Marangoni convection in an ewline Oldroyd-B fluid layer with ewline throughflow

2007 ◽  
Vol 85 (9) ◽  
pp. 947-955 ◽  
Author(s):  
S Saravanan
Keyword(s):  
Approximate Solution ◽  
Marangoni Number ◽  
Marangoni Convection ◽  
Fluid Layer ◽  
Linear Analysis ◽  
Wave Number ◽  
Retardation Time ◽  
Viscoelastic Parameters ◽  
Critical Marangoni Number ◽  
The Galerkin Method

The onset of Marangoni convection in a horizontal Oldroyd-B fluid layer in the presence of a vertical throughflow is determined by linear analysis. We find an approximate solution to the corresponding eigenvalue problem using the Galerkin method. The effects of viscoelastic parameters on the critical Marangoni number, wave number, and frequency are discussed. The study also reveals the existence of a critical retardation time for which the oscillatory motion reaches its maximum strength. This study has possible implications in microgravity situations. PACS No.: 47.20.Gv

The influence of Coriolis force on surface-tension-driven convection

1966 ◽  
Vol 26 (4) ◽  
pp. 807-818 ◽  
Author(s):  
A. Vidal ◽  
Andreas Acrivos
Keyword(s):  
Surface Tension ◽  
Flow Pattern ◽  
Coriolis Force ◽  
Fluid Layer ◽  
Functional Relation ◽  
Wave Number ◽  
Neutral Stability ◽  
Uniform Rotation ◽  
Critical Marangoni Number ◽  
Deep Layers

The effect of uniform rotation on surface-tension-driven convection in an evaporating fluid layer is considered both theoretically and experimentally. The theoretical analysis follows the usual small-disturbance approach of perturbation theory and leads, at the neutral state, to a functional relation between the Marangoni and Taylor numbers which is then computed numerically. In addition, it is shown analytically that, in the limit of rapid rotation, the velocity and temperature fluctuations are confined to a thin Ekman layer near the surface, and that Mc = 4·42T½ and ac = 0·5T¼, where Mc and ac are, respectively, the critical Marangoni number and the critical wave number for neutral stability, and T is the Taylor number.The experimental part deals primarily with the flow pattern of a 50% solution of ethyl ether in n-heptane evaporating into still air. In this case, the convective flow is surface-tension-driven and its structure was observed using schlieren optics. In the absence of rotation, the flow shows a remarkable cellular pattern when the layer is shallow, but when the depth of the layer is increased the pattern quickly becomes highly irregular. In contrast, for T > 103, a cellular structure is always observed even for deep layers, a result which is attributable to the stabilizing effect of the Coriolis force. A further increase in T leaves the flow pattern unchanged except that the size of the cells is found to decrease as T−¼ which is in agreement with the results of the linear stability analysis.

scholarly journals Concordancing in ESP Class Rooms

2014 ◽  
Vol 4 (3) ◽  
pp. 434-439
Author(s):  
Sameh Benna ◽  
Olfa Bayoudh
Keyword(s):  
Rayleigh Number ◽  
Heat Transport ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Linear Analysis ◽  
Wave Number ◽  
Gravity Modulation ◽  
Non Linear ◽  
The Stability ◽  
Time Periodic

The effect of time periodic body force (or g-jitter or gravity modulation) on the onset of Rayleigh-Bnard electro-convention in a micropolar fluid layer is investigated by making linear and non-linear stability analysis. The stability of the horizontal fluid layer heated from below is examined by assuming time periodic body acceleration. This normally occurs in satellites and in vehicles connected with micro gravity simulation studies. A linear and non-linear analysis is performed to show that gravity modulation can significantly affect the stability limits of the system. The linear theory is based on normal mode analysis and perturbation method. Small amplitude of modulation is used to compute the critical Rayleigh number and wave number. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation. The non-linear analysis is based on the truncated Fourier series representation. The resulting non-autonomous Lorenz model is solved numerically to quantify the heat transport. It is observed that the gravity modulation leads to delayed convection and reduced heat transport.

scholarly journals Non-Darcian-Bènard Double Diffusive Magneto-Marangoni Convection in a Two Layer System with Constant Heat Source/Sink

2021 ◽  
pp. 4039-4055
Author(s):  
N. Manjunatha ◽  
R. Sumithra
Keyword(s):  
Porous Layer ◽  
Marangoni Number ◽  
Marangoni Convection ◽  
Fluid Layer ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Type I ◽  
Layer System ◽  
Constant Heat ◽  
Double Diffusive

The problem of non-Darcian-Bènard double diffusive magneto-Marangoni convection   is considered in a horizontal infinite two layer system. The system consists of a two-component fluid layer placed above a porous layer, saturated with the same fluid with a constant heat sources/sink in both the layers, in the presence of a vertical magnetic field.   The lower porous layer is bounded by rigid boundary, while the upper boundary of the fluid region is free with the presence of Marangoni effects.  The system of ordinary differential equations obtained after normal mode analysis is solved in a closed form for the eigenvalue and the Thermal Marangoni Number (TMN) for two cases of Thermal Boundary Combinations (TBC); these are type (i) Adiabatic-Adiabatic and type (ii) Adiabatic-Isothermal.  The corresponding two TMNs   are obtained and the impacts of the porous parameter, solute Marangoni number, modified internal Rayleigh numbers, viscosity ratio, and the diffusivity ratios on the non-Darcian-Bènard double diffusive magneto - Marangoni convection are studied in detail.

Combined effects of nonuniform temperature gradients and heat source on double diffusive Benard-Marangoni convection in a porous-fluid system in the presence of vertical magnetic field

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
N. Manjunatha ◽  
R. Sumithra ◽  
R.K. Vanishree
Keyword(s):  
Magnetic Field ◽  
Heat Source ◽  
Marangoni Number ◽  
Marangoni Convection ◽  
Fluid Layer ◽  
Temperature Gradients ◽  
Vertical Magnetic Field ◽  
Nonuniform Temperature ◽  
Fluid System ◽  
Double Diffusive

The physical configuration of the problem is a porous-fluid layer which is horizontally unbounded, in the presence of uniform heat source/sink in the layers enclosed by adiabatic and isothermal boundaries. The problem of double diffusive Bènard-Marangoni convection in the presence of vertical magnetic field is investigated on this porous-fluid system for non-Darcian case and is subjected to uniform and nonuniform temperature gradients. The eigenvalue, thermal Marangoni number is obtained in the closed form for lower rigid and upper free with surface tension velocity boundary conditions. The influence of various parameters on the Marangoni number against thermal ratio is discussed. It is observed that the heat absorption in the fluid layer and the applied magnetic field play an important role in controlling Benard-Marangoni convection. The parameters which direct this convection are determined and the effect of porous parameter is relatively interesting.

The onset of transient convective instability

1975 ◽  
Vol 71 (3) ◽  
pp. 441-454 ◽  
Author(s):  
D. A. Nield
Keyword(s):  
Temperature Gradient ◽  
Marangoni Number ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Step Function ◽  
Temperature Profiles ◽  
Special Cases ◽  
Flux Boundary Conditions ◽  
Basic Temperature ◽  
The Galerkin Method

The stability of a horizontal fluid layer when the thermal (or concentration) gradient is not uniform is examined by means of linear stability analysis. Both buoyancy and surface-tension effects are considered, and the analogous problem for a porous medium is also treated. Attention is focused on the situation where the critical Rayleigh number (or Marangoni number) is less than that for a linear thermal gradient, and the convection is not (in general) maintained. The case of constant-flux boundary conditions is examined because then a simple application of the Galerkin method gives useful results and general basic temperature profiles are readily treated. Numerical results are obtained for special cases, and some general conclusions about the destabilizing effects, with respect to disturbances of infinitely long wavelength, of various basic temperature profiles are presented. If the basic temperature gradient (considered positive, for a fluid which expands on heating, if the temperature decreases upwards) is nowhere negative, then the profile which leads to the smallest critical Rayleigh (or Marangoni) number is one in which the temperature changes stepwise (at the level at which the velocity, if motion were to occur, would be vertical) but is otherwise uniform. If, as well as being non-negative, the temperature gradient is a monotonic function of the depth, then the most unstable temperature profile is one for which the temperature gradient is a step function of the depth.

Surface tension driven oscillatory instability in a rotating fluid layer

1969 ◽  
Vol 39 (1) ◽  
pp. 49-55 ◽  
Author(s):  
G. A. McConaghy ◽  
B. A. Finlayson
Keyword(s):  
Surface Tension ◽  
Convective Instability ◽  
Marangoni Number ◽  
Fluid Layer ◽  
Oscillatory Instability ◽  
Taylor Number ◽  
Rotating Fluid ◽  
Asymptotic Equations ◽  
Critical Marangoni Number ◽  
Prandtl Numbers

Oscillatory convective instability is shown to occur in a rotating fluid layer when convection is caused by surface-tension gradients at a free surface. The asymptotic equations, valid when the Taylor number approaches infinity, are solved analytically, and the critical Marangoni number is evaluated numerically. Fluids with Prandtl numbers above 0·201 will exhibit only stationary instability. Fluids with smaller Prandtl numbers will exhibit oscillatory instability with the critical Marangoni number varying as M0T½ where M0 depends on the Prandtl number and T is the Taylor number.

Marangoni Convection in Radiating Fluids

1987 ◽  
Vol 109 (3) ◽  
pp. 717-721 ◽  
Author(s):  
Y. Bayazitoglu ◽  
T. T. Lam
Keyword(s):  
Marangoni Convection ◽  
Fluid Layer ◽  
Lower Surface ◽  
Linear Stability Theory ◽  
Critical Conditions ◽  
Microgravity Environment ◽  
Wide Range ◽  
Critical Marangoni Number ◽  
Radiating Fluids ◽  
Convective Fluid

The onset of Marangoni convection driven by surface tension gradients in radiating fluid layers is studied. The system considered consists of a fluid layer of infinite horizontal extent which is confined between a free upper surface and a rigid isothermal lower surface. The radiative boundaries of black–black, mirror–mirror, and black–mirror are considered. The critical conditions leading to the onset of convective fluid motions in a microgravity environment are determined numerically by linear stability theory. The perturbation equations are solved as a Bolza problem in the calculus of variations. The results are presented in terms of the critical Marangoni number and optical thickness for a wide range of some radiative parameters, including the Planck number, nongrayness of the fluid, and the emissivity of the boundaries. It is found that radiation suppresses Marangoni convection during material processing in space.

On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity

1964 ◽  
Vol 19 (3) ◽  
pp. 321-340 ◽  
Author(s):  
L. E. Scriven ◽  
C. V. Sternling
Keyword(s):  
Surface Tension ◽  
Marangoni Number ◽  
Wave Number ◽  
Simple Criterion ◽  
Surface Viscosity ◽  
Unstable Surface ◽  
Critical Marangoni Number ◽  
Liquid Pools ◽  
Limiting Case ◽  
Shape Deformations

The onset of steady, cellular convection driven by surface tension gradients on a thin layer of liquid is examined in an extension of Pearson's (1958) stability analysis. By accounting for the possibility of shape deformations of the free surface it is found that there is no critical Marangoni number for the onset of stationary instability and that the limiting case of ‘zero wave-number’ is always unstable. Surface viscosity of a Newtonian interface is found to inhibit stationary instability. A simple criterion is found for distinguishing visually the dominant force, buoyancy or surface tension, in cellular convection in liquid pools.

Onset of Thermosolutal Convection in a Liquid Layer Having Deformable Free Surface – I. Stationary Convection

1992 ◽  
Vol 47 (4) ◽  
pp. 554-560
Author(s):  
B. S. Dandapat ◽  
B. P. Kumar
Keyword(s):  
Free Surface ◽  
Marangoni Number ◽  
Surface Deformation ◽  
Bond Number ◽  
Thermosolutal Convection ◽  
Linear Stability Theory ◽  
Wave Number ◽  
Critical Marangoni Number ◽  
The Stability ◽  
Effect Of Surface

AbstractThe effect of surface deformation on the onset of thermosolutal convection in a horizontal thin layer heated from below and salted from above is examined, using linear stability theory. It is found that two critical Crispation numbers Cr1 and Cr2 exist. For Cr ≦ Cr1 the instability mechanism remains unefTected by the deformation of the free surface, whereas for Cr1 < Cr < Cr2 the critical Marangoni number (Mc) decreases, showing instability due to deformation. If Cr = Cr2, Mc is obtained for two values of the wave number. When Cr > Cr2 , Mc decreases as the wave number tends to zero. Further, the effect of the Marangoni number, Biot number, Bond number etc. on the stability characteristics of the problem is discussed.

Non-Newtonian oscillatory layer flow, approximate solution

1979 ◽  
Vol 44 (10) ◽  
pp. 2908-2914 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Approximate Solution ◽  
Galerkin Method ◽  
Horizontal Plane ◽  
Oscillatory Flow ◽  
Oscillatory Boundary Layer ◽  
Layer Flow ◽  
Pseudoplastic Liquid ◽  
The Galerkin Method

The problem of the oscillatory flow of pseudoplastic liquid in vicinity of the infinitely long horizontal plane is formulated in stresses. For Re i.e. for conditions of oscillatory boundary layer the problem is solved approximately by the Galerkin method.

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