Analysis of cooling of a conducting fluid film of non-uniform thickness on a rotating disk
TL;DR: In this paper, the evolution equation of the free surface of a rotating disk has been solved numerically by solving the evolution equations of the non-uniform thickness of conducting liquid films.
Abstract: The unsteady thin conducting liquid film of non-uniform thickness on a rotating disk which is cooled axisymmetrically from below has been analysed numerically by solving the evolution equation of the free surface. Transient film profiles for different initial liquid film distributions have been obtained. The results reveal that the thinning process and film planarisation are markedly influenced by the heat dissipating or cooling parameter β, Prandtl number σ and Reynolds number Re.
Citations
More filters
TL;DR: In this article, a numerical integration technique based on particle swarm optimization is proposed to investigate the effects of internal heat generation/absorption, on MHD boundary-layer flow of different types of nano-fluids over a rotating disk with uniform suction.
Abstract: In this paper, a numerical integration technique, based on particle swarm optimization is proposed to investigate the effects of internal heat generation/absorption, on MHD boundary-layer flow of different types of nano-fluids over a rotating disk with uniform suction. Thermo-physical properties are modeled based on a wide range of experimental data. In the model, effect of nature of base fluid, nature of nano-particle material, size of nano particle, concentration of nanoparticle in the base fluid, nano-thermal layer formed around the nano particle etc. are taken into consideration. The two dimensional non-linear partial differential equations governing the flow are reduced to a system of coupled non-linear ordinary differential equations by using similarity transformations. These non-linear equations have been solved by using shooting based integration technique along with particle swarm optimization. In this study, four different types of water bases nanofluids are compared with respect to heat transfer enhancement, and the effects of nano-particle concentration, nanoparticle size and heat generation/absorption parameters are studied in detail. The effects of different parameters on the dimensionless velocity profile and temperature distribution are discussed graphically. It is found that out of the four nano fluids considered, the heat transfer rate for CuO water based nano fluid is highest. It is also concluded that small sized nano-particles, high suction and high heat absorption increase the heat transfer rate.
12 citations
TL;DR: In this article, a nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and its stability characteristics have been examined using linear theory.
Abstract: A theoretical analysis of the thermal effects on the dynamics of a thin nonuniform film of a nonvolatile incompressible viscous fluid on a heated rotating disk has been considered and the effects of temperature-dependent viscosity and surface tension have been analyzed. A nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and its stability characteristics have been examined using linear theory. It has been observed that the infinitesimal disturbances decay for small wave numbers and are transiently stable for large wave numbers, for both zero and nonzero values of Biot number.
11 citations
Dissertation•
01 Jan 2010TL;DR: In this paper, a methode originale permettant de discriminer les different sources of chaleur is proposed, combinant les approches mecanique, thermique, and aerodynamique.
Abstract: La chaleur degagee dans un palier a roulement fonctionnant a grande vitesse necessite un refroidissement externe afin d’eviter la degradation du lubrifiant et du mecanisme. La technologie actuelle consiste ainsi a injecter dans celui-ci un jet d’huile qui permet a la fois la lubrification des surfaces en contact mais egalement l’evacuation de la chaleur. La comprehension des mecanismes de lubrification necessite donc de mener des investigations conjointes sur les pertes de puissance au sein du roulement et sur les echauffements correspondants. La perte de puissance associee a la trainee aerodynamique exercee par le brouillard d’huile sur les elements roulants est extremement delicate a estimer du fait de la complexite des ecoulements. Il existe ainsi un degre de liberte sur la maniere d’aborder cette perte, qui historiquement a toujours ete ajustee de maniere a egaliser les pertes de puissance globales calculee et mesuree. Ce phenomene a permis de masquer la divergence d’opinions concernant la prise en compte ou non de la force de roulement hydrodynamique au contact bille/bague. Une methode originale permettant de discriminer les differentes sources de chaleur est proposee, combinant les approches mecanique, thermique et aerodynamique. Il est ainsi demontre que les forces de roulement hydrodynamique et de trainee aerodynamique ne peuvent pas etre negligees dans un roulement a billes grande vitesse. L’outil numerique developpe s’avere performant et rapide pour modeliser le comportement thermo mecanique d’un roulement en regime stationnaire et transitoire. Des investigations sur un scenario d’interruption de la lubrification sont ainsi egalement realisees. Ces aspects representent une avancee technique dans la comprehension du role de l’huile tant comme lubrifiant que comme fluide caloporteur
9 citations
TL;DR: In this paper, the effects of a magnetic field on the dynamics of a thin nonuniform conducting film of an incompressible viscous fluid on a rotating disk has been considered, and a nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and solved numerically.
Abstract: A theoretical analysis of the effects of a magnetic field on the dynamics of a thin nonuniform conducting film of an incompressible viscous fluid on a rotating disk has been considered A nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and has been solved numerically The temporal evolution of the free surface of the fluid and the rate of retention of the liquid film on the spinning disk have been obtained for different values of Hartmann number M, evaporative mass flux parameter E, and Reynolds number Re The results show that the relative volume of the fluid retained on the spinning disk is enhanced by the presence of the magnetic field The stability characteristics of the evolution equation have been examined using linear theory For both zero and nonzero values of the nondimensional parameter describing the magnetic field, the results show that (a) the infinitesimal disturbances decay for small wave numbers and are transiently stable for larger wave numbers when there is either no mass transfer or there is evaporation from the film surface, and although the magnitude of the disturbance amplitude is larger when the magnetic field is present, it decays to zero earlier than for the case when the magnetic field is absent, and (b) when absorption is present at the film surface, the film exhibits three different domains of stability: disturbances of small wave numbers decay, disturbances of intermediate wave numbers grow transiently, and those of large wave numbers grow exponentially The range of stable wave numbers increases with increase in Hartmann number
3 citations
TL;DR: In this article , the surface tension profiles of epoxy-amine reactive systems were investigated using the Wilhelmy plate method and Fourier transform infrared (FTIR) spectroscopy was used to verify in situ formation of carbamate.
Abstract: Epoxy-amine reactive systems, including their surface tension, have been studied due to their use and importance in composites and adhesives in laboratory and industrial applications. Understanding how the system's surface tension changes during curing could help target applications for tailored composites. Using the Wilhelmy plate method, surface tensions for epoxy-curing agent systems were investigated under different environments. While the epoxy exhibited an expected negative temperature coefficient of −0.096 mN/m/°C, the curing agent exhibited a positive temperature coefficient of 0.073 mN/m/°C, which is due to the curing agent reacting with atmospheric CO2 to form carbamate through a zwitterion pathway and functional groups accumulating at the surface of the reacting systems. Carbamate formation results in a surface tension below that of the individual constituents in the epoxy-amine curing agent system. Fourier transform infrared (FTIR) spectroscopy was used to verify in situ formation of carbamate, and by reducing the system's temperature, it was demonstrated that the system surface tension profiles displayed micellar surfactant-like characteristics. FTIR was used to explore the difference in composition between the surface and the bulk, in particular carbamate formation at the surface, resulting in a lowering of the surface tension of reacting systems.
References
More filters
845 citations
TL;DR: In this paper, it was shown that initially irregular fluid distributions tend toward uniformity under centrifugation, and means of computing times required to produce uniform layers of given thickness at given angular velocity and fluid viscosity are demonstrated.
Abstract: Equations describing the flow of a Newtonian liquid on a rotating disk have been solved so that characteristic curves and surface contours at successive times for any assumed initial fluid distribution may be constructed. It is shown that centrifugation of a fluid layer that is initially uniform does not disturb the uniformity as the height of the layer is reduced. It is also shown that initially irregular fluid distributions tend toward uniformity under centrifugation, and means of computing times required to produce uniform layers of given thickness at given angular velocity and fluid viscosity are demonstrated. Contour surfaces for a number of exemplary initial distributions (Gaussian, slowly falling, Gaussian plus uniform, sinusoidal) have been constructed. Edge effects on rotating planes with rising rims, and fluid flow on rotating nonplanar surfaces, are considered.
696 citations
TL;DR: In this article, the authors consider horizontal static liquid layers on planar solid boundaries and analyse their instabilities, including the effects of mass loss (or gain) and non-equilibrium thermodynamic effects.
Abstract: We consider horizontal static liquid layers on planar solid boundaries and analyse their instabilities. The layers are either evaporating, when the plates are heated, or condensing, when the plates are cooled. Vapour recoil, thermocapillary, and rupture instabilities are discussed, along with the effects of mass loss (or gain) and non-equilibrium thermodynamic effects. Particular attention is paid to the development of dryout. We derive long-wave evolution equations for the interface shapes that govern the two-dimensional nonlinear stability of the layers subject to the above coupled mechanisms. These equations are analysed and their predictions discussed. Previous theoretical and experimental results are reviewed and compared with the present results. Finally, we discuss limitations of the modelling and extend our derivation to the case of three-dimensional disturbances.
648 citations
TL;DR: In this article, a model for the description of thin films prepared from solution by spinning is presented, and the thickness of the film and the time of drying can be calculated as functions of various processing parameters.
Abstract: A model is presented for the description of thin films prepared from solution by spinning. Using only the centrifugal force, linear shear forces, and uniform evaporation of the solvent, the thickness of the film and the time of drying can be calculated as functions of the various processing parameters. The model is compared with experimental results obtained on positive photoresists and excellent agreement is obtained. When adequate care are is taken, the liquid forms a level surface during spinning, and the film thickness becomes uniform and independent of the size of the substrate. The film thickness h shows the following dependence on spin speed f, initial viscosity ν0, and evaporation rate e:h∝f−2/3νo1/3e1/3, and e is proportional to f1/2.
628 citations
01 Nov 1982
TL;DR: In this article, a nonlinear evolution equation is derived for h ( x, t ), the film thickness, and this strongly nonlinear partial differential equation is solved by numerical methods as part of an initial value problem for periodic boundary conditions in x, the lateral space dimension.
Abstract: The present work aims at examining nonlinear effects on film rupture by investigating the stability of thin films to finite amplitude disturbances. The dynamics of the liquid film is formulated using the Navier-Stokes equations augmented by a body force describing the London/van der Waals attractions. The liquid film is assumed to be charge neutralized, nondraining, and laterally unbounded. A nonlinear evolution equation is derived for h ( x , t ), the film thickness. This strongly nonlinear partial differential equation is solved by numerical methods as part of an initial-value problem for periodic boundary conditions in x , the lateral space dimension. Given this model, one obtains true rupture in the sense that the film thickness becomes zero in a finite time. The results reveal rupture characteristics and effects of nonlinearities on the rupture properties.
426 citations