scholarly journals Asymptotic Modeling of the Thin Film Flow with a Pressure-Dependent Viscosity

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Eduard Marušić-Paloka ◽  
Igor Pažanin
Keyword(s):  
Thin Film ◽  
Film Thickness ◽  
Asymptotic Analysis ◽  
Film Flow ◽  
Thin Film Flow ◽  
Asymptotic Modeling ◽  
Governing System ◽  
Expansion Technique ◽  
Pressure Dependent Viscosity ◽  
Dependent Viscosity

We study the lubrication process with incompressible fluid taking into account the dependence of the viscosity on the pressure. Assuming that the viscosity-pressure relation is given by the well-known Barus law, we derive an effective model using asymptotic analysis with respect to the film thickness. The key idea is to conveniently transform the governing system and then apply two-scale expansion technique.

scholarly journals Triple Solutions of Carreau Thin Film Flow with Thermocapillarity and Injection on an Unsteady Stretching Sheet

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3177 ◽  
Author(s):  
Kohilavani Naganthran ◽  
Ishak Hashim ◽  
Roslinda Nazar
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Differential Equations ◽  
Film Thickness ◽  
Stretching Sheet ◽  
Film Flow ◽  
Problem Solver ◽  
Thin Film Flow ◽  
Unsteady Stretching Sheet ◽  
Negative Film

Thin films and coatings which have a high demand in a variety of industries—such as manufacturing, optics, and photonics—need regular improvement to sustain industrial productivity. Thus, the present work examined the problem of the Carreau thin film flow and heat transfer with the influence of thermocapillarity over an unsteady stretching sheet, numerically. The sheet is permeable, and there is an injection effect at the surface of the stretching sheet. The similarity transformation reduced the partial differential equations into a system of ordinary differential equations which is then solved numerically by the MATLAB boundary value problem solver bvp4c. The more substantial effect of injection was found to be the reduction of the film thickness at the free surface and development of a better rate of convective heat transfer. However, the increment in the thermocapillarity number thickens the film, reduces the drag force, and weakens the rate of heat transfer past the stretching sheet. The triple solutions are identified when the governing parameters vary, but two of the solutions gave negative film thickness. Detecting solutions with the most negative film thickness is essential because it implies the interruption in the laminar flow over the stretching sheet, which then affects the thin film growing process.

scholarly journals Heat Transfer Analysis of Cu and Al 2 0 3 Dispersed in Ethylene Glycol as a Base Fluid over a Stretchable Permeable Sheet of MHD Thin-film Flow

2021 ◽  
Author(s):  
Zeeshan Khan ◽  
Ilyas Khan
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Differential Equations ◽  
Ethylene Glycol ◽  
Film Thickness ◽  
Film Flow ◽  
Heat Transfer Analysis ◽  
Hybrid Nanofluid ◽  
Thin Film Flow ◽  
Thin Film Thickness

Abstract The process of thin films is commonly utilized to improve the surface characteristics of materials. A thin film helps to improve the absorption, depreciation, flexibility, lighting, transport, and electromagnetic efficiency of a bulk material medium. Thin film treatment can be especially helpful in nanotechnology. As a result, the current study investigates the computational process of heat relocation analysis in a thin-film MHD flow embedded in hybrid nanoparticles, which combines the spherical copper and alumina dispersed in ethylene glycol as the conventional heat transfer Newtonian fluid model over a stretching sheet. Important elements such as thermophoresis and Brownian movement are used to explain the characteristics of heat and mass transfer analysis. Nonlinear higher differential equations (ODEs) were attained by transforming partial differential equations (PDEs) into governing equations when implementing the similarity transformation technique. The resulting nonlinear ODEs have been utilized by using the homotopy analysis method (MHD). The natures of the thin-film flow and heat transfer through the various values of the pertinent parameters: unsteadiness, nanoparticle volume fraction, thin-film thickness, magnetic interaction and intensity suction/injection are deliberated. The approximate consequences for flow rate and temperature distributions and physical quantities in terms of local skin friction and Nusselt number were obtained and analysed via graphs and tables. As a consequence, the suction has a more prodigious effect on the hybrid nanofluid than on the injection fluid for all the investigated parameters. It is worth acknowledging that the existence of the nanoparticles and MHD in the viscous hybrid nanofluid tends to enhance the temperature profile but decay the particle movement in the thin-film flow. It is perceived that the velocity and temperature fields decline with increasing unsteadiness, thin-film thickness and suction/injection parameters.

scholarly journals Thin Film Flow in MHD Third Grade Fluid on a Vertical Belt with Temperature Dependent Viscosity

PLoS ONE ◽  
2014 ◽  
Vol 9 (6) ◽  
pp. e97552 ◽  
Author(s):  
Taza Gul ◽  
Saed Islam ◽  
Rehan Ali Shah ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Thin Film Flow ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Grade Fluid ◽  
Dependent Viscosity

scholarly journals MHD dissipative Casson nanofluid liquid film flow due to an unsteady stretching sheet with radiation influence and slip velocity phenomenon

2022 ◽  
Vol 11 (1) ◽  
pp. 463-472
Author(s):  
Elham Alali ◽  
Ahmed M. Megahed
Keyword(s):  
Thin Film ◽  
Mass Transfer ◽  
Film Thickness ◽  
Liquid Film ◽  
Slip Velocity ◽  
Film Flow ◽  
Physical Parameters ◽  
Thin Film Flow ◽  
Thin Film Layer ◽  
Film Layer

Abstract The problem of non-Newtonian Casson thin film flow of an electrically conducting fluid on a horizontal elastic sheet was studied using suitable dimensionless transformations on equations representing the problem. The thin film flow and heat mechanism coupled with mass transfer characteristics are basically governed by the slip velocity, magnetic field, and the dissipation phenomenon. The present numerical analysis by the shooting method was carried out to study the detailed, fully developed heat and mass transfer techniques in the laminar thin film layer by solving the competent controlling equations with eight dominant parameters for the thin liquid film. Additionally, the predicted drag force via skin-friction coefficient and Nusselt and Sherwood numbers were correlated. In view of the present study, a smaller magnetic parameter or a smaller slip velocity parameter exerts very good influence on the development of the liquid film thickness for the non-Newtonian Casson model. Furthermore, a boost in the parameter of unsteadiness causes an increase in both velocity distribution and concentration distribution in thin film layer while an increase in the same parameter causes a reduction in the film thickness. Likewise, the present results are observed to be in an excellent agreement with those offered previously by other authors. Finally, some of the physical parameters in this study, which can serve as improvement factors for heat mass transfer and thermophysical characteristics, make nanofluids premium candidates for important future engineering applications.

Thin-Film Flow Over a Rotating Plate: An Assessment of the Suitability of VOF and Eulerian Thin-Film Methods for the Numerical Simulation of Isothermal Thin-Film Flows

2015 ◽  
Author(s):  
B. Kakimpa ◽  
H. P. Morvan ◽  
S. Hibberd
Keyword(s):  
Thin Film ◽  
Film Thickness ◽  
Film Flow ◽  
Computational Cost ◽  
Inlet Temperature ◽  
Thin Film Flow ◽  
Vof Model ◽  
Fluid Properties ◽  
Thickness Variations ◽  
Rotating Plate

An isothermal thin-film flow over a rotating plate has been simulated using the depth-averaged Eulerian Thin-Film modelling (ETFM) approach. The model setup is based on published experimental and numerical Volume of Fluid (VOF) CFD studies of the same problem to allow for model validation. A range of controlled film inlet heights and mass flow rates are explored together with varied plate rotational speeds ranging from a stationary plate (50rpm) to 200 rpm. While the VOF model has previously been shown to accurately reproduce film thickness, the Eulerian thin-film model is shown to provide predictions of comparable accuracy at a much lower computational cost. The model is also shown to be able to reproduce the film solution’s sensitivity to variations in fluid properties due to changes in inlet temperature. A full 3D domain has been used in this study and the ETFM model is also shown to be able to reproduce azimuthal film thickness variations and surface features similar to those previously observed in experiments.

Thermal energy transport in thin film flow of nanofluid over a decelerating rotating disk

2021 ◽  
pp. 095440892110507
Author(s):  
Latif Ahmad ◽  
Jawad Ahmed ◽  
Awais Ahmed
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Film Thickness ◽  
Energy Transport ◽  
Film Flow ◽  
Rotating Disk ◽  
Brownian Diffusion ◽  
Thin Film Flow ◽  
Thickness Skin ◽  
Buongiorno Model

The thin film flow in nanotechnology is one of the most modern progresses in the study of thin films. This includes coating with nanocomposite materials, thus providing the materials improved mechanical properties due to a so-called size effect. The ultimate functional properties that can be gained are of high adherence, wear resistance, thermal conductivity, oxidation resistance, higher toughness and hardness. This article studies the transient motion of nanofluid thin film over a disk rotating with angular velocity inversely proportional to the time. The importance of Lorentz force arises due to the axial projection of magnetic flux is studied on thin film flow and heat transfer. Two active mechanisms of nanoparticles, namely thermophoresis and Brownian diffusion, are discussed using Buongiorno model. By adopting a similarity method, the velocity distribution thermal and concentration fields above the rotating disk are simulated numerically and assessed graphically. Numerical illustrations for nanofluid film thickness, skin friction and heat and mass transfer rates are depicted against the impacts of several influential parameters. Results highlight that film thickness reduces with unsteadiness and rotation parameters. The results also spectacle that the involvement of a magnetic beam reduces the velocity of nanofluid film. Further, it is observed that thermophoresis and Brownian motion effects make a better influence in enhancing the heat transfer rate.

scholarly journals Thin-Film Flow of an Inhomogeneous Fluid with Density-Dependent Viscosity

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 30 ◽  
Author(s):  
Lorenzo Fusi ◽  
Angiolo Farina ◽  
Fabio Rosso ◽  
Kumbakonam Rajagopal
Keyword(s):  
Thin Film ◽  
Analytical Solution ◽  
Film Flow ◽  
Mathematical Problem ◽  
Order Partial Differential Equation ◽  
Thin Film Flow ◽  
Order Problem ◽  
Mechanics Of Materials ◽  
Constitutive Response ◽  
Dependent Viscosity

In this paper, we study the pressure-driven thin film flow of an inhomogeneous incompressible fluid in which its viscosity depends on the density. The constitutive response of this class of fluids can be derived using a thermodynamical framework put into place to describe the dissipative response of materials where the materials’ stored energy depends on the gradient of the density (Mechanics of Materials, 2006, 38, pp. 233–242). Assuming a small aspect ratio for the channel, we use the lubrication approximation and focus on the leading order problem. We show the mathematical problem reduce to a nonlinear first order partial differential equation (PDE) for the density in which the coefficients are integral operators. The problem is solved numerically and plots that describe the evolution of the density in the fluid domain are displayed. We also show that it was possible to determine an analytical solution of the problem when the boundary data are small perturbations of the homogeneous case. Finally, we use such an analytical solution to validate the numerical scheme.

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