Stability of heterogeneous flows to nonaxisymmetric disturbances

The stability of heterogeneous fluids has been extensively investigated by TAYLOl~ (1931), SYI~OE (1933), MILES (196i), HOW~a~D and GuPTA (1962) and others. These results have also been extended to include the stability Of cylindrical masses of fluid but mostly for axisymmetric disturbances. When the fluid is homogeneous and incompressible and is having a 'solid body' rotation the stability for nonaxisymmetric disturbances has been investigated by HOWARD and GO-eTA (1962), LvI)WlEO (1961) and PEDLEY (1968). In the case of a homogeneous fluid, in addition to the solid body rotation, the presence of even ~ small axial shear makes the system unstable as has been shown by LIIDWlEG (1961) for a narrow gap and by PEDLEu (1968) without this restriction. In this paper we consider the stability for non-axisymmetrical disturbances of a cylindrical mass of heterogeneous fluid, with an exponential variation of density in the radial direction and having both axial and azimuthal velocities. Assuming the dependence of the radial perturbation velocity on r ~o be of the form u = ?l-'~H(r), we discuss two cases m = t/2 and 1. The general stability criteria, for both cases, have been derived. In the second case (m-----1), as an illustration the general stability criterion is applied to the Poiseuille type flow and a bound for instability is obtained. The growth rate of the most rapidly growing disturbances is also determined

A model for manufacture of nano-sized smart materials free from impurities

ReviewThe importance of nano-sized smart materials in structural engineering, biomedical engineering, and in military applications is discussed. It is shown that the solidification of poorly conducting alloys involved in the manufacture of these materials gives rise to surface and convective instabilities. Different types of surface and convective instabilities are briefly discussed. These instabilities produce a mushy zone regarded as dendrites of nano-sized crystals. These dendrites arising from instabilities are regarded as impurities. To manufacture nano-sized smart materials free from impurities, it is essential to control both surface and convective instabilities. We discuss here briefly, different types of convective and surface instabilities in a poorly conducting fluid. We also discuss different mechanisms of control of these instabilities. Different analytical and numerical techniques used to investigate these instabilities under different boundary conditions are discussed. In this review the moment method is explained to find the condition for the onset of convection, and porous lining is used to suppress the growth rate of surface instability. This is useful in the manufacture of nano-sized smart materials free from impurities. Different methods to obtain the required basic equations and the corresponding boundary conditions are briefly discussed.published_or_final_versio

Natural convection through vertical porous stratum

The combined effect of Darcy and viscous resistances on the fully developed natural convection of a fluid between two heated vertical plates is investigated. When Darcy and viscous dissipations, in the energy equation, are negligible the energy and momentum equations become decoupled and we obtain the modified Poiseuille flow distribution through porous media. The deviation of the velocity and temperature distributions from those existing in modified Poiseuille flow are presented for various porous number σ = b k, b is the spacing between the plates and k is the permeability of the porous medium) when dissipations are not neglected. It is shown that the increase in porous number rapidly decreases the influence of both viscous and Darcy dissipations on velocity and temperature profiles. Therefore, by suitable adjustment of dissipation terms, it is possible to control the temperature distribution which will be of some use in plant physiology. © 1977

Temperature distribution in Couette flow past a permeable bed

The temperature distribution in a steady plane Couette flow having one permeable bounding wall is investigated in the presence of buoyancy force N0 when N0>0, it is shown that heat is transported both by convection and diffusion. The effect of convection is to increase the magnitude of the temperature distribution both in the free and Darcy flows. In particular, it is shown that the wall shear has no significant effect on the temperature distribution. The rate of heat transfer between the fluid and the surface is also calculated and it is shown that, it increases with the porous parameter σ. Although the viscous dissipation has very little effect on the temperature distribution yet its effect is significant on heat transfer. © 1977 Indian Academy of Sciences

Rayleigh Taylor instability in a thin film bounded by a porous layer

The Rayleigh Taylor stability in a finite thickness layer of a viscous fluid bounded below by a densely packed thick porous thick porous layer and above by a rigid surface has been studied subject to linear anal. using approxns. in effect similar to lubrication and Stokes approxns. The problem is studied anal. It is shown that the nature of the linear stability curve is controlled by the slip parameter α and the thickness of the fluid layer h, while its shape is controlled by the ratio of the surface tension to the normal stress

Natural convection past inclined porous layers

Combined Rayleigh-​Benard convection and Tollmien-​Schlichting type of instability of a fluid in an inclined layer bounded by 2 permeable bed was studied. Several types of flow, depending on the value of the Prandtl no., Pr, were studied using a fast-​convergent-​power series technique. Two different convective movements, longitudinal and transverse rolls, based on different Pr, are reported. The effect of slip at the nominal surface is to augment the instability and change the crit. Grashof no., Gr, and crit. Rayleigh no., Ra, markedly for small permeability parameter σ, being independent of Gr and Ra for large σ. The effect of inclination φ is to inhibit the onset of instability in the case of air and to augment it in the case of Hg. At max. inclination (i.e., φ = π​/2)​, the instability sets in as transverse rolls, irresp. of the value of Pr. In the case of Hg, the transverse rolls exist for all φ, whereas in the case of air, they are limited only to certain φ. The cell pattern changes dramatically in the range φ = π​/6 to π​/4

A Weak Nonlinear Stability Analysis of Double Diffusive Convection with Cross-diffusion in a Fluid-saturated Porous Medium

he effect of “Cross Diffusion” on the linear and nonlinear stability of double diffusive convection in a fluid-saturated porous medium has been studied analytically. In the case of linear theory, the normal mode technique has been used and the condition for the maintenance of “finger” and “diffusive” instabilities have been obtained. It has been found that fingers can form by taking cross diffusion terms of appropriate sign and magnitude even though both components make stabilizing contributions to the net vertical density gradient. It has also been shown that “finger” and “diffusive” instabilities can never occur simultaneously. The nonlinear theory is based on the truncated representation of Fourier series and it has been found that the finite amplitude convection may occur when both initial property gradients are stabilizing. Further, the region of finite amplitude instability always encloses the region of infinitesimal oscillatory instability. The effects of permeability and cross-diffusion terms on the heat and mass transports have also been clearly brought out

Non-linear Oberbeck-electroconvection in a poorly conducting fluid through a vertical channel in the presence of an electric field

Non-linear Oberbeck-electroconvection (OBEC) in a poorly electrically conducting fluid through a vertical channel, when the walls are held at different temperatures with temperature difference perpendicular to gravity, is studied using the modified Navier stokes equation in the presence of both induced and an applied electric field. Both analytical and numerical solutions for the non-linear coupled equations governing the motion are obtained and found that analytical solutions agree well with numerical solutions for values of the buoyancy parameter N < 1. It is shown that OBEC can be controlled by maintaining the temperature difference either in the same direction or opposing the potential difference with a suitable value of electric number W. The effect of W on velocity, temperature, rate of heat transfer, skin friction and mass flow rate are computed and the results are depicted graphically. We found that analytical results agree well with numerical results for small values of N. We also found that an increase in W accelerates the flow and hence increases linearly the skin friction and mass flow rate. © 2007 Elsevier Ltd. All rights reserved

Effect of buoyancy on the free surface flow past a permeable bed [Auftrieb und Wärmeübertragung an laminar parallel angeströmten Oberflächen poröser Körper]

Die laminare Strömung entlang poröser Grenzflächen wird in Anwesenheit von Auftriebskräften theoretisch untersucht. Die Übereinstimmung zwischen Theorie und Experimenten von Rajasekhara [1] ist dann gut, wenn Strömungsgleitung an der porösen Oberfläche vorausgesetzt wird. Die Auftriebskräfte erhöhen die Geschwindigkeitsverteilung bei Wärmezufuhr (No>0) und verringern sie bei Kühlung (No0). Umgekehrte Verhältnisse liegen für No<0 vor. Insbesondere stellt sich heraus, daß der Wärmeübergang mit steigender Erwärmung der Strömung zunimmt