Heat Flow Conditions Research Articles

LDPE and PP thermal diffusivity in molten state

Experimental results are reported for measuring the thermal diffusivity of two polymer species: low density polyethylene (LDPE) and polypropylene (PP). Measurements were taken in unsteady state heat flow conditions around the materials' melting temperature, using a device specially constructed for this purpose. The experimental results for the sample's temperature profile (temperature gradient product) were adjusted with the theoretical results obtained by solving the heat conduction equation. Diffusivity values were α=6.92×(10)^(-7) m^2⁄s for LDPE and α=5.53×(10)^(-7) m^2⁄s for PP. This was pioneering work in measuring this property at high temperatures in non Experimental results are reported for measuring the thermal diffusivity of two polymer species: low density polyethylene (LDPE) and polypropylene (PP). Measurements were taken in unsteady state heat flow conditions around the materials’ melting temperature, using a device specially constructed for this purpose. The experimental results for the sample’s temperature profile (temperature gradient product) were adjusted with the theoretical results obtained by solving the heat conduction equation. Diffusivity values were α =6.92 x 10-7 m2/s for LDPE and α =5.53 x 10-7 m2/s for PP. This was pioneering work in measuring this property at high temperatures in non-stationary state heat flow conditions and should be useful in the search for improving the conditions for processing these materials. -stationary state heat flow conditions and should be useful in the search for improving the conditions for processing these materials.

Interrelation of cell spacing, intermetallic compounds and hardness on a directionally solidified Al–1.0Fe–1.0Ni alloy

Al–Fe–Ni alloys show very promising properties for applications in industrial furnaces and petrochemical plants. Mechanical strength and corrosion resistance are obvious requirements concerning such applications. As-cast Al–Fe–Ni alloys allow the development of some intermetallic compounds (IMCs), which depend on both the alloy composition and solidification conditions, i.e., growth rate and cooling rate. Some typical phases are Al3Fe, Al6Fe, Al3Ni and Al9FeNi. The isolated or simultaneous occurrence of these IMCs is expected to affect the mechanical properties. In the present investigation, an Al–1.0wt%Fe–1.0wt%Ni alloy was directionally solidified under transient heat flow conditions, allowing a wide spectrum of cooling rates to be examined (from 36.5 to 0.8K/s). A comprehensive characterization was performed including Thermo-Calc computations, experimental cooling rates, scanning electron microscopy (SEM), cellular spacing, XRD spectra and Vickers microhardness. It was found that rod-like Al9FeNi IMC in the boundaries of Al-rich cells prevailed along the entire Al–Fe–Ni alloy casting. A Hall–Petch equation relating hardness to the cell spacing is proposed.

Structure of hydrothermal convection in the Upper Rhine Graben as inferred from corrected temperature data and basin-scale numerical models

Geothermal anomalies in sedimentary basins are strongly controlled by fluid circulation within permeable zones. Exploration of new targets requires the understanding of how and why hydrothermal circulation patterns establish in a particular zone. This study presents a new compilation of newly corrected bottom-hole temperature data in the French part of the Upper Rhine Graben, where the Soultz-sous-Forêts temperature anomaly is locked beneath a local horst structure. After a geostatistically constrained interpolation procedure, maps and cross-sections are extracted from the 3D thermal block, together with the associated standard deviations. Thermal anomalies are preferentially associated with the thickest zones of the permeable fractured Buntsandstein (sandstones) formation, in apparent contradiction with previous models where two major fault zones were suggested to control fluid flow. The underlying fractured granitic basement hosts fluid circulation patterns which are apparently controlled at large-scale by the inclined basement–sediments interface. Based on these observations, numerical models of hydrothermal convection including an inclined basement–sediments interface, a local horst structure, and realistic petrophysical properties have been carried out. The depth-decrease of permeability, the inclination of the interface and the fixed heat flow condition at the base of the model, explain why only a few upwellings can be triggered. Thermal anomalies and a measured temperature profile can be reproduced when fault permeability equals 10−14m2. Interestingly, structure of convective patterns also exhibits a second and hotter upwelling, in the Rittershoffen area, 8km east of the Soultz-sous-Forêts upwelling zone, where another geothermal exploration project is now underway. The understanding of hydrothermal convection with realistic fluid and rock properties clearly appears as a predictive tool for geothermal exploration strategies.

The effect of the growth rate on microsegregation: Experimental investigation in hypoeutectic Al–Fe and Al–Cu alloys directionally solidified

Hypoeutectic Al–Cu and Al–Fe alloys were directionally solidified under unsteady-state heat flow conditions in a water-cooled solidification setup. The experimental cooling curves allowed solidification thermal parameters: tip cooling rate (T˙) and tip growth rate (VL) to be experimentally determined and correlated with the scale of the dendritic (Al–Cu alloys) and cellular (Al–Fe alloys) patterns. Experimental microsegregation profiles from the central part of the dendrite/cell cores to the limit of the interdendritic/intercellular regions were determined for different growth rates. The effect of the growth rate was incorporated into an effective partition coefficient that has been determined for the range of growth rates experimentally examined and both Scheil and Clyne–Kurz models were used in the prediction of microsegregation profiles. It was found that both models have significant deviations from the experimental data. Since the calculated results using the theoretical models yielded appreciable discrepancies from the experimental data, an experimental equation is proposed, showing a good agreement with the experimental data for the entire range of solid fractions and experimental tip growth rates, for any alloy experimentally examined.

Practical correlations for thermal resistance of horizontal enclosed airspaces with upward heat flow for building applications

The thermal resistance (R-value) of an enclosed airspace depends on the emissivity of all surfaces that bound the airspace, the size and orientation of the airspace, the direction of heat transfer through the airspace, and the respective temperatures of all surfaces that define the airspace. A table is provided in the 2009 ASHRAE Handbook of Fundamentals (Chapter 26) that contains the R-values of enclosed airspaces. The ASHRAE table is extensively used by modellers, architects and building designers in the design for thermal resistance of building enclosures. This table provides R-values for enclosed airspaces for different values of airspace thickness, effective emittance, mean airspace temperature, and temperature differences across the airspace. The effect of the airspace aspect ratio (length/thickness) on the R-value is not accounted for in the ASHRAE table. However, in previous studies, it was shown that the aspect ratio of the airspace can affect its R-value.In this paper, previous studies undertaken by the author that focused on determining the R-value for vertical enclosed airspaces and horizontal enclosed airspaces with downward heat flow are extended to investigate the effect of the aspect ratio on the R-value of horizontal enclosed airspaces under an upward heat flow condition for different airspace thicknesses and having a wide range of values for effective emittance, mean temperature, and temperature differences across the horizontal airspaces. The R-values predicted from numerical simulation are compared with those provided in the ASHRAE table. Considerations were also given to investigate the potential increase in the R-values of enclosed airspaces when a thin sheet is placed horizontally in the middle of the airspace and whose surfaces have different values of emissivity. Thereafter, practical correlations are developed for determining the R-values of horizontal enclosed airspaces for future use by modellers, architects and building designers. The simplicity of these correlations for horizontal airspaces with upward heat flow along with those that were previously developed for vertical airspaces and horizontal airspaces with downward heat flow suggests that these correlations could be included in the ASHRAE Handbook of Fundamentals.

Heat Transfer Characteristics of Inward, Outward and Upward Solidification of an Al-1.5wt%Fe Alloy in Cylindrical Chill Molds

In this work, three water-cooled experimental solidification devices were developed, and experiments were carried out with an Al-1.5wt%Fe alloy. The three experimental setups consist of vertical cylindrical steel molds with each of them having different zones cooled by water. For the inward solidification, a cooled tube is used having its upper and bottom part thermally insulated. For the outward solidification, a cooled tube, forming an inner part, is concentrically placed inside a cylindrical mold, which is thermally insulated from the environment, by using insulating materials. For the upward solidification, the bottom part of the mold is water-cooled and consists of a thin (3 mm) disc of carbon steel, whilst the cylindrical surface is covered with insulating material to avoid lateral heat losses. A numerical solidification model based on the finite difference method is applied for the simulation of the three aforementioned cases of solidification from the chilled surface considering transient heat flow conditions. Experimental thermal readings in the castings have been used for the determination of the transient overall metal/coolant heat transfer coefficient, h, through a numerical-experimental fit of casting thermal profiles based on inverse heat transfer calculations. It was found a significant variation of h as a function of time during solidification in the three cylindrical set-ups experimentally examined, including a remarkable increase in h during the outward solidification. Introduction

Microstructural Evolution during the Directional Transient Solidification of a Hypomonotectic Al-0.9wt%Pb Alloy

In the present study a hypomonotectic Al-0.9wt%Pb alloy was directionally solidified under transient heat flow conditions and the microstructure evolution was analyzed. The solidification thermal parameters such as the growth rate, the cooling rate and the temperature gradient were experimentally determined by cooling curves recorded by thermocouples positioned along the casting length. The monotectic structure was characterized by metallography and a microstructural transition was observed. From the casting cooled surface up to a certain position in the casting the microstructure was characterized by well-distributed Pb-rich droplets in the aluminum-rich matrix, followed by a mixture of fibers and strings of pearls from this point to the top of the casting. The interphase spacing (λ) and the diameter of Pb-rich particles were also measured along the casting length and experimental growth laws relating these microstructural features to the experimental thermal parameters are proposed.

Unsteady-State Directional Solidification of a Hypoperitectic Pb-9.5wt%Bi Alloy

Although considerable attention has been paid to studies on the unidirectional solidification of peritectic alloys, most of these investigations are carried out under steady-state solidification, where both the growth rate and the thermal gradient can be independently controlled and held constant in time. In this work, a hypoperitectic Pb-9.5wt%Bi alloy was directionally solidified under unsteady-state heat flow conditions and the microstructure evolution was analyzed. Continuous temperature measurements in the casting were monitored during solidification, using a data acquisition system and a bank of six type J thermocouples positioned along the casting length. Thermal parameters such as the growth rate (v) and the cooling rate () were experimentally determined by the experimental cooling curves. The solidification microstructure was characterized by a dendritic morphology along the entire casting length. The primary (l1) and secondary (l2) dendrite arm spacings were measured and experimental growth laws relating them to the solidification thermal parameters v and are proposed.

Transient response of longitudinal rectangular fins to step change in base temperature and in base heat flow conditions

In this paper, we construct solutions for model describing heat transfer in longitudinal rectangular fins. The imposed boundary conditions are the step change in the base temperature and the step change in base heat flow. Both the thermal conductivity and the heat transfer coefficients are assumed to be power law temperature dependent. We employ the local and nonlocal symmetry techniques to analyze the problem at hand. In one case the reduced equation transforms to the tractable Ermakov–Pinney equation. Nonlocal symmetries are admitted when some arbitrary constants appearing in the governing equations are specified. The exact analytical steady state solutions which satisfy the prescribed boundary conditions are constructed. Since the obtained general exact analytical solutions for the transient state satisfy only the zero initial temperature and adiabatic boundary condition at the fin tip, we sort numerical solutions. The effects of the thermo-geometric fin parameter and the power law exponent on temperature distribution are studied.

Multi-dimensional transient temperature simulation and back-calculation for thermal properties of building materials

Thermal properties (i.e. thermal conductivity and heat capacity) are important parameters that influence the temperature of building materials and thermal performance of built environment. These properties are required as fundamental inputs for modeling and simulating thermal behavior of built environment. Most existing methods for measuring thermal properties of building materials are based on 1-D steady-state heat transfer theory. The critical challenge for these methods has been the difficulty in achieving a 1-D heat flow condition for the testing specimen. A multi-dimensional transient method is needed to reduce the challenge and requirement on the testing specimen size and shape, and make it possible to accurately measure all the thermal properties from one single test.This paper first developed a multi-dimensional transient model and a practical tool to simulate the transient temperature at any location on a beam or cylinder specimen of any size subject to convection heat transfer. Case studies verified that this model can be used to, if the thermal properties are known, simulate the transient temperature at any location for a specimen of various shapes and sizes, and predict the time to reach a specified target temperature for mechanical and other testing. Secondly, this paper developed and validated partly by case studies on both asphalt and concrete materials a procedure for back-calculating the thermal properties of a specimen of various shapes and sizes. Thermal properties of novel building materials (various initiative cool materials such as porous concrete and high thermal resistance materials) can be easily measured with that procedure.

Enceladus' extreme heat flux as revealed by its relaxed craters

Enceladus' cratered terrains contain large numbers of unusually shallow craters consistent with deformation by viscous relaxation of water ice under conditions of elevated heat flow. Here we use high‐resolution topography to measure the relaxation fraction of craters on Enceladus far from the active South Pole. We find that many craters are shallower than expected, with craters as small as 2 km in diameter having relaxation fractions in excess of 90%. These measurements are compared with numerical simulations of crater relaxation to constrain the minimum heat flux required to reproduce these observations. We find that Enceladus' nominal cold surface temperature (70 K) and low surface gravity strongly inhibit viscous relaxation. Under such conditions less than 3% relaxation occurs over 2 Ga even for relatively large craters (diameter 24 km) and high, constant heat fluxes (150 mW m−2). Greater viscous relaxation occurs if the effective temperature at the top of the lithosphere is greater than the surface temperature due to insulating regolith and/or plume material. Even for an effective temperature of 120 K, however, heat fluxes in excess of 150 mW m−2are required to produce the degree of relaxation observed. Simulations of viscous relaxation of Enceladus' largest craters suggest that relaxation is best explained by a relatively short‐lived period of intense heating that decayed quickly. We show that infilling of craters by plume material cannot explain the extremely shallow craters at equatorial and higher northern latitudes. Thus, like Enceladus' tectonic terrains, the cratered regions of Enceladus have experienced periods of extreme heat flux.

Cellular growth during the transient directional solidification of Zn-rich Zn–Cu monophasic and peritectic alloys

Zn–Cu alloys located in the monophasic and hypoperitectic ranges of compositions of Zn-rich Zn–Cu alloys were directionally solidified under unsteady-state heat flow conditions. The experimental cooling curves allow solidification thermal parameters: tip cooling rate (Ṫ), tip growth rate (VL) and temperature gradient (GL) to be experimentally determined. The observed microstructural evolution of both alloys has shown that a regular cellular morphology prevails along the whole castings lengths. Only the regions very close to the cooled casting surface showed the presence of plate-like cells due to very high cooling rates (higher than 25K/s). The cell spacing (λc) was measured along the castings lengths, and experimental correlations between λc and experimental solidification thermal parameters have been established. Power laws with −0.55 and −1.1 exponents expressing λc as a function of Ṫ and VL, respectively, were found to better represent the growth of cells under transient heat flow conditions for both alloys experimentally examined. The predictions furnished by the Hunt–Lu model underestimate the experimental cell spacings found for both alloys examined. It was shown that the proposed equations relating λc as a function of Ṫ are able to represent both the steady-state and unsteady-state cellular growth of monophasic and peritectic Zn-rich Zn–Cu alloys.

On the growth of the minority phase during downward transient directional solidification of hypomonotectic and monotectic Al–Pb alloys

Al–Pb alloys were solidified under non steady heat flow conditions using a casting assembly in order to promote vertical downward directional solidification. The downward configuration enables the effects of gravity-driven convection on the final microstructure to be evaluated since the collective movement of Pb-rich particles downwards is favored, due to density differences between the two coexisting liquid phases. Investigations have been made of the obtained solidification structures. Growth rates (v) and cooling rates (\( \mathop T\limits^{\cdot} \)) of the Al–Pb alloys solidified downwards were experimentally determined by the cooling curves recorded along the casting length. The monotectic structure was characterized by metallography and a microstructural transition has been observed in all cases. The microstructure was characterized by well-distributed Pb-rich droplets in the aluminum-rich matrix from the casting cooled surface up to a certain position in the casting, followed by a mixture of fibers and strings of pearls from this point to the bottom of the casting. The increase in alloy lead content delays the formation of fibers for alloys solidified downwards, which occurs for v < 0.48 mm/s and v < 0.15 mm/s for Al–0.9 wt%Pb and Al–1.2 wt%Pb alloys, respectively. Experimental power laws relating the interphase spacing, λ, to v and characterized by −2.0 and −6.5 exponents, were found to represent the growth of droplets and fibers, respectively, for both alloys solidified downwards.

Shrinkage-based die design for drying ceramic parts

Drying of ceramic parts with complex geometry has been studied with emphasis on the effects of shrinkage on their final dimensions. The first step was to understand the processes governing moisture loss from a porous medium through experimental measurements yielding the coefficient of moisture expansion. As a result, non-homogeneous dimensional changes (shrinkage) occur in three-dimensional artefacts with varying cross-section. The moisture diffusion problem governed by Fick’s laws was solved numerically by analogy to the heat conduction problem. To this end the correspondence was established between physical parameters, variables and boundary conditions of heat flow and diffusion, characteristically the coefficient of moisture expansion being analogous to the coefficient of thermal expansion. The numerical model established and solved using finite element analysis predicted moisture distribution inside the part as well as the resulting change in its shape. Validation of numerical predictions was first ensured in two dimensions by modelling a simple slab and comparing with experimental measurements. Validation for a fully three-dimensional shape required use of the well-established iterative closest point algorithm for surface point matching and subsequently the creation of an error map. The reverse of this numerical model was used to predict the appropriate die geometry starting with the shape of the desired part by taking into account the variable drying shrinkage allowance, and the relevant steps are outlined.

Growth of tertiary dendritic arms during the transient directional solidification of hypoeutectic Pb–Sb alloys

Despite the importance of a complete characterization of dendritic patterns in castings, the availability of studies on the development of tertiary dendrite arms is scarce in the literature. In the present study, the tip cooling rate, local solidification time, primary and tertiary dendrite arm spacings have been determined in Pb–Sb alloys castings directionally solidified under unsteady-state heat flow conditions. The alloys compositions experimentally examined are widely used in the as-cast condition for the manufacture of positive and negative grids of lead-acid batteries. The initial growth of tertiary dendritic arms from the secondary branches was found to occur only for a Pb–3.5 wt% Sb alloy at cooling rates in the range 0.4–0.2 K/s, with no evidence of this spacing pattern for Pb–Sb alloys having lower solute content. Tertiary dendritic branches have been observed along the entire casting lengths for alloys of the Pb–Sb hypoeutectic range having compositions higher than 4.0 wt% Sb. It is shown that a power function experimental law with a characteristic −0.55 exponent is able to characterize the tertiary spacing evolution with the solidification cooling rate for alloys compositions ≥4.0 wt% Sb. The only exception was the Pb–3.5 wt% Sb alloy for which λ 3 exhibited significant lower values when compared with the experimental values obtained for the other Pb–Sb alloys for a same solidification cooling rate.

Single and two-phase flow modeling and analysis of a coaxial vacuum tube solar collector

In this paper, an analytical steady state model is developed to study the thermal performance of an individual vacuum tube solar collector with coaxial piping (direct flow type) incorporating both single and two-phase flows. A system of equations which describe the different heat transfer mechanisms and flow conditions was established, discretised, and solved in an iterative manner. For the case of good vacuum condition (10−5 mb) the calculated efficiency curve for single phase flow deviates significantly from the experiments with increasing collector temperature, but agrees well for the case of gas conduction inside the glass envelope at very low pressure (≪1 mb) due to the corresponding increase in overall heat loss coefficient (U-value). For two-phase flow, the occurrence and propagation of flow boiling and condensation inside the collector piping under saturated condition is hypothesized. The modeling results indicate that for all-liquid-single-phase fluid flow, the collector efficiency decreases with decreasing mass flow rate. Once the fluid reaches the boiling point at a certain mass flow rate, no significant reduction in efficiency is observed anymore, which is in accordance with the experimental study.

Thermal properties of the forest soil cover material at a characteristic moisture content

We have investigated by the methods of a given stationary heat flow and calorimetry the heat conductivity and the heat capacity of the typical soil cover materials of a coniferous forest such as fallen-off pine needles, moss, and lichen. Samples of the investigated materials differed in the bulk density and moisture content that were varied over the ranges characteristic of the natural conditions of the geographic latitudes of Belarus. The elucidated laws of the change in the thermal characteristics of the above materials were investigated with the use of the generalized models of the heat transfer in heterophase media and self-consistent calculation of a layered medium with percolation in the direction parallel to the thermal energy transfer.

Microstructure morphologies during the transient solidification of hypomonotectic and monotectic Al–Pb alloys

The solidification cooling rate ( T), growth rate ( v), temperature gradient ( G), interphase spacing ( λ) and diameter ( d) of the Pb-rich phase have been experimentally determined for a hypomonotectic Al–0.9 wt%Pb and a monotectic Al–1.2 wt%Pb alloys directionally solidified under unsteady-state heat flow conditions. It is shown for both cases that, from the cooled bottom of the casting up to a certain position along the casting length, the microstructure was characterized by well-dispersed Pb-rich droplets in the aluminum-rich matrix, followed by a region of morphological transition (with the Pb-rich phase formed by droplets and fibers) and finally by a mixture of fibers and strings of pearls for positions closer to the top of the casting. It has been also observed that such microstructural transition was anticipated for the alloy with higher solute content. It is shown that the correlation between the morphology of the Pb-rich phase and the growth rate can be synthesized as follows: Al–0.9 wt%Pb alloy, droplets for v > 1.0 mm/s and fibers for v < 0.65 mm/s; Al–1.2 wt%Pb alloy, droplets for v > 1.1 mm/s and fibers for v < 0.87 mm/s. Experimental growth laws relating the interphase spacing to both G and v are proposed.

Determination of heat transfer coefficients at metal–mold interface during horizontal unsteady-state directional solidification of Sn–Pb alloys

This paper presents a theoretical–experimental study of the metal–mold heat transfer coefficients during horizontal directional solidification of Sn–Pb hypoeutectic alloys (5 wt%Pb, 15 wt%Pb, 20 wt%Pb and 25 wt%Pb) in presence of thermo-solutal convection. A water-cooled solidification experimental apparatus has been developed, and specimens have been solidified under unsteady state heat flow conditions. Five computer guided thermocouples have been connected with the metal, and the time–temperature data have been recorded automatically. A numerical technique which compares theoretical and experimental thermal profiles is used for investigating the influence of solute content on h i values. This has permitted the evaluation of the variation of metal–mold heat transfer coefficients along the solidification of Sn–Pb alloys, as well as the analysis of the effects of thermo-solutal convection. The interfacial heat transfer coefficients of alloys studied are represented by equations which show the time dependence during the process. The experimental and calculated values have shown a very good agreement. A comparative analysis between the results of this work and those from the literature proposed to analyze the metal–mold heat transfer coefficients during upward and downward vertical solidification of Sn–Pb hypoeutectic alloys is conducted.

Intrinsic permeability of materials ranging from sand to rock-fill using natural air convection tests

Air convection within coarse rock-fills enhances winter-time heat extraction from underlying soils. Modeling this phenomenon requires the knowledge of intrinsic permeability. This study focuses on the measurement of intrinsic permeability using natural air convection within a 1 m3 test cell. Upward heat flow conditions are applied to various specimens. Test results are analyzed using a theoretical solution of natural convection in a square enclosure. Four materials were studied, with effective particle sizes (d10) ranging from 90 to 150 mm and porosities ranging from 0.37 to 0.41. The results showed that intrinsic permeability increases with increasing d10. The experimental results were adequately predicted by the Kozeny–Carman and Chapuis equations. Only slight deviations were observed, which is considered acceptable given that these equations were developed for materials with much smaller values of d10. The experimental results of this study confirm the value of intrinsic permeability recently used in a study of natural convection within a rock-fill dam in northern Quebec, Canada.