New Models in the Theory of the Hydrodynamic Lubrication of Rough Surfaces

1988 ◽  
Vol 110 (3) ◽  
pp. 402-407 ◽  
Author(s):  
G. Bayada ◽  
M. Chambat
Keyword(s):  
Thin Film ◽  
Qualitative Study ◽  
Stokes System ◽  
Film Flow ◽  
Hydrodynamic Lubrication ◽  
Three Dimensional ◽  
Thin Film Flow ◽  
New Models ◽  
Small Parameters ◽  
The Mean

Recent advances in mathematical analysis of problems described by several small parameters equations are used to revisit the general roughness problem. In this paper, we put forward a new qualitative study of a thin film flow with a rapidly varying gap. Using an asymptotic analysis of the three-dimensional Stokes system we obtain a family of new generalized Reynolds equations. We are led to distinguish three different cases in which the periodic roughness wavelength is on the order of, greater or shorter than the mean thickness of the gap.

scholarly journals Three-Dimensional Casson Nanofluid Thin Film Flow over an Inclined Rotating Disk with the Impact of Heat Generation/Consumption and Thermal Radiation

Coatings ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 248 ◽  
Author(s):  
Anwar Saeed ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Muhammad Jawad ◽  
Asad Ullah ◽  
...  
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Boundary Layer ◽  
Energy Transport ◽  
Film Flow ◽  
Three Dimensional ◽  
Concentration Profiles ◽  
Thin Film Flow ◽  
The Impact

In this research, the three-dimensional nanofluid thin-film flow of Casson fluid over an inclined steady rotating plane is examined. A thermal radiated nanofluid thin film flow is considered with suction/injection effects. With the help of similarity variables, the partial differential equations (PDEs) are converted into a system of ordinary differential equations (ODEs). The obtained ODEs are solved by the homotopy analysis method (HAM) with the association of MATHEMATICA software. The boundary-layer over an inclined steady rotating plane is plotted and explored in detail for the velocity, temperature, and concentration profiles. Also, the surface rate of heat transfer and shear stress are described in detail. The impact of numerous embedded parameters, such as the Schmidt number, Brownian motion parameter, thermophoretic parameter, and Casson parameter (Sc, Nb, Nt, γ), etc., were examined on the velocity, temperature, and concentration profiles, respectively. The essential terms of the Nusselt number and Sherwood number were also examined numerically and physically for the temperature and concentration profiles. It was observed that the radiation source improves the energy transport to enhance the flow motion. The smaller values of the Prandtl number, Pr, augmented the thermal boundary-layer and decreased the flow field. The increasing values of the rotation parameter decreased the thermal boundary layer thickness. These outputs are examined physically and numerically and are also discussed.

Three-dimensional thin film flow over and around an obstacle on an inclined plane

2009 ◽  
Vol 21 (3) ◽  
pp. 032102 ◽  
Author(s):  
S. J. Baxter ◽  
H. Power ◽  
K. A. Cliffe ◽  
S. Hibberd
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Three Dimensional ◽  
Thin Film Flow ◽  
Inclined Plane

scholarly journals Inertial two- and three-dimensional thin film flow over topography

2011 ◽  
Vol 50 (5-6) ◽  
pp. 537-542 ◽  
Author(s):  
S. Veremieiev ◽  
H.M. Thompson ◽  
Y.C. Lee ◽  
P.H. Gaskell
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Three Dimensional ◽  
Thin Film Flow ◽  
Flow Over Topography

Micro-Inertia Effects in Laminar Thin-Film Flow Past a Sinusoidal Boundary

1997 ◽  
Vol 119 (1) ◽  
pp. 211-216 ◽  
Author(s):  
Jin Hu ◽  
Hans J. Leutheusser
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Hydrodynamic Lubrication ◽  
Dynamic Properties ◽  
Navier Stokes ◽  
Thin Film Flow ◽  
Navier Stokes Equation ◽  
Inertia Effects ◽  
Experimental Findings ◽  
Film Flows

Micro-inertia effects of surface roughness on hydrodynamic lubrication are analyzed in the light of similitude principles, viz. a newly conceived reduced Reynolds number and the classical parameter of relative roughness. In particular, the dynamic properties of laminar sheet flow in a two-dimensional channel between a sinusoidal wall and a flat wall are studied. FEM solutions of the Navier-Stokes equation are compared with corresponding experimental findings. The latter are gathered in an especially designed laminar-flow wind tunnel. Conclusions are drawn concerning the roughness sensitivity of laminar thin-film flows.

scholarly journals Thin film flow of an Oldroyd 6-constant fluid over a moving belt: an analytic approximate solution

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 44-64 ◽  
Author(s):  
Remus-Daniel Ene ◽  
Vasile Marinca ◽  
Valentin Bogdan Marinca
Keyword(s):  
Thin Film ◽  
Differential Equation ◽  
Constant Velocity ◽  
Basic Equation ◽  
Film Flow ◽  
Nonlinear Problems ◽  
Approximate Solutions ◽  
Thin Film Flow ◽  
Small Parameters ◽  
Optimal Homotopy Asymptotic Method

AbstractIn this paper the thin film flow of an Oldroyd 6-constant fluid on a vertically moving belt is investigated. The basic equation of a non-Newtonian fluid in a container with a wide moving belt which passes through the container moving vertically upward with constant velocity, is reduced to an ordinary nonlinear differential equation. This equation is solved approximately by means of the Optimal Homotopy Asymptotic Method (OHAM). The solutions take into account the behavior of Newtonian and non-Newtonian fluids. Our procedure intended for solving nonlinear problems does not need small parameters in the equation and provides a convenient way to control the convergence of the approximate solutions.

scholarly journals Significance of magnetic Reynolds number in a three-dimensional squeezing Darcy–Forchheimer hydromagnetic nanofluid thin-film flow between two rotating disks

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Saima Riasat ◽  
Muhammad Ramzan ◽  
Seifedine Kadry ◽  
Yu-Ming Chu
Keyword(s):  
Thin Film ◽  
Carbon Nanotubes ◽  
Reynolds Number ◽  
Film Flow ◽  
Three Dimensional ◽  
Magnetic Reynolds Number ◽  
Partial Slip ◽  
Rotating Disks ◽  
Thin Film Flow ◽  
Multiwalled Carbon

Abstract The remarkable aspects of carbon nanotubes like featherweight, durability, exceptional electrical and thermal conduction capabilities, and physicochemical stability make them desirous materials for electrochemical devices. Having such astonishing characteristics of nanotubes in mind our aspiration is to examine the squeezing three dimensional Darcy–Forchheimer hydromagnetic nanofluid thin-film flow amid two rotating disks with suspended multiwalled carbon nanotubes (MWCNTs) submerged into the base fluid water. The analysis is done by invoking partial slip effect at the boundary in attendance of autocatalytic reactions. The mathematical model consists of axial and azimuthal momentum and magnetic fields respectively. The tangential and axial velocity profiles and components of the magnetic field are examined numerically by employing the bvp4c method for varying magnetic, rotational, and squeezing Reynolds number. The torque effect near the upper and lower disks are studied critically using their graphical depiction. The values of the torque at the upper and lower disks are obtained for rotational and squeezed Reynolds numbers and are found in an excellent concurrence when compared with the existing literature. Numerically it is computed that the torque at the lower disk is higher in comparison to the upper disk for mounting estimates of the squeezed Reynolds number and the dimensionless parameter for magnetic force in an axial direction. From the graphical illustrations, it is learned that thermal profile declines for increasing values of the squeezed Reynolds number.

Predicting Three-Dimensional Inertial Thin Film Flow over Micro-Scale Topography

2011 ◽  
pp. 833-838
Author(s):  
Sergii Veremieiev ◽  
Philip H. Gaskell ◽  
Yeaw Chu Lee ◽  
Harvey M. Thompson
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Three Dimensional ◽  
Thin Film Flow ◽  
Micro Scale
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