Volume of a liquid drop detaching from a sphere

A theoretical and experimental study is conducted to investigate the detached volume from a pendant drop on the surface of a sphere. Observation of drop detachment by high‐speed video camera reveals that the movement of the upper part of the neck of the drop is quite slow compared to that of the detaching lower part. The surface profile of the upper part was calculated approximately as a static problem using the axisymmetric Laplace equation. Using the drop profile, the system energy, including the work done by the solid–liquid wetting behavior, was calculated. Based on the condition of minimum energy, the volume of the detached part V was calculated. The volume V increases with the sphere diameter and approaches the value for the pendant drop attached to a plate. In addition, V is strongly dependent on the wettability between the sphere and the liquid and decreases with the receding contact angle. The detached volume of the water drop was measured for spheres of porous brick of various diameters. The experimental and theoretical results were found to be in good agreement. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20305     

A numerical study of air entrapment during the droplet impact on a solid substrate

A numerical investigation is conducted to study the air entrapment phenomenon when two different liquids such as water and diesel droplet are impacted on the solid surface. The beginning of the air entrapment process was observed during droplet impact on a solid substrate forming a dimple underneath the droplet. The air film thus trapped underneath the droplet started evolving into the air bubble. This journey of evolution mainly comprises phases like an inertial retraction of air film, contraction, and pinch-off of the secondary droplet inside the air bubble for a water droplet impact case. The volume of fluid approach has been utilized to track the progress of air film evolution. The influence of surface wettability has been observed on the evolution of air film into the air bubble by taking four different values of contact angle pertaining to the hydrophilic surface (θ = 10° and 35°) and hydrophobic surface (θ = 90° and θ = 120°). The air bubble was found to get detached from the substrate for the hydrophilic surface (θ = 35°) and observed to remain attached to the substrate for the hydrophobic surface. The variation of pressure underneath the droplet was also investigated as the droplet reaches the substrate. The effect of surface tension has been studied on the evolution of air film by impacting the diesel droplet on the same substrate keeping the same wettability condition (θ = 35°). The lower surface tension of the diesel droplet as compared to the water droplet delayed the process of air film evolution and consequently decreases the retraction speed of air film. Also, the air bubble remains attached to the surface. Furthermore, the air bubble detaches from the surface for an even higher wettability condition (θ = 10°). Thus surface wettability and surface tension become two important factors governing the development of entrapped air film and bubble elimination in many practical applications.     

Scattering characteristics of liquid droplets spun off from rotating disk edge

Scattering characteristics of liquid droplets spun off from a rotating disk edge are experimentally investigated. In the present research, aluminum disks are utilized and ethanol is employed for liquid. Scattering phenomena of the droplets are captured by the high-speed digital camera. Frequency distribution of the droplet diameter is evaluated from these images and distributions of horizontal flying velocity and angle of the droplets were measured by PTV. Liquid filaments are stretched outward from the stagnant liquid layer by centrifugal force and skew complicatedly by aerodynamic force. Some peaks appear in the distribution of the scattered droplet diameter and they are origi- nated from large terminal droplets and small droplets generated from filamentwise breakup. Most of the scattered droplets fly slightly inside in the tangential direction of the disk edge. The droplets spun off from the thin disk scatter widely compared with that from the thick one.     

液滴在倾斜表面上的固化特征研究

采用平滑铝表面为基底,以去离子水为介质,对低温条件下倾斜表面上运动液滴的固化特征进行了研究,分析了液滴的固化时间特征,并探讨了基底倾斜角、液滴体积以及基底表面浸润性对液滴固化时间的影响。结果表明：当基底倾斜角小于液滴在铝表面上的临界滑动角时,液滴固化时间保持不变;当基底倾斜角大于临界滑动角时,随着倾斜角增大,液滴固化时间变短。随着液滴体积增大,虽然湿接触面积增大,但是液滴高度也增大,液滴固化时间随之延长。基底表面的疏水性越好,液滴与固体表面的湿接触面积越少,液滴高度越高,因此液滴固化时间越长。基于传热学理论建立了双圆法模型,利用其预测运动液滴的固化时间,并将计算值与实验值进行了比较,发现两者吻合良好。     

Simulation of heat transfer and hydrodynamics over a free rotating disk using an improved radial velocity profile

INTRODUCTIONIn many casess hydrodynamics and heat tlansfer inrotating-disk systems may be successfully simulatedusing integral methods. Restrictions imposed by theboundary layer approach are well-known. However,advanced integral methods employing justified modelassumptions in each specific case are quite competitive in comparison with modern CFD-paCkages. Commonly accepted advantages of the integral methodsare relative simple and high speed in calculations.Integral methods in the case o…     

An unsteady flow structure on a heated rotating disk under mixed convection

A flow field under mixed convection on a heated rotating disk has been measured using an ultrasonic velocity profiler (UVP). The measured velocity field is a spatio‐temporal one as a function of radial coordinates and time. The objective of this paper is to clarify the vortex structure caused by the instability between buoyancy and centrifugal force. The vortex appears under typical conditions of Reynolds numbers and Grashof numbers and it moves toward the outside of the disk. This behavior can be classified into two patterns. The size of the vortex structure decreases with an increasing Reynolds number and increases with the Grashof number. The traveling velocity of the vortex increases with the Grashof number. Moreover, it decreases with an increasing Reynolds number in spite of increasing centrifugal force. According to these results, the region dominated by natural, forced, and mixed convection is classified in the relationship between Reynolds and Grashof numbers. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(6): 407–418, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20074     

MHD nonlinear natural convection flow of a micropolar nanofluid past a nonisothermal rotating disk

The aim of this analysis is to examine the steady, laminar boundary layer flow of a micropolar nanofluid owing to a rotating disk in the presence of a magnetic field and thermal and solutal nonlinear convection and nonisothermal parameters. The governing joined partial differential equations are converted into nonlinear ordinary differential equations by means of available transformations. The equations are calculated using the method bvp4c from Matlab software. The convergence test has been maintained; for the number of spots greater than the appropriate mesh number of points, the precision is not influenced, but the set time is boosted. Moreover, various quantities of the main parameters on skin friction coefficients, wall couple stress coefficients, Nusselt number, Sherwood number, velocities, temperature, and concentration of nanofluid are analyzed by means of tables and graphs. The results indicate that the presence of the nonisothermal parameter boosts the radial skin friction, temperature, and Sherwood number but causes decaying concentration distributions, the azimuthal skin friction coefficient, and Nusselt number that indicate the diffusion of momentum occurs more around the surface of the rotating disk.     

高位进气转静系旋转盘流动与换热的数值模拟

采用扩展混合长度湍流模型和S IM PLE算法,用共轭数值计算的方法模拟航空发动机涡轮盘冷却系统的高位进气、径向出流转静系旋转盘腔模型的流场和温度场,分析了其盘面平均努塞尔数N uav随旋转雷诺数R eω和流量系数Cw的变化。结果表明,随着转速和冷气流量的提高换热得以增强,但在本次计算范围内提高转速对换热的增强幅度小于提高冷气流量对换热的增强幅度。     

Heat Transfer and Fluid Flow over a Single Disk in a Fluid Rotating as a Rigid Body

Laminar heat transfer problem is analyzed for a disk rotating with the angular speed ωin a co-rotating fluid (with the angular speed Ω). The fluid is swirled in accordance with a forced-vortex law, it rotates as a solid body at β= Ω/ω= const. Radial variation of the disk's surface temperature follows a power law. An exact numerical solution of the problem is obtained basing on the self-similar profiles of the local temperature of fluid, its static pressure and velocity components. Numerical computations were done at the Prandtl numbers Pr = 1(?)0.71. It is shown that with increasing βboth radial and tangential components of shear stresses decrease, and to zero value at β= 1. Nusselt number is practically constant at β= 0(?) 0.3 (and even has a point of a maximum in this region); Nu decrease noticeably for larger βvalues.     

Significance of thermal radiation on dusty fluid flow over a stretching rotating disk with convective boundary condition

This paper explores the flow of dusty fluid over a stretching rotating disk with thermal radiation. Further, the convective boundary condition is considered in this modeling. The described governing equations are reduced to ordinary differential equations by using apt similarity transformations and then they are numerically solved using Runge–Kutta–Fehlberg-45 scheme. To gain a clear understanding of the current boundary layer flow problem, the graphical results of the velocity and thermal profiles, shear stresses at the disk, and Nusselt number are drawn. Results reveal that the increase in the value of the porosity parameter reduces the velocity of both particle and fluid phases. The increase in the value of the Biot number improves the temperature gradient of both particle and fluid phases. The rise in the value of the radiation parameter advances the heat transference of both phases. The rise in the value of the Biot number improves the rate of heat transfer. Finally, increasing the value of the radiation parameter improves the rate of heat transfer.     

Impact of activation energy and gyrotactic microorganisms on flow of Casson hybrid nanofluid over a rotating moving disk

Many models of various non-Newtonian fluid flows for different geometries are available for analyzing the mass and heat transfer. Nevertheless, for researchers, it is challenging to choose the most suitable model for a specific geometry. Here, we have adopted a modified Buongiorno model to explore the impact of activation energy on the Casson hybrid nanofluid flow over an upward/downward-moving rotating disk filled with the gyrotactic microorganisms. Moreover, the external magnetic field can establish the magnetic effect, which normalizes the features of heat, mass transfer, and fluid flow. Here, we used silver and copper as nanoparticles suspended in human blood as the carrier fluid. The modeled partial differential equations are converted to ordinary differential equations by opting suitable similarity variables. The numerical solutions of these reduced equations are attained by means of Runge–Kutta–Fehlberg fourth-fifth-order method by adopting a shooting scheme. An investigation of the attained outcomes reveals that the flow field is affected appreciably by the activation energy, bioconvection, and magnetic effect. Peclet and concentration difference numbers diminish the microorganism's profile. A rise in values of the Brownian motion parameter leads to an increase in the rate of heat transfer.     

Modeling of liquid water transport in a proton exchange membrane fuel cell gas flow channel with dynamic wettability

Liquid water transport in the gas flow channel is significantly important for the water removal and management in proton exchange membrane fuel cells. Previous numerical studies consider a single and constant static contact angle for the liquid water transport on the channel surface, which is insufficient to account for the dynamic wettability behavior of the flow. In this study, a dynamic wettability model is developed that incorporates the sliding angle and dynamic contact angles for the simulation of water transport in the flow channel. It is found that both the sliding and dynamic contact angles have significant impact on the characteristics of the water transport and dynamics in the flow channel. Water spreading on the channel surface is elliptic, and its minor and major axes oscillate out of phase with the droplet height. The pressure loss for the 2‐phase flow in the channel is directly related to this oscillation and deformation of the droplet shape. Flow channel surface with a small sliding angle facilitates the water transport and removal and reduces the associated pressure loss in the channel. The conventional static wettability model would overpredict droplet deformation and breakup as well as the pressure loss in the channel.     

Influence of Hall and Joule heating on a magnetic nanofluid (Fe3O4) flow on a rotating disk with generalized slip condition

This study analyzes Hall current and Joule heating effects on the ferro-nanofluid flow by the rotation of the disk incorporated with generalized slip condition. By using the well-known Von Karman transformation, formulated flow equations are modeled into ordinary differential equations. Numerical solutions of the governing flow equations are attained by utilizing the shooting method consolidated with the fourth-order Runge–Kutta scheme. The impacts of different parameters on skin friction coefficient, velocity, temperature, and Nusselt number are given in graphs and tables and investigated in detail. Furthermore, an association with formerly published articles is given and met in remarkable correspondence.     

Motion of droplets induced by the Marangoni force on a wall with a temperature gradient

Motion of silicone oil and water droplets induced by the Marangoni force was numerically simulated by using two‐ and three‐dimensional second‐order finite difference methods with the CIP and the level set methods. The surface tension was introduced by the continuum surface force (CSF) method. The results clearly showed the flow induced by the Marangoni force and the dependence of droplet velocity on droplet size, contact angle, temperature gradient, and fluid properties. The Marangoni force balanced with the viscous force in the small contact angle case; on the other hand, in the large contact angle case, it balanced with the normal component of surface tension. As for the effect of fluid properties on droplet motion, the temperature coefficient of surface tension had a much larger effect than did viscosity, thermal diffusivity, or surface tension. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(2): 81–93, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20004     

Analytical solution of generalized coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads

In this article, a fully analytical solution of the generalized coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads, based on Lord–Shulman model, is presented. The general forms of axisymmetric thermal and mechanical boundary conditions as arbitrary time-dependent heat transfer and traction, respectively, are considered at the inner and outer radii of the disk. The governing equations are solved analytically using the principle of superposition and the Fourier–Bessel transform. The general closed form solutions are presented for temperature and displacement fields. To validate the solutions, the results of this study are compared with the numerical results available in the literature, which show good agreement. For the temperature, displacement and stresses, radial distributions, and time histories are plotted and discussed. The propagation of thermoelastic waves and their reflection from the boundary of the disk are clearly shown. Moreover, effects of relaxation time and angular velocity on temperature, displacement, and stress fields are investigated.     

FHD flow and heat transfer over a porous rotating disk accounting for Coriolis force along with viscous dissipation and thermal radiation

The prime concern of the current findings includes the effect of viscous dissipation and nonlinear thermal radiation on the study of ferrofluid flow and heat transfer past a porous rotating disk. The time-independent flow of incompressible ferrofluid is modeled for the considered geometry, and via similarity transformations, the given system is converted to a dimensionless system of the nonlinear ordinary differential equations. Here, the findings are explored computationally with help of Maple software. The study exhibits the effect of the involved emerging parameters: the interaction parameter $B$, Prandtl number $Pr$, rotation parameter $R$, radiation parameter $Qr$, Eckert number $Ec$, and these are discussed graphically. Moreover, the numerical values of heat transfer rate and skin frictions are also presented in tabular form. From the perspective of numerical findings, it is perceived that the radial flow is dominant when we increase the rotation of the disk. Furthermore, the magnitude of magnetic-fluid temperature is enhanced with the surge in the magnetic field, viscous dissipation, and thermal radiation mechanism. Finally, the current research can successfully fill a gap in the existing literature.     

加热板液滴蒸发的理论分析及实验研究

液滴蒸发是由气-液浓度差驱动的一种常见而复杂的扩散现象.通过实验与理论相结合对去离子水在玻璃表面和有机硅油表面的蒸发特性进行研究,测量了液滴接触角和接触直径随时间的动态演变过程.结果 发现:玻璃表面的液滴蒸发为典型的定底半径模式和混合模式;而液滴在有机硅油表面较为特殊,除了定底半径模式和混合模式还有周期性的黏滑模式.出...     

On MHD and slip flow over a rotating porous disk with variable properties

The steady laminar magnetohydrodynamics (MHD) flow of a viscous Newtonian and electrically conducting fluid over a rotating disk with slip boundary condition is investigated taken into account the variable fluid properties (density, (ρ), viscosity, (μ) and thermal conductivity, (κ)). These fluid properties are taken to be dependent on temperature. The governing equations, which are partial and coupled, are transformed to ordinary ones by utilizing the similarity variables introduced by von Karman and the resulting equation system is solved numerically by using a shooting method. The resulting velocity and temperature distributions are shown graphically for different value of parameters entering into the problem. The numerical values of the radial and tangential skin-friction coefficients and the rate of heat transfer coefficient are shown in tabular form.     

Three‐dimensional boundary layer flow over a rotating disk with power‐law stretching in a nanofluid containing gyrotactic microorganisms

The nanofluid model containing microorganisms over a rotating disk with power‐law stretching is constructed in this paper. The combined effects of nanoparticles and microorganisms in nanofluid are investigated by solving the governing equations numerically. The numerical solutions of the skin friction coefficient and local Nusselt number are in agreement with the corresponding previously published results. The quantities of physical interest are graphically presented and discussed in detail. It is found that the power‐law stretching index has produced profound influence on the flow as well as the heat and mass transfer.     

Binary chemical reaction with activation energy in radiative rotating disk flow of Bingham plastic fluid

This article presents flow, heat and mass transfer phenomena in Bingham plastic fluid. The flow channel is considered to be a rotating disk with a slip which is different in span and streamwise directions, and heat transfer is investigated using dissipation term of the fluid. Arrhenius activation energy and binary chemical reaction are the imperative features of the study of mass transfer. Bingham plastic fluid and anisotropic slip are the key factors of the study due to their numerous applications in manufacturing industries. On the other hand, the radiative heat transfer phenomenon is considered which is widely used in nuclear and power generating systems. The partial differential equations that govern the flow, and heat and mass transfer are converted into ordinary differential equations by utilizing von Kármán's similarity transformation for rotating disk flows. The velocity, temperature, and concentration profiles and some important physical quantities are examined against important flow parameters. It is observed that the thermal radiation showed an increasing effect on temperature profile and the activation energy enhanced the mass transfer rate. The radial slip increased the volumetric flow rate and reduced the boundary layer thickness. The tangential slip reduced the volumetric flow rate and increased the boundary layer thickness.