A study on thermal conductivity of a quasi‐ordered liquid layer on a solid substrate

In the present paper, a study on thermal conductivity of a quasi‐ordered liquid layer on a solid surface was performed by molecular dynamic simulation. Results showed that the motion of the molecules and their radial distribution function in the quasi‐ordered liquid layer were similar to those of solid molecules. By using the Green–Kubo formula, the thermal conductivity of the layer was calculated. It was found that it increased with the increase of the parameters of ordering. The size effect and the influence of the boundary condition were also discussed. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(7): 429–434, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20171     

Solidification of electrically conducting liquid flow driven by shear and pressure gradients subject to viscous and Joule heating

Solidification of a liquid in motion driven by shear and pressure gradients occurs in many natural settings and technological applications. When the liquid is electrically conducting, its solidification rates can potentially be modulated by an imposed magnetic field. The shearing motion results in viscous dissipation and the Lorentz force induced by the magnetic field causes Joule heating of the fluid, which can influence the structure of the flow, thermal fields, and thereby the solidification process. In this study, a mathematical model is developed to study the combined effects of shear and pressure gradients in the presence of a magnetic field on the solidification of a liquid between two parallel plates, with one of them being insulated and under constant motion, and the other being cooled convectively and at rest. Under the quasi-steady assumption, closed-form semianalytical solutions are obtained for the instantaneous location of the solid–liquid interface, Nusselt number, and dimensionless power density as a function of various characteristic parameters such as the Hartmann number, pressure gradient parameter, Brinkman number, and Biot number. Furthermore, an interesting remelt or steady-state condition for the interfacial location is derived as arising from the competing effects of the solid side heat flux and viscous dissipation and Joule heating on the liquid side. The newly derived analytical results are shown to reduce to the various classical results in the limiting cases. A detailed systematic study is performed by the numerical solution of the semianalytical formulation, and the effects of different characteristic parameters on the solidification process are discussed.     

Solidification of a liquid about a cylindrical pipe

The temperature distribution and the rate of removal of heat by a coolant are predicted for the process of solidification of a liquid about a cold, isothermal pipe. The heat balance integral method incorporating spacial sub-division is used. It is found that acceptable results can be obtained by using only a small number of sub-divisions together with a piece-wise, linear profile. Furthermore, the results illustrate that the sensitivity which is normally associated with the heat balance integral method is overcome.     

Solidification of a supercooled liquid in stagnation-point flow

The solidification of a thermally supercooled liquid in stagnation-point flow is investigated. Due to the advancing solidifying front, both the temperature and flow fields are time dependent. A numerical solution to the problem using an interface tracking method is compared to analytical solutions obtained for instantaneous similarity (short time solution) and quasi-steady state (long time solution). The results show that the velocity of the solid-liquid interface eventually reaches a constant value and that the magnitude of the interface velocity increases with greater thermal supercooling. The solution to this problem provides insight into more complicated solidification problems relating to crystal growth.     

Stability of free convection in a narrow porous layer subject to rotation

The stability and onset of convection in a narrow, fluid saturated porous layer subject to a centrifugal body force due to rotation is investigated analytically. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number. As a result, the corresponding eigenfunctions are evaluated at the convection threshold.     

Mushy zone equilibrium solidification of a semitransparent layer subject to radiative and convective cooling

Equilibrium solidification in a semitransparent planar layer is studied using an isothermal mushy zone model. The layer is made up of a pure material being emitting, absorbing and isotropically scattering and is subject to radiative and convective cooling. The model involves solving simultaneously the transient energy equation and the radiation transport equation. An implicit finite volume scheme is employed to solve the energy equation, with the discrete ordinate method being used to deal with the radiation transport. A systematical parametric study is performed and the effects of various materials optical properties and processing conditions are investigated. It is found that decreasing the optical thickness and increasing the scattering albedo both lead to a wider mushy zone and a slower rate of solidification.     

Solidification of a ternary melt from a cooled boundary, or nonlinear dynamics of mushy layers

We present a mathematical model and its analytical solution describing directional solidification of a ternary (three-component) system cooled from below. We focus on the solidification theory in the presence of two distinct mushy layers: (1) solidification along a liquidus surface is characterized by a primary mushy layer, and (2) solidification along a cotectic line is characterized by a secondary (cotectic) mushy layer. We consider the case when the phase transition temperatures in two mushy layers represent arbitrary functions of the compositions. We obtain an exact analytical solution of the nonlinear set of equations and boundary conditions in the case of a self-similar solidification scenario. Model predictions are in good agreement with existing experimental data.     

On oscillatory Marangoni convection in a rotating fluid layer subject to a uniform heat flux from below

Linear stability theory is applied to the problem of Marangoni convection in a rotating horizontal fluid layer subject to a uniform heat flux from below. The fluid layer is bounded from below by a rigid boundary and above by a deformable free surface. We show how the P_r–T_a parameter space is divided into regions in which steady or oscillatory convection is preferred.     

Convection and instability of thermocapillary flow in a liquid bridge subject to a non-uniform rotating magnetic field

A three-dimensional liquid bridge is considered in this study to numerically investigate the effects of an external non-uniform rotating magnetic field (RMF) on the thermocapillary flow in semiconductor melt under microgravity. Simulations are carried out to examine the convection and instability features of the thermocapillary flow over a range of Marangoni numbers (Ma = 15–50) under a non-uniform RMF. The present results show that applying an external non-uniform RMF enhances the maximum tangential velocity and depresses the maximum axial velocity. As a consequence, an approximately axisymmetric flow is maintained in the melt under the effect of the non-uniform RMF, which is beneficial for growing high quality crystal. Further investigation of the thermocapillary flow subject to different non-uniform RMFs (corresponding to Taylor numbers Ta = 3.8 × 10²–1.86 × 10⁴ and Rotating Reynolds number Re_ω = 2.2 × 10⁴) reveals that the thermocapillary convection may undergo a transition from the approximately axisymmetric steady flow to a periodically oscillatory flow for Ma above a critical value. The critical Ma generally increases with the intensity of the non-uniform RMF.     

Evaporation-induced Benard convection in a thin liquid layer

Evaporation-induced Benard convection in a thin liquid layer is found to occur in experimentally and theoretically as a separate mechanism from Rayleigh–Benard and Marangon–Benard types of convection. The phenomenon is induced by evaporation at the liquid surface, irrespective of the liquid layer bottom being heated or adiabatic. The mechanism is theoretically investigated by numerically solving the two-dimensional governing equations through discretization by means of a finite difference technique. Experimentally, cellular flow patterns are disclosed by means of a tracer method, and the temperature–time history is monitored in the liquid layer using thermocouple measurements. It is found that evaporation at the free surface of a thin liquid layer results in a negative temperature gradient in the upper stratum, in which cellular convection occurs irrespective of zero temperature gradient prevailing in the remaining lower stratum. In other words, a thin liquid layer having an evaporating surface forms two strata: heat convection with fluid motion in the upper stratum, and insulation in the lower stationary one. Copyright © 2002 John Wiley & Sons, Ltd.     

A boundary layer analysis of electro-magneto-hydrodynamic forced convective transport over a melting slab

In this work, a boundary layer based integral approach is employed for analyzing the coupled problem of electro-magneto-hydrodynamic convection and melting of an electrically conducting material. The melting process is assumed to occur on a semi-infinite flat horizontal slab. The simultaneous non-linear ordinary differential equations, originated out of the boundary layer analysis, are solved by employing the fourth order Runge–Kutta method, in a novel iterative framework. Simulation studies are executed for representative systems of materials, with a wide range of variation of processing parameters. Effects of melt superheat and the strengths of magnetic and electric fields on the melting process are analyzed in details. Fundamental physical principles are subsequently outlined for controlling the melting process through combined electrical and magnetic fields, on the employment of judicious combinations of the relevant operating parameters.     

Solidification and melting behaviors and characteristics of molten salt in cold filling pipe

The solidification and melting phenomena and performances of molten salt during cold filling process in a straight pipe are numerically investigated using volume of fluid model. As the molten salt is filled into a cold pipe, the molten salt adjacent to the cold wall is rapidly cooled, and the solidification phenomena appears. After the whole pipe is filled, the solidification layer begins to melt by high temperature fluid heating. Because of the solidification layer, the flow section obviously shrinks, and the pressure loss remarkably increases. During the solidification and melting processes, the fluid temperature in the region with phase change only varies near the freezing point, and it quickly rises after the melting process. Because of the absorption or release of latent heat, the boundary heat flux of molten salt is increased in the solidification region, while it will be decreased in the melting region. As the inlet temperature rises, the pressure loss apparently decreases with the thickness of solidification layer decreasing. However, when the inlet flow velocity increases, the thickness of solidification layer decreases, but the flow resistance without phase change increases, so the pressure loss has a maximum at moderate flow velocity.     

Soret effect on the boundary layer flow regime in a vertical porous enclosure subject to horizontal heat and mass fluxes

The combined thermo- and double-diffusive convection in a vertical tall porous cavity subject to horizontal heat and mass fluxes was investigated analytically and numerically using the Darcy model with the Boussinesq approximation. The investigation focused on the effect of Soret diffusion on the boundary layer flow regime. The governing parameters were the thermal Rayleigh number, R_T, the Lewis number, Le, the buoyancy ratio, N, the Soret parameter, M, which characterized the Soret effect, and the aspect ratio of the enclosure, A_r. The results demonstrated the existence of a boundary layer flow solution for which the Soret parameter had a strong effect on the heat and mass transfer characteristics. For M ≠ 1 and M ≠ −1/Le, the profiles of the vertical velocity component, v, temperature, T, and solute concentration, S, exhibited boundary layer behaviors at high Rayleigh numbers. Furthermore, as R_T increased, the temperature and solute concentration became vertically and linearly stratified in the core region of the enclosure. The thermo-diffusion effect on the boundary layer thickness, δ, was discussed for a wide range of the governing parameters. It was demonstrated analytically that the thickness of the boundary layer could either increase or decrease when the Soret parameter was varied, depending on the sign of the buoyancy ratio. The effect of R_T on the fluid flow properties and heat and mass transfer characteristics was also investigated.     

Thermocapillary instability in a horizontal liquid layer subjected to a transverse magnetic field and irradiation

With the presence of a transverse magnetic field and external incident radiation, thermocapillary instability in a horizontal liquid layer is investigated using linear stability theory. Assuming that the neutral state is stationary, the critical conditions leading to the onset of convective motion are determined numerically. This article examines the effects of the magnetic field, non-uniform volumetric energy source and radiative surface properties on convective instability. The dependence of the stability characteristics on the optical thickness, surface reflectivity, the magnetic field intensity, and the external radiative sources is analyzed in detail.     

A cubic heat balance integral method for one-dimensional melting of a finite thickness layer

The work in this paper concerns the one-dimensional melting of a finite thickness layer. An asymptotic series solution describes the temperature in the melt regions. In the solid region the thermal boundary layers are approximated by a cubic polynomial. Results are compared with the exact solution for a semi-infinite block, and shown to agree to within less than 1%. The method is then applied to a situation where no analytical solution is available. A finite thickness frozen solid is placed on a warm substrate in a warm environment: initially the base of the solid heats to the melting temperature when a single melted region develops and subsequently a second melting front appears on the top boundary. We also present an example relevant to heating an ice layer from below, which occurs with de-icing systems.     

Free convection heat and mass transfer during pool penetration into a melting miscible substrate

A theoretical investigation is made of the process of free convection melting of a solid slab by an overlying hot liquid pool. The solid, when molten, is lighter than and miscible with the pool material. Systematic mathematical approximations to the Boussinesq equations of motion are performed to determine the behavior of the temperature and the concentration fields in two different flow regions. These are the boundary layer region at the melting interface and the turbulent core region in the bulk pool. The dependence of the melting rate on various controlling parameters, including the Grashof number based on the pool-to-substrate density ratio, the external Stefan number based on the pool-to-substrate temperature difference, and the internal Stefan number based on the freezing-point depression, is obtained by matching the boundary layer solution and the turbulent core solution in the region of overlap. Comparison of the present theory is made with existing experiments and found to be good.     

Study on the performance of a proton exchange membrane fuel cell related to the structure design of a gas diffusion layer substrate

Although characteristics of the gas diffusion layer (GDL) affect the performance of a proton exchange membrane fuel cell (PEMFC), mass transfer mechanisms inside the GDL and the performance of the PEMFC have not been directly correlated. To determine the design parameters of the GDL, the effects of substrate design of the GDL on performance of a PEMFC are investigated. By adding an active carbon fiber (ACF), which has a high surface area, the substrate is designed to have a different pore size structure. The results show that steady-state and transient responses are determined by capillary pressure gradient characteristics of the GDL made by pore size distribution of the substrate. The small macro-pore functions as water-retaining passage and the large macro-pore functions as water-removal passage. It is concluded that both small and large macro-pore must be present on the substrate to facilitate its function in a wide range of operating conditions.     

On evaporation of thin liquid films subjected to ultrasonic substrate vibration

Theoretical and experimental studies on evaporation of thin and ultrathin liquid films (all volatile or liquid solutions) are desirable, but scarce. In this context, excitation of thin liquid films by (ultrasonic) vibration is also an interesting theoretical and applied research direction affecting the hydrodynamics, stability, and evaporation of thin liquid films. In this study, the evaporation history of drop-cast stationary and excited thin liquid films subjected to vertical and horizontal ultrasonic vibration is studied, and unprecedented results are obtained and discussed. The evaporation history of two model thin liquid films is captured using video camera and high precision digital balance. Since evaporation of excited thin films by substrate vibration resembles forced convection, the convective heat transfer coefficient and consequently the evaporation rate of the excited thin films are expected to increase compared to those of non-excited thin films. Experimental results substantiate this hypothesis. It is further shown and discussed that the films excited by horizontal ultrasonic substrate vibration evaporate faster than those excited by vertical vibration.     

Thermocapillary flow in an annular liquid layer painted on a moving fiber

In the present paper, a theoretical model is studied on the flow in the liquid annular film, which is ejected from a vessel with relatively higher temperature and painted on the moving solid fiber. A temperature gradient, driving a thermocapillary flow, is formed on the free surface because of the heat transfer from the liquid with relatively higher temperature to the environmental gas with relatively lower temperature. The thermocapillary flow may change the radii profile of the liquid film. This process analyzed is based on the approximations of lubrication theory and perturbation theory, and the equation of the liquid layer radii and the process of thermal hydrodynamics in the liquid layer are solved for a temperature distribution on the solid fiber.