The onset of Darcy-Brinkman thermosolutal convection in a horizontal porous media

On the basis of Brinkman model, the onset of double-diffusive (thermosolutal) convection with a reaction term in a horizontal sparsely packed porous media is studied using the normal mode analysis. The effects of Brinkman term, the reaction term, the normalized porosity ε and Lewis number Le on the Rayleigh number for stationary and oscillatory case are presented graphically. The Darcy number destabilize the system in case of both stationary and oscillatory mode. The effects of Lewis number and reaction term depend on the value of the values of solutal Rayleigh number. Furthermore, some results of Darcy model can be recovered in limit cases.     

Stability analysis of double-diffusive convection of Maxwell fluid in a porous medium heated from below

Linear stability analysis of Maxwell fluid in the Bénard problem for a double-diffusive mixture in a porous medium is studied based on the Darcy-Maxwell model. The critical Rayleigh number and the corresponding wave number for the exchange of stability are obtained. On the other hand, the effect of the relaxation time of Maxwell fluid on the critical Rayleigh number is discussed. In limiting cases, some results published previously are recovered from our results.     

Vortex fields and the Lamb-Stokes dissipation relation of fluid dynamics

Energy dissipation in Newtonian fluids containing a unified vortex field is shown to depend on , where η, ? and ζ=u×? are viscosity, vorticity and swirl. This term augments viscous dissipation where stream tube geometry is curved, e.g., in turbulent or helical flows.     

MHD flow and mass transfer of a upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species

This article looks at the mass transfer of the steady two-dimensional magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid past a porous shrinking sheet in the presence of chemical reaction. The resulting nonlinear partial differential equations are reduced to the system of nonlinear ordinary differential equations by means of similarity transformations. Expressions of velocity and the concentration fields are obtained using the homotopy analysis method (HAM). The convergence of the obtained series solutions is explicitly discussed. The influences of sundry parameters on the velocity and the concentration fields are made and discussed in detail. The values of the skin friction coefficient and the surface mass transfer for various interesting parameters are also tabulated.     

Three-layer magnetoconvection

It is believed that some stars have two or more convection zones in close proximity near to the stellar photosphere. These zones are separated by convectively stable regions that are relatively narrow. Due to the close proximity of these regions it is important to construct mathematical models to understand the transport and mixing of passive and dynamic quantities. One key quantity of interest is a magnetic field, a dynamic vector quantity, that can drastically alter the convectively driven flows, and have an important role in coupling the different layers. In this Letter we present the first investigation into the effect of an imposed magnetic field in such a geometry. We focus our attention on the effect of field strength and show that, while there are some similarities with results for magnetic field evolution in a single layer, new and interesting phenomena are also present in a three layer system.     

A fractal model for heat transfer of nanofluids by convection in a pool

Based on the fractal distribution of nanoparticles, a fractal model for heat transfer of nanofluids is presented in the Letter. Considering heat convection between nanoparticles and liquids due to the Brownian motion of nanoparticles in fluids, the formula of calculating heat flux of nanofluids by convection is given. The proposed model is expressed as a function of the average size of nanoparticle, concentration of nanoparticle, fractal dimension of nanoparticle, temperature and properties of fluids. It is shown that the fractal model is effectual according to a good agreement between the model predictions and experimental data.     

Route to chaos in the rising dynamics of a bubble chain in a polymeric fluid

We investigate the chaotic dynamics of a bubble chain rising in a polymeric fluid by the experimental temporary measurements, cognitive modelling and analytical analysis. The competition between the stress creation and the relaxation displays complex dynamical features and leads to chaos through a sequence of period doubling bifurcations.     

MHD Boundary Layer Flow of a Non-Newtonian Fluid on a Moving Surface with a Power-Law Velocity

A theoretical analysis for MHD boundary layer flow on a moving surface with the power-law velocity is presented. An accurate expression of the skin friction coefficient is derived. The analytical approximate solution is obtained by means of Adomian decomposition methods. The reliability and efficiency of the approximate solutions are verified by numerical ones in the literature.     

The influence of heat transfer in an MHD second grade fluid film over an unsteady stretching sheet

The flow and heat transfer problem of a second grade fluid film over an unsteady stretching sheet is considered. The fluid is incompressible and electrically conducting in the presence of a uniform applied magnetic field. The series solutions of the governing boundary value problems are obtained by employing homotopy analysis method (HAM). The convergence of the developed solutions is discussed explicitly. The dependence of velocity and temperature profiles on various parameters is shown and discussed through graphs. The values of skin-friction coefficient, Nusselt number and free surface temperature are given in tabular form for various emerging parameters.     

On MHD transient flow of a Maxwell fluid in a porous medium and rotating frame

Analytic solution for unsteady magnetohydrodynamic (MHD) flow is constructed in a rotating non-Newtonian fluid through a porous medium. Constitutive equations for a Maxwell fluid have been taken into consideration. The hydromagnetic flow in the uniformly rotating fluid is generated by a suddenly moved infinite plate in its own plane. Analytic solution of the governing flow problem is obtained by means of the Fourier sine transform. It is shown that the obtained solution satisfies both the associate partial differential equation and the initial and boundary conditions. The solution for a Navier-Stokes fluid is recovered if λ→0. The steady state solution is also obtained for t→∞.     

Heat and mass transfer analysis on the flow of a second grade fluid in the presence of chemical reaction

The laminar flow problem of convective heat transfer for a second grade fluid over a semi-infinite plate in the presence of species concentration and chemical reaction is investigated. The governing equations are transformed into a dimensionless system of three non-linear coupled partial differential equations. These equations have been solved analytically subject to the relevant boundary conditions by employing a homotopy analysis method (HAM). It is noted that for the arising system, the HAM performs extremely well in terms of efficiency and simplicity. The influence of dimensionless pertinent parameters on the velocity, temperature and concentration fields has been examined carefully.     

Spatial variations of the mean and statistical quantities in the thermal boundary layers of turbulent convection

We have studied the dynamics of the contact line of a viscous liquid on a solid substrate with macroscopic random defects. We have first characterized the friction force f₀ at microscopic scale for a substrate without defects; f₀ is found to be a strongly nonlinear function of the velocity U of the contact line. In presence of macroscopic defects, we find that the applied force F(U) is simply shifted with respect to f₀(U) by a constant: we do not observe any critical behavior at the depinning transition. The only observable effect of the substrate disorder is to increase the hysteresis. We have also performed realistic numerical simulation of the motion of the contact line. Using the same values of the parameters as in the experiment, we find that the experimental data is qualitatively well reproduced. In light of experimental and numerical results, we discuss the possibility of measuring a true critical behavior.Received: 6 October 2003, Published online: 19 February 2004PACS: 46.65. + g Random phenomena and media - 64.60.Ht Dynamic critical phenomena - 68.08.Bc Wetting     

Thermal instability of a rotating saturated porous medium heated from below and submitted to rotation

In this work, we study the problem of onset of thermal convection in a rotating saturated porous medium heated from below. The effect of rotation is restricted to the Coriolis force, neglecting thus the centrifugal effects, the porous medium is described by Brinkman's model. The linear eigenvalue problem is solved by means of a modified Galerkin method. The behavior of the critical temperature gradient is discussed in terms of various parameters of the system for both stationary and overstable convections. Finally a weakly nonlinear analysis is provided to derive amplitude equations and to study the onset of Küppers-Lortz instability. Received 24 June 2002 / Received in final form 11 September 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: tdesaive@ulg.ac.be     

Wire coating by withdrawal from a bath of fourth order fluid

This Letter looks an analysis for withdrawal of cylinder. The flow depends upon the wire velocity. The fluid considered is a fourth order fluid. The problem is modeled using cylindrical coordinates for velocity and pressure distributions. The solution of the governing equation is obtained using homotopy analysis method (HAM). The variations of the velocity, volume flow rate, radius of coated wire, shear stress and force on the total wire are presented graphically and discussed for emerging non-Newtonian parameter.     

Temperature-Dependent Viscosity Effects on Non-Darcy Hydrodynamic Free Convection Heat Transfer from a Vertical Wedge in Porous Media

An analysis is presented to investigate the effect of temperature-dependent viscosity on free convection flow along a vertical wedge adjacent to a porous medium in the presence of heat generation or absorption. The governing fundamental equations are transformed into the system of ordinary differential equations using scaling group of transformations and are solved numerically by using the fifth-order Rung-Kutta method with shooting technique for various values of the physical parameters. The effects of variable viscosity parameter on the velocity, temperature and concentration are discussed. Numerical results for the problem considered are given and illustrated graphically.     

Cross-diffusive effects on the onset of double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

Double-diffusive stationary and oscillatory instabilities at the marginal state in a saturated porous horizontal fluid layer heated and salted from above are investigated theoretically under the Darcy's framework for a porous medium. The contributions of Soret and Dufour coefficients are taken into account in the analysis. Linear stability analysis shows that the critical value of the Darcy-Rayleigh number depends on cross-diffusive parameters at marginally stationary convection, while the marginal state characterized by oscillatory convection does not depend on the cross-diffusion terms even if the condition and frequency of oscillatory convection depends on the cross-diffusive parameters. The critical value of the Darcy-Rayleigh number increases with increasing value of the solutal Darcy-Rayleigh number in the absence of cross-diffusive parameters. The critical Darcy-Rayleigh number decreases with increasing Soret number, resulting in destabilization of the system, while its value increases with increasing Dufour number, resulting in stabilization of the system at the marginal state characterized by stationary convection. The analysis reveals that the Dufour and Soret parameters as well as the porosity parameter play an important role in deciding the type of instability at the onset. This analysis also indicates that the stationary convection is followed by the oscillatory convection for certain fluid mixtures. It is interesting to note that the roles of cross-diffusive parameters on the double-diffusive system heated and salted from above are reciprocal to the double-diffusive system heated and salted from below.     

Axisymmetry Breaking to Travelling Waves in the Cylinder with Partially Heated Sidewall

The transition from an axisymmetric stationary flow to three-dimensional time-dependent flows is carefully studied in a vertical cylinder partially heated from the side, with the aspect ratio A = 2 and Prandtl number Pτ=0.021. The flow develops from the steady toroidal pattern beyond the first instability threshold, breaks the axisymmetric state at a Rayleigh number near 2000, and transits to standing or travelling azimuthal waves. A new result is observed that a slightly unstable flow pattern of standing waves exists and will transit to stable travelling waves after a long time evolution. The onset of oscillations is associated with a supercritical Hopf bifurcation in a system with O（2） symmetry.     

Influence of thermal treatment of low dielectric constant SiOC(H) films using MTES/O2 deposited by PECVD

Low dielectric constant SiOC(H) films are deposited on p-type Si(100) substrates by plasma enhanced chemical vapor deposition (PECVD) using methyltriethoxysilane (MTES, C₇H₁₈O₃Si) and oxygen gas as precursors. The SiOC(H) films are deposited at room temperature, 100, 200, 300 and 400 °C and then annealed at 100, 200, 300 and 400 °C temperatures for 30 min in vacuum. The influence of deposition temperature and annealing on SiOC(H) films are investigated. Film thickness and refractive index are measured by field emission scanning electron microscopy and ellipsometry, respectively. Chemical bonding characteristics of as-deposited and annealed films are investigated by Fourier transform infrared (FTIR) spectroscopy in the absorbance mode. As more carbon atoms are incorporated into the SiOC(H) films, both film density and refractive index are decreased due to nano pore structure of the film. In the SiOC(H) film, CH₃ group as an end group is introduced into OSiO network, thereby reducing the density to decrease the dielectric constant thereof. The dielectric constant of SiOC(H) film is evaluated by C-V measurements using metal-insulator-semiconductor (MIS), Al/SiOC(H)/p-Si structure and it is found to be as low as 2.2 for annealed samples deposited at 400 °C.     

Onset of Unsteady Horizontal Convection in Rectangular Tank at Pr=1

The horizontal convection within a rectangular tank is numerically simulated. The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf bifurcation of Ra from steady solutions to periodic solutions, and the critical Rayleigh number Rac is obtained to be Rac = 5.5377×10^8 for the middle plume forcing at Pr = 1, which is much larger than the value previously obtained. In addition, the unstable perturbations are always generated from the central jet, which implies that the onset of instability is due to velocity shear （shear instability） other than thermally dynamics （thermal instability）. Finally, Paparella and Young＇s first hypotheses [J. Fluid Mech. 466 （2002） 205] about the destabilization of the flow is numerically proven, i.e. the middle plume forcing can lead to a destabilization of the flow.