Formula For Conductivity Research Articles

Non-uniform temperature distribution's impact on downhole weight on bit (DWOB) measurement and the novel compensatory method

Non-uniform temperature distribution of DWOB measuring devices has a great effect on the accuracies of weight on bit (WOB) readings. To study the influence, two types of non-uniform temperature distributions of the WOB measuring device were created. The relationship between the two temperature distributions was studied with the further transform of heat conduction formulas. Then the strain of the measuring device was acquired under the two temperature distributions. And the relations of the strain in the two conditions was obtained with the further transform of compatibility equations and constitutive equations. To quantify the influence of non-uniform temperature distribution, a contrast simulation without non-uniform temperature distribution was carried out. The simulated results showed that the WOB errors were 9.33 kN and 46.25 kN. This paper proposed a novel compensating method based on the deduced relationships above, with which the WOB error was eliminated to 0.4 kN. To further validate the new method, the laboratory heating and cooling experiments were carried out. The experiment showed that the biggest WOB error was eliminated to 1.7 kN while the original error was up to 60 kN. Then a field experiment was conducted. Eight connection processes are chosen to further elaborate the temperature difference's impact and the related compensatory method. The economic loss caused by the WOB measuring inaccuracy was calculated, which was up to 1.17% of the drilling cost per meter. The work presented herein can serve as guidance for the DWOB measurement.

Hall viscosity and nonlocal conductivity of gapped graphene

We calculate the Hall viscosity and the nonlocal (i.e., dependent on wave vector $\bm q$) Hall conductivity of "gapped graphene" (a non-topological insulator with two valleys) in the presence of a strong perpendicular magnetic field. Using the linear-response theory at zero temperature within the Dirac approximation for the Landau levels, we present analytical expressions for both valley and total Hall viscosity and conductivity up to $\bm q^2$ at all frequencies. Although the final formulas for total Hall viscosity and conductivity are similar to the ones previously obtained for gapless graphene, the derivation reveals a significant difference between the two systems. First of all, both the Hall viscosity and the Hall conductivity vanish when the Fermi level lies in the gap that separates the lowest Landau level in the conduction band from the highest Landau level in the valence band. It is only when the Fermi level {\it is not} in the gap that the familiar formulas of gapless graphene are recovered. Second, in the case of gapped graphene, it is not possible (at least within our present approach) to define a single-valley Hall viscosity: this quantity diverges with a strength proportional to the magnitude of the gap. It is only when both valleys are included that the diverging terms, having opposite signs in the two valleys, cancel out and the familiar result is recovered. In contrast to this, the nonlocal Hall conductivity is finite in each valley. These results indicate that the Hoyos-Son formula connecting the Hall viscosity to the coefficient of $q^2$ in the small-$q$ expansion of the $q$-dependent Hall conductivity cannot be applied to each valley, but only to the system as a whole. The problem of defining a "valley Hall viscosity" remains open.

Study on Calculation Formula of Field-Saturated Hydraulic Conductivity based on Permeability Test for the Ground above the Water Table

Study on Calculation Formula of Field-Saturated Hydraulic Conductivity based on Permeability Test for the Ground above the Water Table

Formulation of heat conduction and thermal conductivity of metals

Abstract The well-known low-pressure monatomic gas thermal conductivity expression is based on the Maxwell-Boltzmann velocity distribution and involves the mean particle velocity, the gas heat capacity at constant volume and the particle mean free path. The extension of the formula to a free electron Fermi gas, using the Fermi velocity along with the Sommerfeld electronic heat capacity, was demonstrated in the literature using the Boltzmann transport equation. A different formulation of heat conduction in sufficiently pure metals, yielding the same formula for the thermal conductivity, is provided in the present investigation using the free electron Fermi gas energy distribution with the thermal conductivity determined from the net heat transfer occurring due to random motions of the free electrons in the presence of temperature gradient. Potential applications of this approach include extension of the present kinetic model incorporating quantum effects to cases in which electron scattering occurs such as in nanowires and hollow nanowires.

Dynamical gauge fields and anomalous transport at strong coupling

Anomalous transport coefficients are known to be universal in the absence of dynamical gauge fields. We calculate the corrections to these universal values due to dynamical gluon fields at strong coupling, at finite temperature and finite density, using the holographic duality. We show that the consistent chiral magnetic and chiral vortical currents receive no corrections, while we derive a semi-analytic formula for the chiral separation conductivity. We determine these corrections in the large color, large flavor limit, in terms of a series expansion in the anomalous dimension Δ of the axial current in terms of physical parameters Δ, temperature, electric and chiral chemical potentials and the flavor to color ratio frac{N_f}{N_c} . Our results are applicable to a generic class of chiral gauge theories that allow for a holographic description in the gravity approximation. We also determine the dynamical gluon corrections to the chiral vortical separation current in a particular example in the absence of external axial fields.

Experimental and theoretical study on thermal properties of porous PDMS

Groups of porous polydimethylsiloxane (p-PDMS) with different porosities were fabricated, and thermal properties of them were measured. Theoretical prediction applying an asymptotic homogenization method is also presented. Good agreements between the experimental results and theoretical ones are achieved. Studies show the thermal properties of p-PDMS evidently alter with the porosity, whereas they are nearly independent on the pore size. A fitted formula of the thermal conductivity with respect to the porosity is suggested. Disturbance due to temperature is also studied experimentally. Results presented here make a preparation for further thermal analysis and structural optimization of flexible electronics based on p-PDMS.

Thermal driven flows inside a square enclosure saturated with nanofluids: Convection heat functions and transfer rate revisions from a homogenous model

In former theoretical researches of nanofluid flows, numerical investigations could not agree with experimental observations, particularly regarding whether the mixing nanoparticles will enhance or deteriorate the heat transfer. In the present work, thermal driven buoyancy flows of nanofluids in a square enclosure were modeled by the use of homogeneous assumptions and the effective kinematic viscosity and thermal conductivity formulas. Thoroughly developed heat transfer coefficient is subsequently proposed, aiming to critically evaluate the performance of nanofluid heat transport. Numerical results are presented over a wide range of thermal Rayleigh number (103 ≤ Ra ≤ 106) and nanoparticles volume fraction (0.001 ≤ φ ≤ 0.04). Present modeling results accurately predict both the enhancement and deterioration of the natural convection heat transfer, fully validated by former experimental observations. Overall, mathematical models and Nusselt number definitions proposed in the present work effectively enhance the reliability of numerical modeling researches on the nanofluid heat transfer. Present clarification research on the Nusselt unifications could benefit future development of thermal carrier fluid enhanced by nano-particles.

Effective conductivity of a random suspension of highly conducting spherical particles

• A constructive approach for random 3D composites is developed. • The question of conditionally divergent series for random composites is resolved. • The famous Jeffreys formula for the effective conductivity of suspensions is revised and extended. • A theory of 3D Eisenstein functions is developed. Randomly distributed non-overlapping perfectly conducting spheres are embedded in a conducting matrix with the concentration of inclusions f . Jeffrey (1973) suggested an analytical formula valid up to O ( f 3 ) for macroscopically isotropic random composites. A conditionally convergent sum arose in the spatial averaging . In the present paper, we apply a method of functional equations to random composites and correct Jeffrey’s formula. The main revision concerns the proper investigation of the conditionally convergent sum and correction the f 2 -term. An algorithm for symbolic computations of the effective conductivity tensor is developed and performed up to O ( f 10 3 ) . The obtained formulae explicitly demonstrate the dependence of the effective conductivity tensor on the deterministic and probabilistic distributions of inclusions in the f 2 -term, and in the f 3 -term. This leads to the conclusion that some previous formulae presented as universal, i.e., valid for all random composites, may be actually applied only to dilute or to special composites when interaction between inclusions do not matter.

Multiscale modeling and theoretical prediction for the thermal conductivity of porous plain-woven carbonized silica/phenolic composites

As a typical phenolic resin-based ablative material, silica/phenolic composites are extensively used in the aerospace industry. However, thermodynamic properties of carbonized plain-woven composites formed during ablation process are rarely studied. Toward this end, we propose a multiscale prediction model to investigate the effective thermal conductivity of porous plain-woven carbonized silica/phenolic composites by combining finite element analysis with existing two-phase composite models. A general approach is presented to compute the effective thermal conductivity with varying structural parameters. First, to consider effect of pores in phenolic resin matrix, the porous model is established to calculate the effective thermal conductivity of matrix with different porosities and pore morphologies. Then, heat transfer simulations are conducted on the multiscale model, including the yarn scale in the axial and transverse directions and the woven composite scale in the in-plane and out-of-plane directions. Empirical formulas for effective thermal conductivity are obtained, which comprehensively considers the factors of matrix porosity, fiber volume fraction, and temperature.

Diffusive Heat Waves in Random Conformal Field Theory.

We propose and study a conformal field theory (CFT) model with random position-dependent velocity that, as we argue, naturally emerges as an effective description of heat transport in one-dimensional quantum many-body systems with certain static random impurities. We present exact analytical results that elucidate how purely ballistic heat waves in standard CFT can acquire normal and anomalous diffusive contributions due to our impurities. Our results include impurity-averaged Green's functions describing the time evolution of the energy density and the heat current, and an explicit formula for the thermal conductivity that, in addition to a universal Drude peak, has a nontrivial real regular contribution that depends on details of the impurities.

Research for the heat leakage caused by gaps on barrel insulation structure of reactor pressure vessel

Due to the function requirements of the Cavity Injection and Cooling System, the barrel insulation structure of HPR1000 reactor pressure vessel has been greatly improved compared with the previous projects. In the past, the empirical formula method was used to evaluate the thermal properties of the insulation, but the influences of the support structure and the excessive gap on insulation are difficult to evaluate. In this paper, the fitting formula of the equivalent thermal conductivity and the qualitative temperature of the insulation have been obtained firstly through the heat transfer test. Then, ANSYS Fluent was used to simulate the barrel insulation structure with gaps of HPR1000. A circumferential 15° model was established to obtain evaluation method for flow leakage with gaps in hot state, and then a whole model of the barrel insulation structure with gaps was established to obtain heat loss of insulation based on calculation of flow leakage. The sensitivity of gap size and ventilation parameters to heat leakage was further analyzed. Finally, it was indicated that, by minimizing joint gap length, setting of overlaps, controlling cold gap, optimizing structure of insulation support, the effect of heat leakage caused by gaps can be reduced.

Protective Clothing Based on High-temperature Thermal Radiation

Due to the needs of today's society, there must be a particular group of people working in a high-temperature thermal radiation environment. High-temperature environments can quickly cause significant harm to the human body, while thermal protective clothing can effectively reduce the harm to the human body caused by high temperatures. We can solve this problem by building a model. Set up a multi-layer protective clothing for heat conduction formula under the temperature variation of heat conduction model of the MATLAB to map the temperature with time, 3 d surface figure, the variation of the temperature distribution can lead the Excel data tables, and processing the data in the table data, using MATLAB software to curve fitting, the fitting curve of time and skin temperature. At the same time, on the optimal thickness of protective clothing, can be based on the initial conditions and boundary conditions, construct the objective function, and use the improved particle swarm algorithm for solving, specific calculation will difference algorithm as local search of particle swarm optimization algorithm, the particle swarm algorithm with differential evolution algorithm is the local optimization solution as the initial population of generation of differential evolution operations, thickness of solving it is concluded that the optimal approximate solution, and it is concluded that the optimal thickness. The convection and radiation heat transfer coefficients, convection and radiation heat transfer, and skin temperature were calculated. Then, by using the extensibility of CFD simulation and the flexibility of environmental temperature setting, the human thermal radiation stress response model was embedded into the CFD simulation, to predict the real-time changes of human core temperature in a high-temperature thermal radiation environment. Combined with the core temperature threshold and exposure time, people's rescue operation time under different thermal radiation environment conditions can be reasonably scheduled and arranged to reduce the level of thermal stress, improve rescue efficiency and guarantee people's life safety. Finally, the thermal protection clothing is studied to determine the temperature distribution of each layer of thermal protective clothing. It provides a theoretical reference for the functional design of thermal protective clothing.

COMPREHENSIVE METHODS OF EVALUATION OF EFFICIENCY AND OPTIMIZATION OF HEAT-UTILIZATION SYSTEMS

At present, Ukraine has the necessary potential for the implementation of effective energy-saving technologies for heat recovery, and therefore the problem of their development and implementation is relevant for the country's energy sector. The solution of this problem is related to the need for systematic studies of the efficiency of optimization of heat recovery facilities from the standpoint of modern methodological approaches. The paper outlines the main stages in the development of integrated methods for assessing the efficiency and optimization of heat recovery systems based on the principles of exergic analysis, statistical methods for planning the experiment, structured variational methods, multilevel optimization methods, the theory of linear systems and the thermodynamics of irreversible processes. Examples and illustrations illustrate some of the stages in the development of complex methods. The necessary general step in the development of methodologies is the development of new performance criteria. Such criteria are highly sensitive to changes in the regime and design parameters of heat recovery systems due to the inclusion of some exergic characteristics in them. The developed criteria also serve as target optimization functions. For individual elements of heat recovery systems, efficiency and optimization methods usually include the definition of the functional dependencies of the selected efficiency criteria on the main parameters. For this, balance methods of exergic analysis and statistical methods of experiment planning are used. If such dependencies are established, optimization is carried out using known mathematical methods. For complex heat recovery systems involving a large number of elements, it is not possible to establish general analytical dependencies of the optimization objective functions on the parameters of the system when constructing mathematical models necessary for their optimization. Complex methods based on the basic principles of structural-variant methods, methods of multilevel optimization, the theory of linear systems, and the thermodynamics of irreversible processes have been developed for such cases. For this purpose, structural diagrams of plants, block diagrams of multi-level optimization have been developed, complete input matrices have been constructed, mathematical models for the processes under investigation have been developed, formulas have been derived for calculating the loss of exergy power in heat conduction processes and formulas for calculating dissipators of exergy. A well-founded choice of the methodology for evaluating efficiency and optimization raises the effectiveness of optimization, since it allows the use of parameters maximally close to optimal when developing the heat recovery system design, which in turn increases the efficiency of the system. References 14, figures 5.

Viscous Gas Flow between Vertical Walls

A new solution for the Navier–Stokes equations has been found for a plane steady-state shear flow of a viscous gas in the gravity field between two vertical walls. For the temperature dependence of the viscosity factor, Sutherland’s formula is accepted; for the heat conductivity factor, two formulas with the same accuracy are used: a known formula for low temperatures (170–1000 K) and a first-proposed formula for high temperatures (800–1500 K). In each of these temperature ranges, a general solution for the Navier–Stokes equations has been obtained. The solution is expressed in terms of a function which satisfies an ordinary second order differential equation having different forms for low and high temperatures depending on the chosen formula for heat conductivity. For low temperatures, the solution of this equation is obtained numerically; for high temperatures, owing to using the new formula for heat conductivity, analytically. Examples of exact solutions are presented.

Longitudinal conductivity and Hall coefficient in two-dimensional metals with spiral magnetic order

We compute the longitudinal dc conductivity and the Hall conductivity in a two-dimensional metal with spiral magnetic order. Scattering processes are modeled by a momentum-independent relaxation rate $\Gamma$. We derive expressions for the conductivities, which are valid for arbitrary values of $\Gamma$. Both intraband and interband contributions are fully taken into account. For small $\Gamma$, the ratio of interband and intraband contributions is of order $\Gamma^2$. In the limit $\Gamma \to 0$, the conductivity formulas assume a simple quasiparticle form, as derived by Voruganti et. al. [Phys. Rev. B 45, 13945 (1992)]. Using the complete expressions, we can show that relaxation rates in the regime of recent transport experiments for cuprate superconductors in high magnetic fields are sufficiently small to justify the application of these simplified formulas. The longitudinal conductivity exhibits a pronounced nematicity in the spiral state. The drop of the Hall number as a function of doping observed recently in several cuprate compounds can be described with a suitable phenomenological ansatz for the magnetic order parameter.

Analytical investigation of superior gas sensor based on phosphorene

The recent discovery of phosphorene, a 2D allotrope of semiconducting black phosphorus has aroused significant interest for future electronic device applications. Phosphorene isolated from bulk black phosphorus, is an intrinsic p-type material with a variable band gap for a variety of applications. In this study the structure of field effect transistor (FET) is employed where between the drain and source the phosphorene substance is used as the channel. We have developed and proposed analytical models with assuming that the gate voltage changes according to the NO2 concentration variation, then we have derived mathematical model by using phosphorene conductance formula. Classification and Regression trees (CART) algorithm is also intended to obtain another model for the current–voltage characteristic. Studies were carried out by using CART as well as the analytical models. This information was used to compare our developed models with the extracted data from experimental work by Abbas, which indicates a satisfactory agreement and validity of proposed models.

Correlation Analysis of Thermal Physical Indexes in Subway Engineering

By collecting and sorting the thermal physical indexes of the 1, 2, 5, 7 and 11 lines of Shenzhen metro, the relationship between the physical properties and the physical properties of gravel clay was analyzed. The correlation statistics of factors affecting the thermal physical indexes of gravel clay are carried out. The empirical formula of specific heat capacity and heat conductivity are proposed on the basis of moisture content, void ratio and density. It provides a new way to obtain the thermal physical indexes in the investigation and design of the subway engineering.

Research on carbon fiber reinforced thermal polymer/stainless steel laser direct joining

To improve the numerical simulation accuracy of carbon fiber reinforced thermal polymer (CFRTP)/stainless steel laser direct joining (LDJ), a fitting formula of thermal contact conductance was established based on experiments in this paper. Taking into account the thermal contact resistance, a three-dimensional finite element thermal contact model of LDJ was established, and the theoretical simulation and experimental results were compared and analyzed. The result showed that the thermal contact model was more consistent with the reality compared with the traditional model. This thermal contact model could be used to characterize the influence of clamping pressure on the laser joining quality. When the laser power was 318 W and the clamping pressure was 0.1 MPa, the relative error of the melting width was 17.8% for the traditional model and 6.7% for the thermal contact model considering the thermal conductivity. The numerical simulation accuracy could be improved in the process of LDJ. With this numerical model, relationships between the thermal behaviors and the joining parameters were studied numerically. The CFRTP/stainless steel laser joining experiments were also carried out, and the result showed that the joint width measured agreed well with the numerical result.

Convergence of iterative methods based on Neumann series for composite materials: Theory and practice

SummaryIterative fast Fourier transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier space and the constitutive law in real space. The methods correspond to series expansions of appropriate operators and to series expansions for the effective tensor as a function of the component moduli. It is shown that the singularity structure of this function can shed much light on the convergence properties of the iterative fast Fourier transform methods. We look at a model example of a square array of conducting square inclusions for which there is an exact formula for the effective conductivity (Obnosov). Theoretically, some of the methods converge when the inclusions have zero or even negative conductivity. However, the numerics do not always confirm this extended range of convergence and show that accuracy is lost after relatively few iterations. There is little point in iterating beyond this. Accuracy improves when the grid size is reduced, showing that the discrepancy is linked to the discretization. Finally, it is shown that none of the 3 iterative schemes investigated overperforms the others for all possible microstructures and all contrasts.

Canonical Drude Weight for Non-integrable Quantum Spin Chains

The Drude weight is a central quantity for the transport properties of quantum spin chains. The canonical definition of Drude weight is directly related to Kubo formula of conductivity. However, the difficulty in the evaluation of such expression has led to several alternative formulations, accessible to different methods. In particular, the Euclidean, or imaginary-time, Drude weight can be studied via rigorous renormalization group. As a result, in the past years several universality results have been proven for such quantity at zero temperature; remarkably the proof works for both for integrable and non-integrable quantum spin chains. Here we establish the equivalence of Euclidean and canonical Drude weights at zero temperature. Our proof is based on rigorous renormalization group methods, Ward identities, and complex analytic ideas.