Poznańskiej. Budowa Maszyn i Zarządzanie Produkcją
|
2004
|
Nr 1
113-130
EN
In thermodynamics of fluids by convective motion it is understood that a fluid flow which, apart from mechanical quantities, is characterized also by thermal and/or other fields. Dimensionless governing equations are presented for this problem. Dimensionless numbers: the Prandtl number, the Rayleigh number and the Eckert number are introduced. In this paper numerical algorithm for solution of thermal convection in polymer is presented. Rheology model used for polymer is the Carreau model of non-Newtonian fluid. Numerical solutions for convective cooling of Carreau fluid in box are presented.
PL
W termodynamice płynów ruch konwekcyjny płynu jest charakteryzowany nie tylko przez wielkości mechaniczne, ale także przez pole cieplne i inne pola. W artykule przedstawiono bezwymiarowe równania opisujące zagadnienie konwekcji termicznej. W równanich tych wykorzystano liczby bezwymiarowe: Prandtla, Rayleigh i Eckerta. Zamieszczono również algorytm numerycznego rozwiązania problemu konwekcji termicznej w polimerach z wykorzystaniem metody elementów skończonych. Model reologiczny użyty do opisu polimerów to model nienewtonowskiego pfynu Carreau. Przytoczono wyniki numerycze konwekcyjnego ochładzania płynu Carreau w kwadratowym obszarze o „nieskończonej" długości.
17
Content available remote On thermal convection in micropolar fluids in presence of suspended particles
Mohan H., Kumar P., Anjula
Studia Geotechnica et Mechanica
|
2002
|
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.
18
Content available remote On electrically conducting couple-stress fluid heated from below in porous medium in presence of uniform horizontal magnetic field
Sharma R. C., Sharma S.
International Journal of Applied Mechanics and Engineering
|
2001
|
Vol. 6, no 2
251-263
EN
A layer of electrically conducting couple-stress fluid heated from below in porous medium is considered in the presence of uniform horizontal magnetic field. The medium permeability hastens the onset of convection whereas the magnetic field and couple-stress postpone the onset of convection, for the case of stationary convection. The oscillatory modes are introduced by the magnetic field which were not present in the absence of the magnetic field. The overstable case has been considered and a sufficient condition for the non-existence of overstability is obtained.
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