Instabilities in a liquid film flow over an inclined heated porous substrate

Sadiq, I. Mohammed Rizwan; Usha, R.; Joo, Sang Woo

doi:10.1016/j.ces.2010.04.005

Cited by 62 publications

(44 citation statements)

References 38 publications

(62 reference statements)

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“…The slip boundary condition is valid in problems dealing with interaction of fluids with solids at small length scales, such as flows in microfluidics, porous media, and biological systems (arterial flows). Many investigations [27][28][29][30][31][32] have used Navier's concept of slip which states that the relative velocity of the fluid with respect to the wall (slip velocity) is proportional to the shear rate at the wall.…”

Section: Introductionmentioning

confidence: 99%

Effects of velocity slip on the inertialess instability of a contaminated two-layer film flow

Anjalaiah

Usha

2015

Acta Mech

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This manuscript provides a theoretical stability analysis for the configuration of two-layer immiscible flow down an inclined plane with velocity slip along the incline in the limit of zero Reynolds number. Surfactants may be present at the air-liquid interface, liquid-liquid interface, or both. In addition to an Orr-Sommerfeld analysis (again at zero Reynolds number), a long wavelength stability analysis is performed and the results are shown to be consistent. The interface mode, namely the mode of instability that arises because of viscosity stratification, is examined. Stability results (growth rates as a function of slip parameter and neutral stability boundaries) for various configurations of viscosity, surfactant placement, and layer thickness are compared with those of the previous literature and found to agree. It is found that velocity slip along the inclined plane reduces the maximum growth rate of instabilities in configurations where they occur, and the range of unstable wave numbers shrinks as well, indicating that slip has a promise for stabilization. This suggests that there is a possibility of using this favourably as a control option for two-layer flows in the absence or presence of surfactants, in relevant applications by designing the substrate to be a porous substrate with small permeability or a slippery substrate or a rough substrate or a hydrophobic substrate which can be modelled as substrates with velocity slip.

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Section: Introductionmentioning

confidence: 99%

Effects of velocity slip on the inertialess instability of a contaminated two-layer film flow

Anjalaiah

Usha

2015

Acta Mech

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“…To complete the formulation of the problem, we must supplement of the momentum and magnetic field equations with the corresponding boundary conditions. These constraints are information about the solutions at the upper and lower boundaries and at the interfaces between the fluids and thus the system adopted here meets the following boundary conditions (see (Joseph, 1976), (Sisoev et al, 2009), (Sadiq et al, 2010) and (Rosensweig, 1985) ).…”

Section: Geometry and Mathematical Formulationmentioning

confidence: 99%

“…8, No. 2;2016 et al, 2009), (Sadiq et al, 2010), (Rosensweig, 1985), (Funada & Joseph, 2001) and (Bhatia, 1974) ):…”

Section: Geometry and Mathematical Formulationmentioning

confidence: 99%

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Stability Characterization of Three Porous Layers Model in the Presence of Transverse Magnetic Field

AlHamdan¹,

Alkharashi²

2016

JMR

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The current study concerns, the effect of a horizontal magnetic field on the stability of three horizontal finite layers of immiscible fluids in porous media. The problem examines few representatives of porous media, in which the porous media are assumed to be uniform, homogeneous and isotropic. The dispersion relations are derived using suitable boundary and surface conditions in the form of two simultaneous Mathieu equations of damping terms having complex coefficients. The stability conditions of the perturbed system of linear evolution equations are investigated both analytically and numerically and stability diagrams are obtained. The stability diagrams are discussed in detail in terms of various parameters governing the flow on the stability behavior of the system such as the streaming velocity, permeability of the porous medium and the magnetic properties. In the special case of uniform velocity, the fluid motion has been displayed in terms of streamlines concept, in which the streamlines contours are plotted. In the uniform velocity motion, a fourth order polynomial equation with complex coefficients is obtained. According to the complexity of the mathematical treatments, when the periodicity of the velocity is taken into account, the method of multiple scales is applied to obtain stability solution for the considered system. It is found that a stability effect is found for increasing, the magnetic permeability ratio, the magnetic field, and the permeability parameter while the opposite influence is observed for increasing the upper layer velocity.

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“…Therefore, a single equation, describing the energy balance of the mixture, is needed to determine the temperature inside the porous region (one-equation model). Within this context, various authors have studied the stability of thermal convection in superposed fluid and porous layers; see, for example, [22][23][24][25][26][27][28][29][30][31][32][33] and references therein. More recently, the authors of [34] presented Reynolds-averaged simulations for statistically stationary turbulent heat transfer in such domains.…”

Section: Introductionmentioning

confidence: 99%

A thermo-mechanical model for flows in superposed porous and fluid layers with interphasial heat and mass exchange

Papalexandris

Antoniadis

2015

International Journal of Heat and Mass Transfer

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Instabilities in a liquid film flow over an inclined heated porous substrate

Cited by 62 publications

References 38 publications

Effects of velocity slip on the inertialess instability of a contaminated two-layer film flow

Effects of velocity slip on the inertialess instability of a contaminated two-layer film flow

Stability Characterization of Three Porous Layers Model in the Presence of Transverse Magnetic Field

A thermo-mechanical model for flows in superposed porous and fluid layers with interphasial heat and mass exchange

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