Non-Equilibrium Thin-Film Flow in Rotating Disk and Cone

2008 ◽  
Author(s):  
Wallace Woon-Fong Leung
Keyword(s):  
Thin Film ◽  
Mammalian Cells ◽  
Flow Behavior ◽  
Experimental Tests ◽  
Rotating Disk ◽  
Disk Surface ◽  
Thin Film Flow ◽  
Liquid Stream ◽  
Highly Nonlinear ◽  
Rotating Cone

The acceleration of a continuous feed liquid stream in a film “down” the rotating cone and disk is of great interest in centrifuges [1, 2], thin-film reactors and process intensifiers. The mechanism of feed acceleration is determined by an interaction of several different effects. Circumferential viscous forces act to increase the angular momentum. The centrifugal field thus produced establishes a body-force component along the cone/disk surface, thereby driving the flow “down” toward larger radius. The longitudinal flow is however impeded by longitudinal resistance forces. These different effects compete with each other as the flow proceeds, never quite coming to an unchanging equilibrium state. An approximate integral method which was used to explore the “near-equilibrium” flow behavior in earlier work has been extended to investigate the case with large departure from equilibrium. The latter exhibits complicated highly nonlinear effect. Despite this, useful information can be obtained from the theoretical analysis. Experimental results on feed acceleration of liquid streams at various feed rates and rotation speeds in a rotating cone have been used to validate the study. The theoretical study with complementary experimental tests provides insights into how continuous liquid stream in form of a thin film is being accelerated using rotating cones and disks, and the associated shear rates involved. The latter has important bearing in processing shear-sensitive mammalian cells in biopharmaceutical separation with centrifuges and mass transfer in thin-film reactors.

scholarly journals Three-dimensional magnetohydrodynamic nanofluid thin-film flow with heat and mass transfer over an inclined porous rotating disk

2019 ◽  
Vol 11 (8) ◽  
pp. 168781401986975 ◽  
Author(s):  
Muhammad Jawad ◽  
Zahir Shah ◽  
Aurangzeb Khan ◽  
Saeed Islam ◽  
Hakeem Ullah
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Differential Equations ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Liquid System ◽  
Thin Film Flow ◽  
Homotopy Analysis ◽  
Injection Effect ◽  
Film Flows

In the present study, the three-dimensional Darcy–Forchheimer magnetohydrodynamic thin-film nanofluid containing flow over an inclined steady rotating plane is observed. Nanofluid thin-film flows are taken thermally radiated and suction/injection effect is also considered. By similarity variables, the partial differential equations are transformed into a set of first-ordinary differential equations (ODES). By Homotopy Analysis Method, the required ODES is solved. The boundary layer over an inclined steady rotating plane is plotted and observed in detail for the velocity, [Formula: see text], and [Formula: see text] profiles. The influence of various embedded parameters such as variable thickness, [Formula: see text]Pr, and thermophoretic parameter on velocity, [Formula: see text], and [Formula: see text] profile. The influence of many parameters is explained by graphs for the velocity, [Formula: see text], and [Formula: see text]. The crucial terms of Nusselt number and Sherwood number have also been observed numerically and physically for [Formula: see text] and [Formula: see text]. Radiation phenomena is the cause of energy to the liquid system. For more rotation parameters, the thermal boundary-layer thickness is reduced.

scholarly journals Impact of Nonlinear Thermal Radiation on MHD Nanofluid Thin Film Flow over a Horizontally Rotating Disk

2019 ◽  
Vol 9 (8) ◽  
pp. 1533 ◽  
Author(s):  
Zahir Shah ◽  
Abdullah Dawar ◽  
Poom Kumam ◽  
Waris Khan ◽  
Saeed Islam
Keyword(s):  
Thin Film ◽  
Thermal Radiation ◽  
Film Flow ◽  
Rotating Disk ◽  
Point Of View ◽  
Working Fluid ◽  
Nonlinear Thermal Radiation ◽  
Thin Film Flow ◽  
Homotopy Analysis ◽  
The Impact

Nanoscience can be stated as a superlative way of changing the properties of a working fluid. Heat transmission features during the flow of nanofluids are an imperative rule from the industrial and technological point of view. This article presents a thin film flow of viscous nanofluids over a horizontal rotating disk. The impact of non-linear thermal radiation and a uniform magnetic field is emphasized in this work. The governing equations were transformed and solved by the homotopy analysis method and the ND-Solve technique. Both analytical and numerical results are compared graphically and numerically, and excellent agreement was obtained. Skin friction and the Nusselt number were calculated numerically. It is concluded that the thin film thickness of nanofluids reduces with enhanced values of the magnetic parameter. In addition, the nanofluid temperature was augmented with increasing values of the thermal radiation parameter. The impact of emerging parameters on velocities and temperature profiles were obtainable through graphs and were deliberated on in detail.

Transient Thin-Film Flow on a Moving Boundary of Arbitrary Topography

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
Roger E. Khayat ◽  
Tauqeer Muhammad
Keyword(s):  
Thin Film ◽  
Steady State ◽  
Moving Boundary ◽  
Initial Conditions ◽  
Flow Behavior ◽  
Galerkin Projection ◽  
Thin Film Flow ◽  
Flat Substrate ◽  
Thin Film Equations ◽  
Two Dimensional Flow

The transient two-dimensional flow of a thin Newtonian fluid film over a moving substrate of arbitrary shape is examined in this theoretical study. The interplay among inertia, initial conditions, substrate speed, and shape is examined for a fluid emerging from a channel, wherein Couette–Poiseuille conditions are assumed to prevail. The flow is dictated by the thin-film equations of the “boundary layer” type, which are solved by expanding the flow field in terms of orthonormal modes depthwise and using the Galerkin projection method. Both transient and steady-state flows are investigated. Substrate movement is found to have a significant effect on the flow behavior. Initial conditions, decreasing with distance downstream, give rise to the formation of a wave that propagates with time and results in a shocklike structure (formation of a gradient catastrophe) in the flow. In this study, the substrate movement is found to delay shock formation. It is also found that there exists a critical substrate velocity at which the shock is permanently obliterated. Two substrate geometries are considered. For a continuous sinusoidal substrate, the disturbances induced by its movement prohibit the steady-state conditions from being achieved. However, for the case of a flat substrate with a bump, a steady state exists.

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.

Transient thin film flow of nonlinear radiative Maxwell nanofluid over a rotating disk

2019 ◽  
Vol 383 (12) ◽  
pp. 1300-1305 ◽  
Author(s):  
Jawad Ahmed ◽  
Masood Khan ◽  
Latif Ahmad
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Rotating Disk ◽  
Thin Film Flow ◽  
Maxwell Nanofluid

scholarly journals Numerical and Analytical Investigation of an Unsteady Thin Film Nanofluid Flow over an Angular Surface

Processes ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 486 ◽  
Author(s):  
Haroon Rasheed ◽  
Zeeshan Khan ◽  
Ilyas Khan ◽  
Dennis Ching ◽  
Kottakkaran Nisar
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Brownian Motion ◽  
Prandtl Number ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Motion Parameter ◽  
Concentration Profiles ◽  
Thin Film Flow ◽  
Brownian Motion Parameter

In the present study, we examine three-dimensional thin film flow over an angular rotating disk plane in the presence of nanoparticles. The governing basic equations are transformed into ordinary differential equations by using similarity variables. The series solution has been obtained by the homotopy asymptotic method (HAM) for axial velocity, radial velocity, darning flow, induced flow, and temperature and concentration profiles. For the sake of accuracy, the results are also clarified numerically with the help of the BVPh2- midpoint method. The effect of embedded parameters such as the Brownian motion parameter Nb, Schmidt number Sc, thermophoretic parameter and Prandtl number Pr are explored on velocity, temperature and concentration profiles. It is observed that with the increase in the unsteadiness factor S, the thickness of the momentum boundary layer increases, while the Sherwood number Sc, with the association of heat flow from sheet to fluid, reduces with the rise in S and results in a cooling effect. It is also remarkable to note that the thermal boundary layer increases with the increase of the Brownian motion parameter Nb and Prandtl number Pr, hindering the cooling process resulting from heat transfer.

scholarly journals Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise

2021 ◽  
Author(s):  
Konstantinos Dareiotis ◽  
Benjamin Gess ◽  
Manuel V. Gnann ◽  
Günther Grün
Keyword(s):  
Thin Film ◽  
Energy Estimates ◽  
Approximation Procedure ◽  
Thin Film Flow ◽  
Thin Film Equations ◽  
Scalar Conservation Law ◽  
Thin Film Equation ◽  
Degenerate Parabolic ◽  
Scalar Conservation ◽  
Martingale Solutions

AbstractWe prove the existence of non-negative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range of mobilites including the cubic one which occurs under the assumption of a no-slip condition at the liquid-solid interface. Since their introduction more than 15 years ago, by Davidovitch, Moro, and Stone and by Grün, Mecke, and Rauscher, the existence of solutions to stochastic thin-film equations for cubic mobilities has been an open problem, even in the case of sufficiently regular noise. Our proof of global-in-time solutions relies on a careful combination of entropy and energy estimates in conjunction with a tailor-made approximation procedure to control the formation of shocks caused by the nonlinear stochastic scalar conservation law structure of the noise.

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