Thank you very much for reading principles of enhanced heat transfer. As you may know, people have look numerous times for their chosen books like this principles of enhanced heat transfer, but end up in malicious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they are facing with some infectious bugs inside their desktop computer. principles of enhanced heat transfer is available in our book collection an online access to it is set as public so you can get it instantly. Our books collection spans in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the principles of enhanced heat transfer is universally compatible with any devices to read.

Principles Of Enhanced Heat Transfer

The present review deals with the effects of topography and inertia on gravity-driven film flows. The article is organized like a rope ladder, with the rungs of topography and inertia being scaled one after another. We begin with an introduction, where we specify the literature reviewed in our article and highlight the physical significance of this type of fluid motion. Next, we address the effects of different types of topographies on creeping film flow and films in lubrication approximation, and on inertial flow. Then, findings on inertial flow with sidewalls as bounding topography are reviewed. In all these cases, the impact of topography and inertia on both the free surface and the flow field structure is shown. Subsequently, we briefly highlight inverse problem theory. The following penultimate section focuses on the stability of film flows. After a short review on the stability of films over flat inclines which we give for convenience, the stability of films over topography is considered. A discussion on the stability of films with sidewalls as bounding topography follows. In each case, the interaction between topography, flow field, and free surface is shown with the theoretical and experimental methods being discussed. Finally, the paper closes with some concluding remarks and an outlook from the authors’ perspective—one century after the groundbreaking work of Wilhelm Nusselt.

Films over topography: from creeping flow to linear stability, theory, and experiments, a review

The linear stability of a liquid flow bounded by slippery and porous walls is studied for infinitesimal disturbances of arbitrary wavenumbers. The Orr-Sommerfeld type eigenvalue problem is formulated by using the normal mode decomposition and resolved based on the Chebyshev spectral collocation method along with the QZ algorithm. The results are computed numerically in detail for various values of the flow parameters. The presence of an upper wall slip shows a destabilizing effect on the fluid layer mode, but it shows a stabilizing effect on the porous layer mode. On the other hand, the decreasing value of the depth ratio has a stabilizing effect on the fluid layer mode but it has a destabilizing effect on the porous layer mode. In fact, there occurs a competition between the most unstable porous layer mode and the most unstable fluid layer mode to control the primary instability. The most unstable porous layer mode triggers the primary instability unless the upper wall slip dominates the effect of the porous layer otherwise the most unstable fluid layer mode triggers the primary instability. A new phase boundary is detected in the plane of the depth ratio and slip length, which separates the domain of the most unstable porous layer mode from the domain of the most unstable fluid layer mode.

Role of slip on the linear stability of a liquid flow through a porous channel

A study of the linear stability analysis of a shear-imposed fluid flowing down an inclined plane is performed when the free surface of the fluid is covered by an insoluble surfactant. The purpose is to extend the earlier work [H. H. Wei, “Effect of surfactant on the long-wave instability of a shear-imposed liquid flow down an inclined plane,” Phys. Fluids 17, 012103 (2005)] for disturbances of arbitrary wavenumbers. The Orr-Sommerfeld boundary value problem is formulated and solved numerically based on the Chebyshev spectral collocation method. Two temporal modes, the so-called surface mode and surfactant mode, are detected in the long-wave regime. The surfactant mode becomes unstable when the Peclet number exceeds its critical value. In fact, the instability of the surfactant mode occurs on account for the imposed shear stress. Energy budget analysis predicts that the kinetic energy of the infinitesimal disturbance grows with the imposed shear stress. On the other hand, the numerical results reveal that both surface and surfactant modes can be destabilized by increasing the value of the imposed shear stress. Similarly, it is demonstrated that the shear mode becomes more unstable in the presence of the imposed shear stress. However, it can be stabilized by incorporating the insoluble surfactant at the free surface. Apparently, it seems that inertia does not play any role in the surfactant mode in the moderate Reynolds number regime. Furthermore, the competition between surface and shear modes is discussed.

Linear stability analysis of a surfactant-laden shear-imposed falling film

We examine a mathematical model describing the behavior of the precontact lens tear film of a human eye. Our work examines the effect of contact lens thickness and lens permeability on the film dynamics. Also investigated are gravitational effects and the effects of different slip models at the fluid-lens interface. A mathematical model for the evolution of the tear film is derived using a lubrication approximation applied to the hydrodynamic equations of motion in the fluid film and the porous layer. The model is a nonlinear fourth-order partial differential equation subject to boundary conditions and an initial condition for post-blink film evolution. The evolution equation is solved numerically, and the effects of various parameters on the rupture of the thin film are studied. We find that increasing the lens thickness, permeability, and slip all contribute to an increase in the film thinning rate, although for parameter values typical for contact lens wear, these modifications are minor. Gravity plays...

https://absimage.aps.org/image/DFD10/MWS_DFD10-2010-001263.pdf

Thin Film Evolution Over a Thin Porous Layer: Modeling a Tear Film on a Contact Lens

The stability of a gravity-driven film flow on a porous inclined substrate is considered, when the film is contaminated by an insoluble surfactant, in the frame work of Orr-Sommerfeld analysis. The classical long-wave asymptotic expansion for small wave numbers reveals the occurrence of two modes, the Yih mode and the Marangoni mode for a clean/a contaminated film over a porous substrate and this is confirmed by the numerical solution of the Orr-Sommerfeld system using the spectral-Tau collocation method. The results show that the Marangoni mode is always stable and dominates the Yih mode for small Reynolds numbers; as the Reynolds number increases, the growth rate of the Yih mode increases, until, an exchange of stability occurs, and after that the Yih mode dominates. The role of the surfactant is to increase the critical Reynolds number, indicating its stabilizing effect. The growth rate increases with an increase in permeability, in the region where the Yih mode dominates the Marangoni mode. Also, the growth rate is more for a film (both clean and contaminated) over a thicker porous layer than over a thinner one. From the neutral stability maps, it is observed that the critical Reynolds number decreases with an increase in permeability in the case of a thicker porous layer, both for a clean and a contaminated film over it. Further, the range of unstable wave number increases with an increase in the thickness of the porous layer. The film flow system is more unstable for a film over a thicker porous layer than over a thinner one. However, for small wave numbers, it is possible to find the range of values of the parameters characterizing the porous medium for which the film flow can be stabilized for both a clean film/a contaminated film as compared to such a film over an impermeable substrate; further, it is possible to enhance the instability of such a film flow system outside of this stability window, for appropriate choices of the porous substrate characteristics.

https://hal.archives-ouvertes.fr/hal-00931414/document

Thin film flow down a porous substrate in the presence of an insoluble surfactant: Stability analysis

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.

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

Steady solutions of an inverse problem relevant to gravity-driven film flows over an undulated slippery bottom are considered. Given a target free surface shape, the goal is to obtain the corresponding bottom topography of a slippery substrate which causes the specified free surface shape for a film flowing over it. The approaches followed by Sellier (Phys Fluids 20:062106, 2008) for creeping films and by Heining and Aksel (Phys Fluids 21:083605, 2009) for inertial films for reconstructing a rigid bottom topography for a target free surface profile are extended to the reconstruction of a slippery bottom topography. The model equations for film thickness above the bottom topography are derived for creeping flows under lubrication approximation and for inertial films using the weighted-residual integral boundary layer method and are solved numerically. The influence of inertia, slip parameter and surface tension on the shape of the reconstructed bottom topography is analyzed for different prescribed free surface shapes (sinusoidal, trench and bell-shaped). It is observed that the nonlinearities that appear in the reconstructed rigid bottom substrate with no slip at the substrate are suppressed by seeking the bottom substrate to be reconstructed as a slippery substrate. A spatial linear stability analysis of the corresponding direct problem is examined using Floquet theory, and the results reveal that the slip parameter and surface tension have a high influence on the critical Reynolds number. The results provide a strategy for controlling surface defects in a gravity-driven film over a substrate; namely, in order to achieve a target free surface profile, one can design the bottom substrate to be an undulated rough/textured/grooved or a superhydrophobic surface which can be modelled as an undulated smooth substrate with velocity slip at the substrate.

Steady solution and spatial stability of gravity-driven thin-film flow: reconstruction of an uneven slippery bottom substrate

A mathematical model is developed to investigate the dynamics and rupture of a pre-lens tear film on a contact lens. The contact lens is modeled as a saturated porous medium of constant, finite thickness and is described by the Darcy-Brinkman equations with stress-jump condition at the interface. The model incorporates the influence of capillarity, gravitational drainage, contact lens properties such as the permeability, the porosity, and the thickness of the contact lens on the evolution and rupture of a pre-lens tear film, when the eyelid has opened after a blink. Two models are derived for the evolution of a pre-lens tear film thickness using lubrication theory and are solved numerically; the first uses shear-free surface condition and the second, the tangentially immobile free surface condition. The results reveal that life span of a pre-lens tear film is longer on a thinner contact lens for all values of permeability and porosity parameter considered. An increase in permeability of contact lens, poro...

Anjalaiah

Papers

Thin film flow down a porous substrate in the presence of an insoluble surfactant: Stability analysis

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

Steady solution and spatial stability of gravity-driven thin-film flow: reconstruction of an uneven slippery bottom substrate

Dynamics of a pre-lens tear film after a blink: Model, evolution, and rupture