Heat Flow In Solids Research Articles

Lateral heat flux reduction using a lock-in thermography compensation method

The naturally diffusive heat flow in solids often results in differences in surface temperatures. Active thermography (AT) exploits such differences to gain information on the internal structure, morphology, or geometry of technical components or biological specimens. In contrast to sound or light waves, thermal waves are lossy; consequently, it is difficult to interpret measured 2D temperature fields. Most AT evaluation methods are based on 1D approaches, and measured 3D heat fluxes are frequently not considered, which is why edges, small features, or gradients are often blurred. Herein, we present a method for reducing the local temperature gradients at feature areas and minimizing the induced lateral heat flux in optical lock-in thermography (LT) measurements through spatial- and temporal-structured heating. The vanishing lateral gradients convert the problem into a 1D problem, which can be adequately solved by the LT approach. The proposed compensation method can bypass the blind frequency of LT and make the inspection largely independent of the excitation frequency. Furthermore, the edge sharpness and separability of features are improved, ultimately improving the feature-detection efficiency.

Heat Flow Guiding and Modulation by Kinks in a Silicon Nanoribbon.

Tailoring heat flow in solids has profound implications for the innovation of functional thermal devices. However, the current methods face technological challenges related to system complexity, material stability, and operating temperature. In this study, we demonstrated efficient heat flow modulation in a single material without a phase transition, using a simple and entirely material-independent strategy, kinked nanostructure patterning, at near-ambient temperature. By carefully controlling the kink arm length and kink angle of the Si nanoribbons, we achieved a thermal conductivity modulation of up to ∼20%. Our theoretical modeling showed that this modulation results from the competing roles of phonon backscattering and open view channels on heat transport. We also build a regime map based on the existence of an open view channel and provide concrete design guidelines for thermal conductivity modulation considering the kink angle and arm length. This study opens up new opportunities for efficient heat flow manipulation through nanostructure patterning.

Ion Write Microthermotics: Programing Thermal Metamaterials at the Microscale.

Considerable advances in manipulating heat flow in solids have been made through the innovation of artificial thermal structures such as thermal diodes, camouflages, and cloaks. Such thermal devices can be readily constructed only at the macroscale by mechanically assembling different materials with distinct values of thermal conductivity. Here, we extend these concepts to the microscale by demonstrating a monolithic material structure on which nearly arbitrary microscale thermal metamaterial patterns can be written and programmed. It is based on a single, suspended silicon membrane whose thermal conductivity is locally, continuously, and reversibly engineered over a wide range (between 2 and 65 W/m·K) and with fine spatial resolution (10-100 nm) by focused ion irradiation. Our thermal cloak demonstration shows how ion-write microthermotics can be used as a lithography-free platform to create thermal metamaterials that control heat flow at the microscale.

Unified first-principles theory of thermal properties of insulators

The conventional first-principles theory for the thermal and thermodynamic properties of insulators is based on the perturbative treatment of the anharmonicity of crystal bonds. While this theory has been a successful predictive tool for strongly bonded solids such as diamond and silicon, here we show that it fails dramatically for strongly anharmonic (weakly bonded) materials, and that the conventional quasiparticle picture breaks down at relatively low temperatures. To address this failure, we present a unified first-principles theory of the thermodynamic and thermal properties of insulators that captures multiple thermal properties within the same framework across the full range of anharmonicity from strongly bonded to weakly bonded insulators. This theory features a new phonon renormalization approach derived from many-body physics that creates well-defined quasiparticles even at relatively high temperatures, and it accurately captures the effects of strongly anharmonic bonds on phonons and thermal transport. Using a prototypical strongly anharmonic material, sodium chloride (NaCl), as an example, we demonstrate that our new first-principles framework simultaneously captures the apparently contradictory experimental observations of large thermal expansion and low thermal conductivity of NaCl on the one hand, and anomalously weak temperature dependence of phonon modes on the other, while the conventional theory fails in all three cases. We demonstrate that four-phonon scattering due to higher-order anharmonicity significantly lowers the thermal conductivity of NaCl and is required for a proper comparison to experiment. Furthermore, we show that our renormalization framework, along with four-phonon scattering, also successfully predicts the measured phonon frequencies and thermal properties of a weakly anharmonic material, diamond, indicating universal applicability for thermal properties of insulators. Our work gives new insights into the physics of heat flow in solids, and presents a computationally efficient and rigorous framework that captures the thermal and thermodynamic properties of both weakly and strongly bonded insulators simultaneously.

Heat-flow properties of systems with alternate masses or alternate on-site potentials

We address a central issue of phononics: the search of properties or mechanisms to manage the heat flow in reliable materials. We analytically study standard and simple systems modeling the heat flow in solids, namely, the harmonic, self-consistent harmonic and also anharmonic chains of oscillators, and we show an interesting insulating effect: While in the homogeneous models the heat flow decays as the inverse of the particle mass, in the chain with alternate masses it decays as the inverse of the square of the mass difference, that is, it decays essentially as the mass ratio (between the smaller and the larger one) for a large mass difference. A similar effect holds if we alternate on-site potentials instead of particle masses. The existence of such behavior in these different systems, including anharmonic models, indicates that it is a ubiquitous phenomenon with applications in the heat flow control.

Researches of a Novel 2D CMOS Thermal Based Accelerometer

Conventionally the accelerometer behaves like a spring – mass system and its structures involve solid proof mass, which is allowed to move under acceleration conditions. In this paper, we design and fabrication a novel thermal-bubble-based micromachined accelerometer with advantages of minimum solid thermal conductance and high sensitivity successfully. The proposed accelerometer based on thermal convection creates a tiny heated air bubble hermetically sealed inside the sensor package cavity. Four thermopiles around the center heater serve as the temperature sensors to detect two-dimension motion of the chip and also are adequately applied to the technology of inclinometers, anemometers and flow meters. A new micro-link structure is also proposed to enhance the construction of accelerometer with the micro heater and two pairs of thermopiles floating over an etched cavity. The heater and the thermopiles are connected by network-like structure of micro-links, which enhance the structure and greatly reduce the solid heat flow from the heater to the hot junctions of thermopiles. The samples are fabricated by TSMC 0.35μm 2P4M CMOS process which is provided by CIC with outstanding strong structures and uniform quality. Our design is proved to be adequate for commercial batch production. We measure the output signal by inclining the sensor to evaluate the performance of this accelerometer.

Heat flow from wet to dry snowpack layers and associated faceting

AbstractLayers of faceted crystals adjacent to crusts form the failure layers for some unexpected dry-slab avalanches. This paper focuses on the case of facets that form when dry snow overlies wet snow. From a basic equation for heat flow in solids, the approximate freezing time of the wet layer is derived. Seven experiments are described in which a wet layer was placed between two dry-snowlayers in a cold laboratory. Measured freezing times are comparable to the freezing times from the approximate solution assuming that latent heat from the irreducible water content flowed up. In four of the experiments, evidence of faceting was observed at the base of the upper dry snow layer within 5 hours and before the wet layer froze. In all seven experiments faceting was observed in the upper dry layer after the wet layer froze. Simulations performed with the snow-cover model SNOWPACK yield freezing times that agree reasonably with the approximate solution and allow the influence of various parameters on the results to be explored. In addition, simulated temperatures and grain evolution are compared with observations, showing good agreement.

Well Test Analysis in the New Economy

Abstract This paper provides a chronological history of the evolution of advancement in well testing techniques in order to examine how the technology has progressed to its present state. The first factors examined are those that strongly influenced technological development in well-test analysis. The next discussion concerns the problems that still require resolution, and finally, the authors will present what they envision for the future of well-test analysis. Introduction The origin of fluid flow through porous media may be traced back to the experiments run by Darcy during the 19th century to investigate the flow of water, a Newtonian fluid, through a bed of unconsolidated sand filter. This sand filter probably had a fairly high permeability. Darcy's equation was developed and became the basis for significant further development. It was not a great surprise to find that the equations governing flow of a Newtonian fluid in high permeability formations under laminar conditions are identical to those that govern heat flow in solids. The original idea of analyzing pressure vs. time data from a producing or shut-in well to obtain information on the producing stratum first appeared in the field of hydrology. Hydrologists were mainly interested in the behaviour of underground water flow in large aquifers. Shortly thereafter, The is(1) published his work on fluid flow in porous media, which included his point-source solution. Muscat(2) was probably the first to study a problem relating to oil reservoirs-the eventual static pressure behaviour of a shut-in well in a closed oil reservoir. When compared to the initial reservoir pressure, this new static pressure can be used to measure the quantity of hydrocarbons produced up to the time of the test. The need for reliable quantitative analysis has primarily been driven by economics since accurate formation permeability determination is needed for forecasting reservoir production. Initial reservoir pressure and drainage boundaries provide the information needed to determine the amount of hydrocarbon in place. However, determination of well condition (i.e., skin factor) is also necessary to predict how much expenditure will be needed to improve productivity. Since Muscat, literally thousands of papers have been published on the analysis of pressure tests. Numerous new tests have been devised to determine specific reservoir parameters. This explosion in literature was basically due to the ease by which pressure behaviour could be measured and the enormous value of the parameters calculated from these tests. In addition to the information mentioned, pressure tests can be used to estimate:How efficiently a well is completed;The need for and anticipated success of a stimulation treatment;The general type of well treatment desired; and,The degree of connectivity of one well to another. Modern well-test analysis started when Horner(3) and Miller et al.(4) presented their famous papers where semi-log straight lineswere introduced as the first technique for analyzing pressure tests. Within a few years, Van Everdingen and Hurst(5) and Moore et al.(6) introduced other fundamental developments with the concept of wellbore storage.

Effect of laser spot weld energy and duration on melting and absorption

To facilitate pulse Nd–YAG laser spot weld development, it is common practice to adjust the pulse energy, duration, and focus spot size. An accurate understanding of the effect of these parameters on melting, weld appearance, and heat input is thus required. Calorimetric measurements of the net heat input to 304 stainless steel workpieces for laser spot welds have been completed. A pulse Nd–YAG laser was used with varying pulse energies from 1 to 5·5 J, and pulse durations of 2·2 and 7·0 ms. Measurements showed the absorption for spot welds produced using the pulsed Nd–YAG laser to vary from 38 to 67% and to be relatively insensitive to beam intensity. Analysis of the continuous point source equation for conduction heat flow in solids was used to predict the weld size for the pulse energy and duration measured in the experiment. Calculations of the weld pool volume from the weld metallography were used to determine the melting for each spot weld. Comparisons of the measured weld size with the three-dimensional model predicted size indicated that the observed weld pools are larger than is expected from the measured workpiece energy. Analysis of the experimental data and the theoretical model has revealed a substantial increase in melting for short duration pulses versus long duration pulses of the same energy. The benefit of laser spot welding parameter optimisation is hence indicated.

The comparative performance of some finite difference equations for transient heat conduction

AbstractThe established finite difference equations to estimate one‐dimensional transient heat flow in solids are the ‘classical’ form (explicit), and the Crank–Nicolson and ‘pure‐implicit’ forms (both implicit). They are all based on finite difference approximation to the Fourier continuity equation. To these are now added three more explicit forms: exponential linear, exponential inverse cosine and polynomial, which are based on exact solutions to the Fourier equation. The performance of each of the six equations is tested against the exact results of a well known step excitations problem (the Groeber model). The tests consist of examining (i) finite difference errors arising from a single implementation of each form at different stages in the transient cooling process, (ii) the errors that accumulate during part or all of the cooling process (both as regards any bias that is introduced, and also a measure of variance) and (iii) the run times in executing the various forms. The nondimensional time step r was treated as the independent variable, and can be made arbitrarily large, by use of a simple time‐division procedure (otherwise r < ½ for use with the classical form). It is shown that having regard to both error and run time, the polynomial form appears to be the most efficient estimator.

Study of Edge Effect in Photoacoustic Microscopy

The edge effect in microphone photoacoustic microscopy has been studied experimentally. It has been observed that the amplitude of the photoacoustic signal is enhanced nearly exponentially when the exciting laser spot approaches the sample edge. The phase also shows a characteristic shift near the edge. The features of this edge effect are well explained quantitatively by the theory developed by Thomas et al. which takes account of the three-dimensional heat flow in solids. The advantage of the phase image over the amplitude image is also discussed.

Analytic Solutions for Determining Naturally Fractured Reservoir Properties by Well Testing

Abstract A completely unsteady-state theory is developed that describes the well pressure response of infinite, naturally fractured reservoirs of the type composed by high-permeability fractures and tight matrix blocks. The theory exclusively involves flow properties and dimensions of the fractures and the matrix blocks; no extra adjusting parameters are needed for predicting the pressure response of a reservoir with known properties. Comparison of computed pressure-drawdown theoretical curves with results pressure-drawdown theoretical curves with results of a numerical model applied to idealized reservoirs shows a good fit. It is concluded that an evaluation of the following reservoir properties is possible from well-test pressure plots: the fractures' kh product and the pressure plots: the fractures' kh product and the average product of the matrix porosity by a characteristic dimension of the matrix blocks. Thus, the model allows comparison of well-test pressure response with the formation measurements. pressure response with the formation measurements Introduction Barenblatt and Zheltov were first to present the formulation of the problem of radial flow of a slightly compressible fluid in a naturally fractured porous medium. They assumed that flow occurs only in the fracture porous medium, in which matrix blocks of contrasting physical properties deliver their fluid contents. That is, the matrix blocks act as a uniformly distributed source in a fracture medium. In their paper, Barenblatt and Zheltov assume this source's paper, Barenblatt and Zheltov assume this source's strength is proportional to the local pressure loss at the fracture and to an average internal block pressure. An approximate solution to this problem was presented by Warren and Root, resulting in a characterization of the fractured reservoir by two parameters ambiguously related to the actual shape, dimensions, and fluid flow properties of the reservoir. Furthermore, these two properties of the reservoir. Furthermore, these two parameters have been found of "limited value" for parameters have been found of "limited value" for determining some reservoir properties. Warren and Root give a comprehensive bibliography of the instrumental evaluation of fractured reservoirs. A promising method to this end, using sonic and resistivity logs, has been presented by Aguilera. The need to directly relate the fractured reservoir properties to the well-test plots, just as in the properties to the well-test plots, just as in the homogeneous reservoirs, is obvious. THEORY The theory, detailed in the Appendix, involves the following assumed mechanisms of the fluid flow and their corresponding mathematical expressions.At early times of the well test, the flow takes place only in the fractures and is described by the place only in the fractures and is described by the approximate solution of the radial infinite reservoir as applied to the fracture medium:q w 4 f pf = ------------- ln (--------t)..............(1) 4 hf kf y' r2wThis equation accounts for the first part of be fractured-reservoir typical pressure response that, in a semilog plot of pressure vs time, starts as a straight line and then shifts to another parallel straight line (see Figs. 1 and 2).As mentioned above, the matrix blocks act as a uniformly distributed source in the fractured medium. The effect of this source is evident after a certain time lag, since the response of the matrix blocks is slower than the fracture-medium response because of the blocks' "tight" nature.Assuming that the shape of the matrix blocks may be approximated by regular solids, their internal pressure distribution, and hence the flow through pressure distribution, and hence the flow through their surfaces, is a known function found in the theory of heat flow in solids (see Ref. 6). These solutions are given for solids with unitary pressure (temperature) loss at their surfaces as a boundary condition.Considering that the pressure in the fractures surrounding the regular matrix blocks is variable the outflow from the blocks is described through a convolution: SPEJ P. 117

Analytical Theory of Erosion

A mathematical theory of erosion is developed along similar lines to the classical Fourier theory of heat flow in solids. The general theory is considered in some detail, and a few representative examples of its application to stream profiles and valley slopes are suggested in outline.

Measurement of Transferred Heat with Solid Heat Flow Meter

Measurement of Transferred Heat with Solid Heat Flow Meter

Analog Methods for Study of Transient Heat Flow in Solids with Temperature-Dependent Thermal Properties

Analog Methods for Study of Transient Heat Flow in Solids with Temperature-Dependent Thermal Properties

Fuel Technology at Sheffield : Prof. R. J. Sarjant, O. B. E

THE chair of fuel technology in the University of Sheffield has been vacant since the death of Prof. R. V. Wheeler in 1938, and the appointment of Dr. R. J. Sarjant to it assumes added importance in view of the national coal situation and the industrial area served by the University. Dr. Sarjant, who is chairman of the Yorkshire Section of the Institute of Fuel, has wide academic knowledge and industrial experience ; trained under the late Prof. W. A. Bone at the Imperial College of Science and Technology, London, where he worked upon the constitution of coal, he was appointed in 1918 as fuel officer to the Research Department of Messrs. Hadfields, Ltd., there undertaking tasks pioneering in character. He published with Sir Robert Hadfield a number of papers on the uses of solid, liquid and gaseous fuels, gas producer practice, alloy steels for furnaces and chemical engineering, and gave the first course of lectures on furnace heating at the University of Sheffield in 1924. His later investigations dealt with : special aspects of the design of open-hearth, reheating and heat-treatment furnaces ; refractories and moulding sands ; and various metallurgical, physical and radiological fields. In 1937 he was appointed a local director of Messrs. Hadfields, Ltd., and head of its Research Department ; and during the War he rendered valuable service on a number of committees, particularly the Fuel Efficiency Committee of the Ministry of Fuel and Power, being chairman of its Education Sub-Committee which produced a notable war-time publication, “The Efficient Use of Fuel”. He was the author of “Furnace Heating” (1925), and the section on fuel economy in industrial furnaces in “Coal : Its Constitution and Uses” (1936) by Bone and Himus. An account of his most recent research in collaboration with Prof. D. R. Hartree on the variable heat flow in solids has now appeared in the Philosophical Transactions of the Royal Society. Prof. Sarjant's appointment at the University of Sheffield will be widely welcomed.

The calculation of variable heat flow in solids

In many contexts, in laboratory work, in industrial processes and in engineering practice, situations arise in which it is required to determine the flow of heat in bodies under nonsteady conditions. In some cases this can be done by direct experiment, and a few cases are sufficiently simple for formal analytical solutions of the appropriate equations to be obtained and evaluated. But direct experiment is often difficult or impossible, especially under practical conditions of manufacture or operation; and often the conditions of the problem, such as inhomogeneity or the shape of the material, or variation of its thermal properties with temperature, either make the formal solution so complicated that its numerical evaluation is impracticable, or put a formal solution out of the question altogether.