Advanced Mathematical Methods for Scientists and Engineers

The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.

Dynamics and stability of thin liquid films

The viscous flow induced by a shrinking sheet is studied. Existence and (non)uniqueness are proved. Exact solutions, both numerical and in closed form, are found.

/pdf/viscous-flow-due-to-a-shrinking-sheet-1l64h5m1fq.pdf

Viscous flow due to a shrinking sheet

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

Notes on numerical fluid mechanics

The slow steady two-dimensional motion of a viscous incompressible fluid in the unbounded region exterior to a shear free circular cylinder which is impermeable is examined. It is shown that the above problem requires a certain consistency condition for the existence of a solution. In addition, a circle theorem for the biharmonic equation is presented, for the above plane Stokes flow. Some examples are also given.

A note on plane Stokes flow past a shear free impermeable cylinder

An analysis of a laminar squeeze flow of an incompressible Newtonian fluid between parallel plane annuli is presented The local and convective inertia of the flow are considered in the investigation The solution is obtained as a power series in a single nondimensional parameter (squeeze Reynolds number) S, for small values of S Expressions for the pressure and load capacity are given and are compared with those based on the assumption of inertialess flow As applications, the constant velocity squeezing state and the case when the walls perform reciprocating harmonic oscillations with finite amplitude are considered The changes in load capacity with the changes in the parameters that govern the motion have been investigated

An Investigation of a Squeeze Film Between Two Plane Annuli

Finite amplitude instability in a two-fluid plane Poiseuille flow

Linear stability of a plane Poiseuille flow in a channel bounded by anisotropic permeable walls supported by rigid walls is studied. Characteristic instability features due to two-dimensional infinitesimal disturbances of the most unstable wall mode are investigated in detail. A detailed parametric study displays the existence of wall modes, porous modes, and center modes in both the presence and absence of inertial effects. The results reveal that an increase in mean permeability decreases the critical Reynolds number, destabilizing smaller wavenumbers. Although anisotropy has no significant effect on the growth rate at smaller wavenumbers, the impact is substantial at larger wavenumbers, particularly destabilizing short-wave modes and enlarging the bandwidth of unstable wavenumbers. Furthermore, in relation to the configuration with isotropic permeability, the one with larger (smaller) relative wall-normal permeability is more (less) unstable with a large bandwidth of unstable wavenumbers covering short-wave lengths when mean permeability is high and when the fluid channel thickness is the same as the thickness of each of the porous walls. The critical Reynolds number increases with an increase in anisotropic permeability, while the critical wavenumber decreases with an increase in anisotropic permeability. This demonstrates the possibility of enhancing (suppressing) instability by designing the channel walls as one with anisotropic permeability and appropriately tuning the relative wall-normal permeability to be higher (lower). Furthermore, anisotropic permeability can be used to control instabilities for any arbitrary relative thickness of the porous medium beyond a minimum relative thickness that depends on the relative magnitude of wall normal anisotropic permeability.

R. Usha

Papers

A note on plane Stokes flow past a shear free impermeable cylinder

An Investigation of a Squeeze Film Between Two Plane Annuli

Finite amplitude instability in a two-fluid plane Poiseuille flow

Stability of a plane Poiseuille flow in a channel bounded by anisotropic porous walls

Creep flow with concentric permeable spheres in relative motion