Heat Flow Conditions Research Articles

Measurement of Thermal Resistance of Woven Fabrics in Natural and Forced Convections

The objective of this paper is to report the values of thermal resistance in natural and convection heat transfer modes through woven fabrics. An instrument developed on the principle of the guarded hot plate method will be discussed. The instrument is precise up to two decimal places and the accuracy is approximately 14%. The fabrics were tested in a natural as well as forced convective mode with air velocity of 1m/s flowing parallel over the fabric surface. It was observed that the thermal resistance of the fabric in forced convection is less than that in the natural convective mode. The thermal resistance can be predicted with the help of a statistical model when all the constructional parameters are taken together. A polynomial equation consisting of linear, interaction and square terms based on the response surface modelling was developed for both the conditions of heat flow. It was observed that as all constructional parameters, such as warp and weft count, thread spacing, thickness, fabric weight and porosity are taken as variables, the response function; namely thermal resistance can be predicted with a high coefficient of determination and less average error.

Microstructural Development in Al-Ni Alloys Directionally Solidified under Unsteady-State Conditions

Three Al-Ni hypoeutectic alloys were directionally solidified under upward unsteady-state heat-flow conditions. Primary (λ1) and secondary (λ2) dendrite arm spacings were measured along the castings for all alloys and correlated with transient solidification thermal variables. A combined theoretical and experimental approach was used to quantitatively determine such thermal variables, i.e., transient metal/mold heat-transfer coefficients, tip growth rates, thermal gradients, tip cooling rates, and local solidification time. The article also focuses on the dependence of dendrite arm spacings on the alloy solute content. Furthermore, the experimental data concerning the solidification of Al-1.0, 2.5, and 4.7 wt pct Ni alloys are compared with the main predictive dendritic models from the literature.

Cellular growth during transient directional solidification of hypoeutectic Al–Fe alloys

Investigations have been made of the solidification structure of three hypoeutectic Al–Fe alloys, which were directionally solidified under unsteady-state heat flow conditions. The experiments have been carried out by using a casting assembly, which was designed in such way that the heat was extracted only through the water-cooled system at the casting bottom, promoting vertical upward directional solidification. A combined theoretical/experimental approach was used in order to quantitatively determine the solidification parameters: tip growth rate and cooling rate of Al–0.5 wt%Fe, Al–1.0 wt%Fe and Al–1.5 wt%Fe alloys castings. The experimental results include transient metal/mold heat transfer coefficients, hg, determined from comparisons between the experimental thermal profiles in castings and the simulations provided by a finite difference heat flow program. Cellular microstructures prevailed along the entire castings for any alloy experimentally examined. The cell spacing variation with cooling rate and tip growth rate has been characterized by −0.55 and −1.1 experimental power laws, respectively. The experimental cell spacings were compared with the theoretical predictions furnished by cellular growth models.

Microstructural development in Al–Sn alloys directionally solidified under transient heat flow conditions

Despite the wide use of Al–Sn alloys for engineering applications studies on the microstructural development of such materials are rare. Optimized microstructures during the solidification stage of processing can be fundamental for final properties. In the present study, three Al–Sn hypoeutectic alloys were directionally vertically solidified under upward unsteady state heat flow conditions. Primary ( λ 1) and secondary ( λ 2) dendrite arm spacings were measured along the alloys castings and correlated with transient solidification thermal variables. A combined theoretical and experimental approach has been used to quantitatively determine such thermal variables, i.e., transient metal/mold heat transfer coefficients, tip growth rates, thermal gradients, tip cooling rates and local solidification time. The article also focuses on the dependence of dendrite arm spacings on the alloy solute content. Furthermore, the experimental data concerning the solidification of Al 20, 30 and 40 wt% Sn alloys are compared with the main predictive dendritic models from the literature.

DYNAMICS OF AMORPHIZATION INDUCED IN CRYSTALLINE Ge1Sb2Te4 FILMS BY SINGLE FEMTOSECOND PULSES

The dynamics and the conditions of amorphous transitions induced in a Ge 1 Sb 2 Te 4 system upon a single femtosecond (fs) pulse melting were studied by real-time reflectivity measurements. The system has a multilayer structure of 100 nm ZnS – SiO 2/(15–100 nm) Ge 1 Sb 2 Te 4/120 nm ZnS – SiO 2/0.6 mm polycarbonate substrate. It is shown that under optimum conditions amorphization is completed within 900 ps. The thickness of the phase change layer plays an important role in controlling the heat flow conditions in the system upon a fs pulse irradiation. The use of the fs laser pulse leads to a situation in which the pulse energy is deposited within a very short time in a thin surface layer, leading to heating or melting. The so-generated steep temperature gradient is subsequently smoothed by heat diffusion toward the substrate. The relative thermal process and effects are estimated. The calculated results are consisted with those from real-time reflectivity measurements. The mechanism of crystalline to amorphous transition triggered by single fs laser pulses is discussed.

Thermoelastic solutions for annular disks with arbitrary variable thickness

This article presents a unified analytical solution for the analysis of thermal deformations and stresses in elastic annular disks with arbitrary cross-sections of continuously variable thickness. The annular disk is assumed to be under steady heat flow conditions, in which the inner surface of the annular disk is at an initial temperature and the outer surface at zero temperature. The governing second-order differential equation is derived from the basic equations of the thermal annular disks and solved with the aid of some hypergeometric functions. Numerical results for thermal stresses and displacement are given for various annular disks. These disks include annular disks of thickness profiles in the form of general parabolic and exponential functions. Additional annular disks with nonlinearly variable thickness and uniform thickness are also included.

The roles of macrosegregation and of dendritic array spacings on the electrochemical behavior of an Al–4.5 wt.% Cu alloy

The microstructural pattern and the solute redistribution of as-cast aluminum alloys play an important role on the resulting corrosion behavior. However, of the main aluminum alloys, Al–Cu alloys have the lowest negative corrosion potential. The purpose of this work was to evaluate the electrochemical behavior of an Al–4.5 wt.% Cu alloy solidified under unsteady-state heat flow conditions. This evaluation was carried out through the analysis of both potentiodynamic polarization curves and electrochemical impedance spectroscopy (EIS) tests in a 0.5 M NaCl solution at 25 °C. The experimental segregation profile obtained in the solidification experiment was characterized by positive and negative copper content regions at the bottom and the top of the casting, respectively. Likewise, in conventional foundry practice, in a same casting both positive and negative copper segregation regions may occur. Such casting can exhibit different corrosion responses at different locations. The influences of solute redistribution during solidification, the magnitude of dendritic spacing and hence of the Al-rich phase and of Al 2Cu particles distribution along the casting on the corrosion resistance, were examined in samples collected along the casting length. The corrosion rate and impedance parameters (obtained from an equivalent circuit analysis) are also discussed.

Design Optimization of Size and Geometry of Vortex Promoter in a Two-Dimensional Channel

Thermal management of electronic equipment is one of the major technical problems in the development of electronic systems that would meet increasing future demands for speed and reliability. It is necessary to design cooling systems for removing the heat dissipated by the electronic components efficiently and with minimal cost. Vortex promoters have important implications in cooling systems for electronic devices, since these are used to enhance heat transfer from the heating elements. In this paper, an application of dynamic data driven optimization methodology, which employs concurrent use of simulation and experiment, is presented for the design of the vortex promoter to maximize the heat removal rate from multiple protruding heat sources located in a channel, while keeping the pressure drop within reasonable limits. Concurrent use of computer simulation and experiment in real time is shown to be an effective tool for efficient engineering design and optimization. Numerical simulation can effectively be used for low flow rates and low heat inputs. However, with transition to oscillatory and turbulent flows at large values of these quantities, the problem becomes more involved and computational cost increases dramatically. Under these circumstances, experimental systems are used to determine the component temperatures for varying heat input and flow conditions. The design variables are taken as the Reynolds number and the shape and size of the vortex promoter. The problem is a multiobjective design optimization problem, where the objectives are maximizing the total heat transfer rate Q and minimizing the pressure drop ΔP. This multiobjective problem is converted to a single-objective problem by combining the two objective functions in the form of weighted sums.

The variation of the metal/mold heat transfer coefficient along the cross section of cylindrical shaped castings

During solidification, the mathematical analysis of heat flow depends on the transient heat transfer coefficient at the metal/mold interface. The analysis of heat transfer behavior along a cylindrical section is necessary for a better control of solidification in conventional foundry and continuous casting processes. For this purpose, a water-cooled experimental apparatus was developed, and experiments were carried out with Sn–Pb alloys with different melt superheats. The heat transfer coefficients were determined by a theoretical–experimental fit of thermal profiles (IHCP). The results have shown a variation in heat flow conditions along the metal/mold interface provoked by the action of solidification thermal contraction connected with the gravitational effect. In macrostructural terms, this effect was evident with an asymmetric structure due to the variation of metal/mold thermal contact along the cylinder cross section. Experimental equations correlating heat transfer coefficients as a power function of time along the cross section of cylindrical horizontal castings of Sn–Pb alloys are proposed.

Cellular growth during transient directional solidification of Pb–Sb alloys

Cellular spacings and solidification thermal variables were determined for three dilute Pb–Sb alloys, which were solidified under unsteady-state heat flow conditions. The experiments have been carried out by using a casting assembly, which was designed in such way that the heat was extracted only through the water-cooled system at the casting bottom, promoting vertical upward directional solidification. An experimental approach, based on thermal readings collected at six different positions from the casting surface, was used in order to quantitatively determine the solidification thermal variables: tip growth rate and cooling rate of Pb–0.3 wt%Sb, Pb–0.85 wt%Sb and Pb–1.9 wt%Sb alloys castings. After grinding, polishing and etching procedures, both longitudinal and transverse sections of the castings were characterized by a typical cellular microstructure which prevailed along the entire casting. The cell spacing variation with cooling rate and tip growth rate was characterized by −0.55 and −1.1 experimental power laws, respectively. The experimental cell spacings were compared with the theoretical predictions furnished by cellular growth models.

Elastoviscoplastic relaxation of impact crater topography with application to Ganymede and Callisto

We use an elastoviscoplastic rheological model to study the long‐term relaxation of impact crater topography on Ganymede and Callisto. We employ a complete set of rheological parameters for ductile creep in ice Ih and implement a new, shallower initial shape model. Under high heat flow conditions, stresses are relieved in deeper, less viscous material, and the remainder concentrates as flexural (bending) stresses in a viscously stiffer near‐surface layer. Essentially, a mechanical lithosphere forms that focuses stresses but with uplifts and stress levels that are always greater than those obtained for a purely viscous half space. We discuss how classic elastic flexure and purely viscous relaxation are special cases of this more generalized rheological model. Stress concentration in the flexing (i.e., bending) layer can exceed the plastic yield strength of ice for high enough heat flows, weakening the layer somewhat and increasing the total amount of relaxation. These plastic strains tend to be limited to small magnitudes (<0.5%) in a shallow region on the crater floor; such features may be observable in available imagery. The grain size sensitivity of the dominant creep mechanism in ice represents a new input parameter in crater relaxation studies on icy satellites (along with the elastic and plastic moduli, although to a lesser extent). Nevertheless, we find that for reasonable input parameters our simulations reproduce the continuum of relaxation states seen on Ganymede and Callisto. A combination of higher surface temperatures (∼120–130 K) and larger grain sizes (>1 mm) permits both retention and relaxation of topography at the lower and higher ends, respectively, of the anticipated heat flow range. Consideration of relaxed craters in Marius Regio and of the palimpsests and penepalimpsests suggests ancient heat flows in excess of 10 mW m−2, consistent with other estimates.

Evaluation of fracture toughness of as plasma sprayed alumina–13 wt.% titania coatings by micro-indentation techniques

The fracture toughness of the as plasma sprayed alumina–13 wt.% titania (AT-13) coatings was evaluated using micro-indentation techniques. Indentations with smaller loads of 0.49 N show features such as partially melted particles to be extremely hard and brittle. However, the matrix made up of bi-modulus microstructure of splats was much tougher due to operative toughening mechanism for instance, crack bridging, which effectively retarded propagation of the cracks. Log plots of crack length ( C) versus load ( P) for loads varying from 1.96 to 9.8 N occurred with a slope of 0.65 ± 0.095 signifying sub-surface median or palmqvist type cracks to be rampant. The as sprayed microstructure made of pores; partially melted particles and splats were found to be anisotropic with regard to indentation toughness. Cracks were found to initiate and propagate easily in direction parallel to the coating growth directions than along the splat boundaries. Accordingly the bonding between the splats caused by plasma spray process could be deemed to be superior. The preferential directionality developed in the microstructure due to the imposed heat flow conditions essentially has weakened the microstructure.

Thermal conductivity of Tb2(MoO4)3 crystals at low temperatures

AbstractThermal conductivity of the improper ferroic Tb2(MoO4)3 was measured in the range 0.3 K–100 K by the method of the stationary heat flow. An additional maximum in thermal conductivity observed at 0.45 K is due to the anomaly of specific heat corresponding to the antiferromagnetic phase transition. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Thermosolutal convective effects on dendritic array spacings in downward transient directional solidification of Al–Si alloys

Solidification thermal variables, such as tip growth rate, tip cooling rate, local solidification time and dendrite arm spacings, have been measured in Al–Si hypoeutectic alloys directionally solidified under downward transient heat flow conditions. It is a well-known fact that the dendritic spacings can affect not only microsegregation profiles but also the formation of secondary phases within interdendritic regions, which influences mechanical properties of cast structures. A reduced number of studies have been carried out in order to analyze the effects of melt convection within the interdendritic region or to verify the influence of growth direction on dendritic arm spacings. In this work, an experimental approach is used to quantitatively determine the solidification thermal variables. The work also focuses on the dependence of dendrite arm spacings on these solidification thermal variables. The experimental data concerning the solidification of Al 5, 7 and 9 wt.% Si alloys are compared with the main predictive dendritic models from the literature. A comparison between upward and downward unsteady-state results for dendritic spacings has also been conducted.

A Setup for Studying the Low-Temperature Thermal Conductivity of Powder Samples

A setup for studying the thermal conductivity of powder samples in the temperature range 2–200 K using the stationary heat flow method is described. The design of the cryogenic part of the setup allows a sample to be loaded at low temperatures. The effective thermal conductivities of methane hydrate powder and the ice powder obtained upon methane hydrate decomposition were measured, and the true thermal conductivities were determined. A heat exchange gas (helium) at a lowered pressure was used to reduce the interface thermal resistance between the grains in the powders.

A unified model considering force balances for departing vapour bubbles and population balance in subcooled boiling flow

Population balance equations combined with a three-dimensional two-fluid model are employed to predict subcooled boiling flow at low pressure in a vertical annular channel. The MUltiple-SIze-Group (MUSIG) model implemented in CFX4.4 is extended to account for the wall nucleation and condensation in the subcooled boiling regime. A model considering the forces acting on departing bubbles at the heated surface is formulated. This model provides the capacity of complex analyses on the bubble growth and departure for a wide range of wall heat fluxes and flow conditions. Comparison of model predictions against local measurements is made for the void fraction, bubble Sauter mean diameter and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcoolings. Good agreement is achieved with the local radial void fraction, bubble Sauter mean diameter and liquid velocity profiles against measurements. However, significant weakness of the model is evidenced in the prediction of the vapour velocity. Work is in progress to circumvent the deficiency of the MUSIG boiling model by the consideration of additional momentum equations to better represent the momentum forces acting on the range of bubble sizes in the bulk subcooled liquid.

Factors affecting solidification thermal variables along the cross-section of horizontal cylindrical ingots

During solidification the mathematical analysis of heat flow depends on the transient heat transfer coefficient at the metal/mold interface. The analysis of heat transfer behavior along the cross-section of radial geometries is necessary for a better control of solidification in conventional foundry and continuous casting processes. For this purpose, a water-cooled solidification experimental apparatus was developed, and experiments were carried out with Sn–Pb alloys with different melt superheats. The transient metal/mold heat transfer coefficients were determined by a numerical-experimental fit of casting thermal profiles based on inverse heat transfer calculations. The results have shown a significant variation in heat flow conditions along the cylinder cross-section provoked by the simultaneous action of solidification thermal contraction and the gravitational effect. Experimental equations correlating heat transfer coefficients as a power function of time along the cross-section of cylindrical horizontal castings of Sn–Pb alloys are proposed.

Competitive growth of grains in ZA alloys during continuous casting with heated mould

Nucleation and competitive growth of grains in Zn–Al alloys were studied during pulling of ingots under conditions of continuous casting by the Ohno Continuous Casting (OCC) process. Microstructural observation shows that nuclei appearing on the end of the dummy bar have a disordered orientation. However, during competitive growth under conditions of directional heat flow, the ingot grows continuously, and the crystals with less favourable orientations are gradually eliminated. The properties of the alloy greatly influence the selection process. Alloys with a narrow solidification range (ZA5 and ZA8) can directly initiate their columnar structure from nuclei on the end of the dummy bar through competitive growth. Alloys with higher aluminium content (ZA12, ZA22 and ZA27) have a wider solidification range, and their parallel columnar structure evolves only later from the equiaxed crystals on the end of the dummy bar.

Fabrication and characteristics of plasma facing SiC/C functionally graded composite material

A bulk SiC/C functionally graded material (FGM) having a compositional gradient from carbon (C) to silicon carbide (SiC) was obtained by powder metallurgy method with SiC, B and amorphous C powders as starting materials. The average graphite ratio of C was 66% higher than ordinary graphite. Compared with CVI and CVD SiC/C FGM and SiC coating, hot-pressed SiC/C FGM has high effective thermal conductivity while the thickness of SiC layer is 1 mm or so. Under cyclic high-temperature heat flow conditions, SiC/C FGM did not suffer cracking and was shown to be superior in resistance to thermal fatigue. The plasma-relevant performance indicated that it has excellent high-temperature erosion resistance.

Influence of melt convection on dendritic spacings of downward unsteady-state directionally solidified Al–Cu alloys

The dendritic spacings are important microstructural parameters involved in solidification processes. They can affect not only microsegregation profiles but also the formation of secondary phases within interdendritic regions, which influences mechanical properties of cast structures. A small number of studies have been carried out in order to analyze the effects of melt convection within the interdendritic region or to verify the influence of growth direction in the dendritic arm spacings. In this work, a combined theoretical and experimental approach is developed to quantitatively determine solidification thermal variables such as transient metal/mold heat transfer coefficients, tip growth rates, thermal gradients, tip cooling rates and local solidification time during downward unsteady-state solidification of hypoeutectic Al–Cu alloys. These solidification thermal variables are correlated with dendritic spacings, which have been measured along cross and longitudinal sections of ingots solidified under downward unsteady-state heat-flow conditions. Predictive theoretical models for dendritic spacings have been compared with experimental observations. A comparison between upward and downward unsteady-state results for dendritic spacings has also been conducted.