SOLIDIFICATION OF A PURE METAL WITH FINITE THERMAL CAPACITANCE ON A SINUSOIDAL MOLD SURFACE

Previous models of mold microgeometry-induced gap nucleation during pure metal solidification neglected the thermal capacitance of the solidifying shell: this is equivalent to the assumption that the shell has a small Stefan number. Although this assumption leads to steady heat conduction in the shell, and hence simplifies the solution for the thermal field, the corresponding assumption of a small Stefan number material is generally not appropriate for metals. In the present work, we remove the small Stefan number restriction used in a previous model for solidification of a pure metal on a rigid, perfectly conducting mold. The mold has a sinusoidal surface microgeometry for which the ratio of the amplitude to the wavelength is much less than one. This makes the aspect ratio a convenient perturbation parameter. Molten metal initially at its fusion temperature is assumed to wet the mold surface perfectly, which is held a constant temperature below the fusion temperature. The temperature field in the growing metal shell is numerically evaluated, and the instantaneous temperature field is incorporated into an analytical solution for the stress field in the shell. The evolving thermomechanical distortion of the shell is modeled assuming that the shell material follows a thermohypoelastic constitutive law that is a rate formulation of thermoelasticity. The contact pressure profile at the shell/asperity interface, which is indicative of shell distortion due to the asperity geometry, is obtained from the stress field. The effects of the mold wavelength and shell thermal capacitance on the contact pressure, temporal and spatial evolution of gap nucleation at the shell/mold interface, and mean shell thickness are examined for pure aluminum and iron shells.     

STRAIN RATE RELAXATION EFFECT ON FREEZING FRONT GROWTH INSTABILITY DURING PLANAR SOLIDIFICATION OF PURE METALS,PART 1. UNCOUPLED THEORY

Previous models of thermomechanically induced freezing front growth instability have assumed that the casting accumulates elastic strains as it solidifies. While this assumption is useful in providing insight into solidification thermomechanics, it fails to account for inelastic strains that normally accompany elevated temperature deformations. In this paper, growth instability during solidification of a pure metal is reexamined, assuming that the strain rate within the solidifying shell is the sum of elastic, thermal, and viscous components. This requires that a theoretical framework for plane strain thermoviscoelasticity be developed for a solidifying metal. The viscous component leads to strain rate relaxation within the casting and subsequently influences the evolution of the contact pressure and macromorphology of the freezing front. We define a strain rate relaxation parameter that determines the extent to which the casting deforms due to viscous creep. Both short-time and long-time solutions for the contact pressure are developed and subsequently examined for selected values of the strain rate relaxation parameter. The thermal and mechanical fields are assumed to be uncoupled along the metal /mold interface in the present paper while they are coupled along this interface in the companion paper.     

A THERMOMECHANICAL MODEL OF SOLIDIFICATION ON A MOLD MOVING WITH CONSTANT VELOCITY

A thermomechanical model of pure metal solidification on a moving mold plate is considered. The goal of the model is to obtain a formula for the contact pressure at the shell/mold interface as the mold moves into the molten liquid. From the contact pressure it is possible to infer the effects of the mold velocity and the mold microgeometry on the time and location of gap nucleation which results from irregular distortion of the shell as it grows from the melt. The mold, which moves at a constant velocity into the molten liquid, has a sinusoidal surface with a low aspect ratio: this means that its wavelength greatly exceeds its amplitude. The mold is of infinite area and is assumed to be perfectly conducting and thermomechanically rigid. We therefore neglect the complexities associated with the physics of edge constraints and/or free boundaries of the solidifying shell and the interacting distortions between deformable mold and shell materials along their interface. The ratio of the velocity of the solid/liquid interface to the mold velocity is identified as another dimensionless parameter in the analysis. In order to arrive at an analytical solution for the contact pressure along the shell/mold interface, we assume that this parameter is small. This makes the velocity ratio a convenient perturbation parameter for the analysis of thermomechanical distortion of the thin shell material as it grows from the melt. This necessarily limits the analysis to situations where the mold moves at faster rather than slower speeds. It is assumed that there is zero tangential shear stress between the fluid and the solidifying shell. As the molten liquid flows over the mold, it perfectly wets the surface. This precludes wetting effects due to surface tension. A hypoelastic constitutive law, which is a rate formulation of thermoelasticity, is assumed to govern deformation of the shell as it grows from the molten liquid. Latent heat liberated at the freezing front is extracted across a constant contact resistance at the shell/mold interface. Peculiar fluid motion at the tip is neglected. A solution for the contact pressure that is valid near the liquid surface (i.e., the meniscus) is derived from the main theoretical developments. Beyond the time of gap nucleation at the shell/mold interface, the model is no longer valid since it cannot account for gross distortion of the shell (i.e., distortions that greatly exceed the spatial perturbations considered in the model).     

A predictive model for the evolution of the thermal conductance at the casting–die interfaces in high pressure die casting

An analytical model is proposed to predict the time varying thermal conductance at the casting–die interface during solidification of light alloys during High pressure Die Casting. Details of the topography of the interface between the casting and the die are included in the model through the inclusion of solid surface roughness parameters and the mean trapped air layer at the interface. The transitory phase of the interfacial thermal conductance has been related to the degradation of contact as solidification progresses through the casting thickness. The modelled time varying thermal conductance showed very good agreement with experimentally determined values for different alloy compositions and casting geometries. The analysis shows that the parameters that govern the thermal conductance are different for the first stage of contact compared to the second stage of contact when the alloy begins to solidify.     

Physical modeling and numerical investigation of fluid flow and solidification behavior in a slab caster mold using hexa-furcated nozzle

Slag entrapment from metal–slag interface during continuous casting operations has been a major area of concern for steelmakers globally. The presence of inactive regions in the upper region of the mold poses another challenge. Proper flow behavior of the molten metal coming out of the nozzle in the mold is required to overcome these challenges. Nozzle design greatly affects the flow pattern of the molten steel inside the mold. The present investigation is an attempt to study the flow and solidification behavior in a slab caster mold with the use of a novel-designed hexa-furcated nozzle using numerical investigation results. The casting speed and submerged entry nozzle (SEN) depth are varied to study the effect of these parameters on minimizing the inactive zones in the mold and the steel/slag interface fluctuations. The results show that the interface fluctuation increases at higher casting speed and lower SEN depth. The residence time distribution (RTD) analysis was also performed for different cases to investigate the flow behavior. The validation of the fluid flow and RTD curve inside the computational domain is carried out with the use of physical modeling.     

Spatial variation of heat flux at the metal–mold interface due to mold filling effects in gravity die-casting

Most of the research work pertaining to metal–mold heat transfer in casting solidification either assumes no spatial variation in the air gap formation or limits the study to only those experimental systems in which air gap formation is uniform. However, in gravity die-casting, filling effects induce variation in thermal field in the mold and casting regions. In this paper, we show that this thermal field variation greatly influences the time of air gap initiation along a vertical mold wall, which subsequently leads to the spatial variation of air gap and in turn, the heat flux at the metal–mold interface.In order to study the spatial variation of heat flux at the metal–mold interface, an experimental setup that involved mold filling was devised. A Serial-IHCP (inverse heat conduction problem) algorithm was used to estimate the multiple heat flux transients along the metal–mold interface. The analysis indicates that the fluxes at different mold segments (bottom, middle, and top) of the metal–mold interface reaches the peak value at different time steps, which shows that the initiation of air gap differs along the mold wall. The experimental and numerical results show that the heat transfer in the mold is two-dimensional during the entire period of phase change, which is initially caused by the filling effects and further enhanced by the spatial variation of the air gap at the metal–mold interface.     

Development of novel glass-based composite seals for planar intermediate temperature solid oxide fuel cells

Novel glass-based composite seals prepared by tape casting are evaluated as sealing materials in solid oxide fuel cell. The leakage rates are measured at the inlet pressure of 1, 2 and 3 psi under different compressive stresses and temperatures respectively. The results show that all of measured leakage rates are lower than 0.01 sccm cm⁻¹ and increase with higher inlet pressure and lower test temperatures. The leakage rates during thermal cycling are conducted under a compressive stress of 20 psi at 750 °C, which indicate excellent thermal cycle stability of the seals. Good compatibility between seals and the adjacent components provide well interface contact which could avoid the formation of leakage paths. When the seal is applied for single cell testing, the open circuit voltage of 1.13 V and undetectable degradation clearly demonstrate the applicable performance of glass-based composite seal in solid oxide fuel cell.     

THERMOELASTICITY AND CONTACT

Thermoelastic deformations can have a significant effect on the contact between elastic bodies, particularly in cases where the thermal boundary conditions at the interface are influenced by the contact pressure. In the classical Hertzian problem, the size of the contact area depends on the magnitude and direction of heat flow between the bodies. Idealized thermal boundary conditions can lead to ill-posed steady-state problems, but this difficulty is resolved by assuming a pressure-dependent thermal contact resistance. Steady states of the system can be unstable even when they are unique, in which case the behavior is either oscillatory or involves the steady motion of a contact pressure wave along the interface. Analytical and numerical perturbation methods have been developed to investigate the stability problem. These results find applications in heat transfer processes involving solid-solid contact, including the solidification of castings. In brakes and clutches, the heat generated at the sliding interface causes thermal distortion leading to ''frictionally excited thermoelastic instability'' or ''TEI,'' in which contact becomes localized in ''hot spots'' at the interface. Recent results enable us to make good predictions of the conditions under which this occurs.     

Role of the Mold Properties on Gap Nucleation in Solidification

The role of the mold properties on gap nucleation in pure metal solidification is investigated. The mold is assumed to be finite and deformable, and has a sinusoidal surface micro-geometry. Unlike previous models, the model developed herein assumes that the mold material has a non-negligible thermal capacitance. Of particular interest are the roles played by the mold thickness and mold thermal capacitance on the existence of critical mold surface wavelength that corresponds to the situation where both contact pressure and its time derivative simultaneously fall to zero. The present work also assumes that the thermal and mechanical problems in the mold-shell interface are uncoupled. It is shown that the inclusion of the thermal capacitance of the mold material, together with thermal capacitance of the shell and the mold distortion, may be sufficient to predict a critical wavelength beyond which no gap nucleation occurs at the troughs. The role of the mold properties is examined through qualitative comparisons of the present and previous models. Gap nucleation times, associated mean shell thicknesses, and critical wavelengths are calculated for pure copper and pure iron molds under identical process conditions. It is found that a copper mold leads to faster gap nucleation compared to an iron mold. The associated critical wavelengths of iron molds are shown to be larger than those of copper. An optimum mean mold thickness corresponding to the longest gap nucleation time for a given set of process parameters is determined. The effect of the mean pressure on the optimum mold thickness is also investigated.     

Effect of pressure on heat transfer coefficient at the metal/mold interface of A356 aluminum alloy

The aim of this paper is to correlate interfacial heat transfer coefficient (IHTC) to applied external pressure, in which IHTC at the interface between A356 aluminum alloy and metallic mold during the solidification of casting under different pressures were obtained using the inverse heat conduction problem (IHCP) method. The method covers the expedient of comparing theoretical and experimental thermal histories. Temperature profiles obtained from thermocouples were used in a finite difference heat flow program to estimate the transient heat transfer coefficients. The new simple formula was presented for correlation between external pressure and heat transfer coefficient. Acceptable agreement with data in literature shows the accuracy of the proposed formula.     

Research Regarding Heat Exchange Through Nanometric Polysynthetic Thermal Compound to Cooler–CPU Interface

This article documents some of the factors that influence the heat transfer through polysynthetic thermal compounds at the central processing unit (CPU)/heat sink interface. First, special attention is paid to assessing the effect of mechanical and thermal properties of the contacting bodies, applied contact pressures, and surface roughness characteristics, as well as the use of different thermal interface materials on the maximum temperature experienced by the CPU. Second, it can be appreciated that good wetting of the mating surfaces and the retention of asperity micro-contacts can become critical elements in effectively removing the heat generated by the CPU. This study uses the Holman model for calculating the heat transfer, indicating the role of thermal contact resistance. The mathematical results clearly indicate that any strain in the interface material leads to a change in thermal contact resistance, with an effect on CPU overheating. Experimentally obtained images with an atomic force microscope clearly revealed that eliminating micro-gaps using thermal interface materials can facilitate the heat transfer by significantly lowering the thermal contact resistance of the CPU/heat sink assembly. This effect is amplified by the plastic deformation of micro-contacts due to high contact pressures and lower micro-hardness levels.     

NONUNIQUENESS AND STABILITY FOR HEAT CONDUCTION THROUGH A DUPLEX HEAT EXCHANGER TUBE

An analysis is given for radial heat flow through the wall of a duplex heat exchanger tube with a pressure or gap-dependent contact resistance at the interface. Thermal expansion of the tube changes the value of this resistance, and it is shown that for certain thermal conditions there will be more than one steady-state solution. The stability of these multiple solutions is then investigated using a perturbation method, and it is found that there is always an odd number of solutions, alternately stable and unstable.

This kind of behavior has been observed in other thermoelastic contact problems, but this is the first example in which it has been exhibited in a case of contact between similar materials.     

Investigation on the weldline strength of thin-wall injection molded ABS parts

It is well known that the weldline reduces the mechanical performance of the conventional injection molded parts. Yet, systematic researches and reports on weldline strength of thin-wall molded parts are still insufficient. This study investigates the influence of processing conditions on the weldline strength of thin-wall Acrylonitrile Butadiene Styrene Copolymer (ABS) parts. The relevant parameters include melt temperature, mold temperature, injection speed and packing pressure. Tensile tests on specimens of different thickness (1.0, 1.2 and 2.5 mm) are conducted. Comparisons on tensile strength for single-gate molded specimens (without weldline) with those of double-gate molded specimens (with weldline) are presented. From the experimental results, it was found that weldline specimens molded at higher melt temperature, higher mold temperature, faster injection speed and lower packing pressure would result in better mechanical strengths. Higher melt and mold temperatures not only lower the residual stress but also help the diffusion of molecular chains leading to a higher degree of surface bonding at the weldline interface. On the other hand, high packing pressure leads to higher residual stress formation and reduces the molecular bonding rate. In addition, part thickness also exhibits significant effect on weldline strength. A regression analysis combined with fitting model seems to correlate process conditions and weldline strength reduction quite well.     

Effect of decoration film on mold surface temperature during in-mold decoration injection molding process

In-mold decoration (IMD) during injection molding is a relatively new injection molding technique and has been employed for plastic products to improve surface quality and achieving colorful surface design, etc. During IMD processing, the film is preformed as the shape of mold cavity and attached to one side of the mold wall (usually cavity surface), then molten polymer is filled into the cavity. Heat transfer toward the mold cavity side during molding IMD part is significantly retarded because the film is much less thermal conductive than metal mold. To investigate the effect of film on temperature field, polycarbonate (PC) was injection molded under various conditions including coolant temperature, melt temperature, film material and film thickness. Simulations were also conducted to evaluate the melt–film interface temperature and its influence from film initial temperature and film thermal properties. For PC film, it was found that the heat transfer retardation results in the mold temperature drop in cavity surface and the maximum temperature drop as compared to that of conventional injection molding without film may be as high as 17.7 °C. For PET film, this maximum mold temperature drop is about 13 °C. As PC film thickness increases, the retardation-induced mold temperature difference also increases. The initial film temperature (30 °C and 95 °C) may affect the melt–film interface temperature at the contact instant of melt and film by about 12 °C to 17 °C. When thermal conductivity of film increases from 0.1 W/(m–k) to 0.2 W/(m–k), melt–film interface temperature may vary by 22.9 °C. The simulated mold temperature field showed reasonable agreement with experimental results.     

Experimental investigation of contact resistance in adsorber of solar adsorption refrigeration

The key component of a solar adsorption refrigeration unit is the adsorber packed with an adsorbent such as zeolite, active carbon and CaCl₂. One essential problem faced is the poor heat transfer in adsorbers, which strongly influences the performance of the system. Poly-aniline, with the advantage of superior thermal conduction, was introduced into an adsorber to increase the thermal conductivity of the adsorbents. As the thermal conductivity coefficient of adsorbent in the adsorber is enhanced, the thermal contact resistance of the interface becomes a significant proportion and needs to be improved. The heat transfer of solid interfaces, particularly the effects of the adsorbent granule or block with rough surfaces, is studied in this paper. Methods for decreasing the contact resistance using spreading adhesive or exerting pressure on the interface are presented and analysed. A test facility and relevant procedure are developed to measure the effects of different interfaces on the contact resistance. The heat transfer at the interface between the copper surface and the adsorbent granule or block is investigated, and its effect in improving the thermal performance of the adsorber in solar adsorption refrigeration is compared. The experimental results show that exerting pressure or spreading adhesive on the interface can reduce the contact resistance significantly without affecting the mass transfer of the adsorbent in an adsorber.     

Determination of the interfacial heat transfer coefficient h in unidirectional heat flow by Beck's non linear estimation procedure

In the numerical simulation of casting solidification, the thermal behavior of the casting/mold interface is characterized by the interfacial heat transfer coefficient, ‘h’. The determination of h is difficult as it involves the solution of the Inverse Heat Conduction Problem (IHCP). One of the satisfactory solution procedures for solving the IHCP is the Beck's non linear estimation procedure. In this work, this procedure has been used successfully by the authors for the determination of h in steady state unidirectional heat flow.     

Fatigue Analysis of Railway Wheels Under Combined Thermal and Mechanical Loads

Nowadays, the railway vehicles are widely used in many countries as one of the most important transportation systems. Nucleation and growth of fatigue cracks in railway wheels stem from different factors such as wheel-rail rolling contact, thermal loads between wheel-rail and wheel-brake block created in braking process, presence of structural defects in wheel material, and so forth. Also, increasing speed and axle loads of wheels aggravates these factors. These cracks can reduce wheel life and even in severe cases derailment may occur. Therefore, the thermo-mechanical fatigue problem of wheels is a very important issue as is doing an accurate mechanical and thermal analysis of the investigation and estimation of fatigue life of wheels, and also, the prediction of crack behavior under thermo-mechanical loads is necessary. In this article, stress fields created by combined thermal and mechanical loads in railway wheels is investigated. Thermal stresses are usually created as a result of frictional heating produced by applying brake shoes on the wheel tread and also as a result of the occurrence of slip between wheel and rail at the braking stage. The obtained results confirm the important effects of thermal loads on stress fields and fatigue life of wheels. In this article, thermal loads are determined by modeling the contact of the rail-wheel and two brake blocks and by identifying heat partition factors and friction coefficient between these components. One of the other advantages of the presented work is modeling of wheel rotation, while in many of the similar investigations either this rolling is not modeled or its effect is simplified as translating pressure distribution along the rail-wheel contact region. The use of a 3D FE analysis for determination of rail-wheel contact pressure instead of Hertz contact theory is also noteworthy.     

Thermal rectification between two thermoelastic solids with a periodic array of rough zones at the interface

An analysis of the effective thermal contact resistance between two semi-infinite solids in the presence of a periodic array of rough zones at the interface is carried out on the basis of a solution of the corresponding thermoelastic contact problem. The effect of the roughness is modeled by localized thermal contact resistances varying inversely with the contact pressure. The contact problem is reduced to a nonlinear singular integrodifferential equation, and an iterative procedure is proposed for its solving. The results demonstrate that the periodic array of rough zones between two semi-infinite solids exhibits thermal rectification. It is also found that the effective temperature jump and the effective thermal contact resistance are nonlinear functions of a far field heat flux.     

Contact mechanics and thermal conductance of carbon nanotube array interfaces

A model is developed in this work to predict the thermal contact resistance of carbon nanotube (CNT) array interfaces with CNT arrays synthesized directly on substrate surfaces. An analytical model for contact mechanics is first developed in conjunction with prior data from load–displacement experiments to predict the real contact area established in CNT array interfaces as a function of applied pressure. The contact mechanics model is utilized to develop a detailed thermal model that treats the multitude of individual CNT–substrate contacts as parallel resistors and considers the effects on phonon transport of the confined geometry that exist at such contacts. The influence of CNT array properties, e.g. diameter and density, are explicitly incorporated into the thermal model, which agrees well with experimental measurements of thermal resistances as a function of pressure for different types of interfaces. The model reveals that: (1) ballistic thermal resistance dominates at the CNT array interface; (2) the overall performance of CNT array interfaces is most strongly influenced by the thermal resistance at the contacts between free CNT ends and the opposing substrate surface (one-sided interface) or the opposing CNT array (two-sided interface); and (3) dense arrays with high mechanical compliance reduce the thermal contact resistance of CNT array interfaces by increasing the real contact area in the interface.     

Simultaneous measurement of thermal properties by thermal probe using stochastic approximation method

A novel thermal probe method is proposed for the simultaneous measurement of the thermal properties by the Monte Carlo stochastic approximation method. In this method, thermal capacity of probe and thermal contact resistance between probe and sample are considered. An experimental system is set up with the method to validate the measurement accuracy of the method. The thermal properties of several liquid samples as well as solid samples are measured. The results show that: (1) the thermal conductivity and the volumetric heat capacity can be measured with an error of less than 1.2% and 3% respectively, therefore, the measurement accuracy by the method is much higher than the conventional method and (2) the thermal contact resistance has a great effect on thermal conductivity for solid sample, while little influence on thermal conductivity for liquid sample and volumetric heat capacity.