Thermophysical Quantities Research Articles

Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell

This problem deals with the thermo-elastic interaction due to step input of temperature on the stress free boundaries of a homogeneous visco-elastic orthotropic spherical shell in the context of a new consideration of heat conduction with fractional order generalized thermoelasticity. Using the Laplace transformation, the fundamental equations have been expressed in the form of a vector-matrix differential equation which is then solved by eigen value approach and operator theory analysis. The inversion of the transformed solution is carried out by applying a method of Bellman et al (1966). Numerical estimates for thermophysical quantities are obtained for copper like material for weak, normal and strong conductivity and have been depicted graphically to estimate the effects of the fractional order parameter. Comparisons of the results for different theories (TEWED (GN-III), three-phase-lag model) have also been presented and the effect of viscosity is also shown. When the material is isotropic and outer radius of the hollow sphere tends to infinity, the corresponding results agree with that of existing literature.

Fractional Order Two-Temperature Dual-Phase-Lag Thermoelasticity with Variable Thermal Conductivity.

A new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of dual-phase-lag heat conduction with fractional orders. The theory is then adopted to study thermoelastic interaction in an isotropic homogenous semi-infinite generalized thermoelastic solids with variable thermal conductivity whose boundary is subjected to thermal and mechanical loading. The basic equations of the problem have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by using a state space approach. The inversion of Laplace transforms is computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to study the effects of the variable thermal conductivity, temperature discrepancy, and the fractional order parameter.

Two-Temperature Generalized Thermoelasticity in a Fiber-Reinforced Hollow Cylinder Under Thermal Shock

This paper deals with the thermoelastic interactions in a transversely isotropic, infinite hollow cylinder in which the boundaries are stress-free. There is no temperature in the inner boundary and heat flux is applied on the outer boundary. In the context of two-temperature generalized thermoelasticity theory, the three-phase-lag thermoelastic model and Green Naghdi model III (GN-III) are employed to study the thermophysical quantities. The Laplace transform is used to transform the coupled equations into the Laplace transformed domain. Then two different methods, the Galerkin finite element technique and eigen-value approach, are employed to solve the resulting equations in the transformed domain. The numerical inversion of the transform is carried out using Fourier-series expansion techniques. The physical quantities have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (GN-III and three-phase-lag model) and for two different methods are presented.

Study of Two-Temperature Generalized Thermo-Piezoelastic Problem

This article deals with the thermoelastic interaction in a piezoelastic half-space body in which the boundary is stress free and subjected to thermal loading. In the context of two-temperature generalized thermoelasticity theory (IMA-2006) the three-phase-lag (3P) thermoelastic model [1], Green-Naghdi model III (GNIII) and Lord-Shulman model (LS) are employed to study the thermophysical quantities. The theory of 3P lag heat conduction equation leads to a fourth order partial differential equation. The basic equations have been written in the form of vector-matrix differential equation in Laplace-transform domain which is then solved by state-space approach. The numerical inversion of the transform is carried out by a method based on Fourier-series expansion techniques. The numerical estimates of the conductive temperature, the strain and the stress distributions are obtained and are shown graphically. The effect of two-temperature and electric field on the solutions have been studied and the comparison of results among different thermoelastic models are made.

Bulk, Surface, and Gas-Phase Limited Water Transport in Aerosol

The influence of solute species on mass transfer to and from aqueous aerosol droplets is investigated using an electrodynamic balance coupled with light scattering techniques. In particular, we explore the limitations imposed on water evaporation by slow bulk phase diffusion and by the formation of surface organic films. Measurements of evaporation from ionic salt solutions, specifically sodium chloride and ammonium sulfate, are compared with predictions from an analytical model framework, highlighting the uncertainties associated with quantifying gas diffusional transport. The influence of low solubility organic acids on mass transfer is reported and compared to both model predictions and previous work. The limiting value of the evaporation coefficient that can be resolved by this approach, when uncertainties in key thermophysical quantities are accounted for, is estimated. The limitation of slow bulk phase diffusion on the evaporation rate is investigated for gel and glass states formed during the evaporation of magnesium sulfate and sucrose droplets, respectively. Finally, the effect of surfactants on evaporation has been probed, with soluble surfactants (such as sodium dodecyl sulfate) leading to little or no retardation of evaporation through slowing of surface layer kinetics.

Comparison of Approaches for Measuring the Mass Accommodation Coefficient for the Condensation of Water and Sensitivities to Uncertainties in Thermophysical Properties

We compare and contrast measurements of the mass accommodation coefficient of water on a water surface made using ensemble and single particle techniques under conditions of supersaturation and subsaturation, respectively. In particular, we consider measurements made using an expansion chamber, a continuous flow streamwise thermal gradient cloud condensation nuclei chamber, the Leipzig Aerosol Cloud Interaction Simulator, aerosol optical tweezers, and electrodynamic balances. Although this assessment is not intended to be comprehensive, these five techniques are complementary in their approach and give values that span the range from near 0.1 to 1.0 for the mass accommodation coefficient. We use the same semianalytical treatment to assess the sensitivities of the measurements made by the various techniques to thermophysical quantities (diffusion constants, thermal conductivities, saturation pressure of water, latent heat, and solution density) and experimental parameters (saturation value and temperature). This represents the first effort to assess and compare measurements made by different techniques to attempt to reduce the uncertainty in the value of the mass accommodation coefficient. Broadly, we show that the measurements are consistent within the uncertainties inherent to the thermophysical and experimental parameters and that the value of the mass accommodation coefficient should be considered to be larger than 0.5. Accurate control and measurement of the saturation ratio is shown to be critical for a successful investigation of the surface transport kinetics during condensation/evaporation. This invariably requires accurate knowledge of the partial pressure of water, the system temperature, the droplet curvature and the saturation pressure of water. Further, the importance of including and quantifying the transport of heat in interpreting droplet measurements is highlighted; the particular issues associated with interpreting measurements of condensation/evaporation rates with varying pressure are discussed, measurements that are important for resolving the relative importance of gas diffusional transport and surface kinetics.

Fractional order two-temperature thermoelasticity with finite wave speed

In this paper, a new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of heat conduction with fractional orders. The two-temperature Lord–Shulman (2TLS) model and two-temperature Green–Naghdi (2TGN) models of thermoelasticity are combined into a unified formulation using the unified parameters. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain which is then solved by using a state-space approach. The inversions of Laplace transforms are computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to estimate the effects of the temperature discrepancy and the fractional order parameter.

Local Thermomechanical Analysis of a Microphase-Separated Thin Lamellar PS-b-PEO Film

We use atomic force microscopy (AFM) and hot tip AFM (HT-AFM) to thermophysically characterize a 30 nm thick film of poly(styrene-block-ethylene oxide), PS-b-PEO, and to modify its lamellar patterns having spacing of 39 ± 3 nm. AFM tip scans of the polymer film induce either abrasive surface patterns or nanoscale ripples, which depend upon the tip force, temperature, and number of scans. The evolution of the lamellar patterns is explained by the polymer film molecular structure and mode I crack propagation in the polymer combined with the stick-and-slip behavior of the AFM tip. The HT-AFM measurements at various tip-sample temperatures and scanning speeds yield several thermophysical quantities: the PEO melting temperature of 54 ± 12 °C, the PS glass transition temperature of 54 ± 12 °C, the PS-b-PEO specific heat of 3.6 ± 2.7 J g(-1) K(-1), the PEO melting enthalpy of 111 ± 88 J g(-1), and the free energy of Helmholtz for PEO unfolding (and melting) of 10(-20) J nm(-2). These quantities are obtained for PS-b-PEO volumes of 30,000 nm(3), which correspond to 30 ag of the polymer.

Calculation of maximum temperatures in automatic welding and surfacing

Correction of the well-known Rykalin equation for calculating maximum temperatures in the surfacing zone is described. It is proposed to carry out calculations taking into account the factors associated with melting of the parent metal: the latent heat of melting, the temperature to which the parent metal is heated during melting, displacement of molten metal into the tail part of the weld pool, efficient selection of the thermophysical quantities, etc.

A Benchmark Test Set for Alchemical Free Energy Transformations and Its Use to Quantify Error in Common Free Energy Methods.

There is a significant need for improved tools to validate thermophysical quantities computed via molecular simulation. In this paper we present the initial version of a benchmark set of testing methods for calculating free energies of molecular transformation in solution. This set is based on molecular changes common to many molecular design problems, such as insertion and deletion of atomic sites and changing atomic partial charges. We use this benchmark set to compare the statistical efficiency, reliability, and quality of uncertainty estimates for a number of published free energy methods, including thermodynamic integration, free energy perturbation, the Bennett acceptance ratio (BAR) and its multistate equivalent MBAR. We identify MBAR as the consistently best performing method, though other methods are frequently comparable in reliability and accuracy in many cases. We demonstrate that assumptions of Gaussian distributed errors in free energies are usually valid for most methods studied. We demonstrate that bootstrap error estimation is a robust and useful technique for estimating statistical variance for all free energy methods studied. This benchmark set is provided in a number of different file formats with the hope of becoming a useful and general tool for method comparisons.

The Widom line as the crossover between liquid-like and gas-like behaviour in supercritical fluids

By conventional definition, a supercritical fluid is one that doesn’t exhibit distinct liquid- or gas-like states. This may need to be revised in light of measurements that show a sharp change in the speed of sound in supercritical argon when it crosses a well-defined line on its pressure versus temperature phase diagram. According to textbook definitions1, there exists no physical observable able to distinguish a liquid from a gas beyond the critical point, and hence only a single fluid phase is defined. There are, however, some thermophysical quantities, having maxima that define a line emanating from the critical point, named ‘the Widom line’2 in the case of the constant-pressure specific heat. We determined the velocity of nanometric acoustic waves in supercritical fluid argon at high pressures by inelastic X-ray scattering and molecular dynamics simulations. Our study reveals a sharp transition on crossing the Widom line demonstrating how the supercritical region is actually divided into two regions that, although not connected by a first-order singularity, can be identified by different dynamical regimes: gas-like and liquid-like, reminiscent of the subcritical domains. These findings will pave the way to a deeper understanding of hot dense fluids, which are of paramount importance in fundamental and applied sciences.

ANALYTIC EQUATION OF STATE FOR EXP-6 POTENTIAL FLUID AND APPLICATION TO N2 FLUID

An analytical expression for the equation of state and thermo-physical quantities of exponential-6 ( exp- 6) fluid are derived based on the Ross variational perturbation theory. The developed formalism is applied to N 2 fluid. Comparisons of theory and simulations for exp- 6 potential fluid are presented. The agreement of numerical results of pressure and internal energy with Monte Carlo (MC) simulations show that the theoretical model is satisfactory except where a few points from metastable ones appeared in literature. The expression has been applied to fluid nitrogen and the fitting to experimental data of fluid N 2 is surprisingly good. The predictions of pressure in the range of high temperature and high density are satisfactory. It has also been found that the analytic equation of state for exp- 6 potential fluid based on RDF proposed by Sun et al. is better in a wide range of pressures and temperatures than that derived from PY expression. Comparisons show that a potential dependence on temperature and density (or volume) may be necessary for the understanding of interaction between N 2 molecules. The equation of state can also be extended to application of important real gases such as H 2, O 2, CH 4, CO and CO 2.

A New Correlation of Nusselt Number for Impinging Jets

Jet impingement heat transfer has received a remarkable amount of attention by researchers throughout the world for many years due to widespread interest from both academic and industrial points of view. However, the fluid dynamics involved with arrays of jets are very complex and still not completely understood. Therefore, a functional relationship of the Nusselt number, which involves thermophysical and dynamic quantities as well as geometric parameters, is still not univocally and generally established. In this research analysis, some empirical equations, which are available in the literature for arrays of round impinging jets, are reviewed, and a new, simpler correlation is developed that better represents experimental data published by several researchers.

Thermophysical characterization of ZrN and (Zr,Pu)N

Nitride compounds are currently considered as possible fuels for advanced nuclear reactors. Among the relevant properties to be investigated, thermophysical quantities such as heat capacity and thermal diffusivity/conductivity are key to ensure safe operation of the fuel in the reactor. Both physical and chemical phenomenological experimental activities are included in this effort. The experimental procedures were optimized to limit oxidation of materials in presence of even small quantities of oxygen and moisture, especially during the measurements at high temperature. Heat capacity and thermal diffusivity/conductivity were measured for ZrN and (Zr,Pu)N compounds. A consistent set of results was obtained from low- and high-temperature C p measurements for both materials. The excess C p of solution was estimated. Increasing trends with temperature were observed for the thermal diffusivity and conductivity of both materials in the temperature range considered, confirming the metallic behavior of this class of materials. The presence of Pu causes an almost constant decrease of the thermal conductivity compared to the pure ZrN matrix.

Analytic equation of state and thermodynamic properties for He–H 2 fluid mixtures over a wide range of pressures and temperatures

The analytical expressions for the equation of state and thermo-physical quantities of Exp-6 fluid are derived based on the Ross variational perturbation theory and with the quantum effect taken into account. The formalism developed is applied to the He–H 2 mixtures. The agreement of numerical results of pressure and internal energy with MC simulations is shown far better than the analytic equation of state developed by [I. Ali, S.M. Osman, N. Sulaiman, R.N. Singh, Phys. Rev. E 69 (2004) 0561045]. The isotherms for pressure, internal energy and packing factor for five concentrations and four temperatures versus volume are calculated and analyzed. The numerical results for excess Gibbs free energy and entropy of mixing are presented. The variation of the excess Gibbs free energy of mixing, and the variation of the excess entropy of mixing versus temperature and pressure are different from and similar to that of Ali et al., respectively.

Equation of state and thermodynamic functions for the fcc soft-core multiple-Yukawa solid and application to fullerenes with compressible molecular radius

The generalized free volume theory is applied to the soft-core multiple-Yukawa solid, and the hard-core multiple-Yukawa is included in as a special case. The expressions for equation of state and internal energy are derived. The formalism developed is applied to the ${\mathrm{C}}_{60}$, ${\mathrm{C}}_{76}$, and ${\mathrm{C}}_{84}$ solids. The effective diameter of ${\mathrm{C}}_{60}$ molecule is taken as the experimental value; the parameters of the double Yukawa (DY) potential for carbon-carbon atoms are determined through fitting the experimental data of cohesive energy, the lattice constant, and the compression curve of ${\mathrm{C}}_{60}$ solid at ambient temperature. The effective diameter of ${\mathrm{C}}_{76}$ and ${\mathrm{C}}_{84}$ molecules are determined through fitting the experimental lattice constants at ambient temperature. The numerical results of ${\mathrm{C}}_{60}$ solid from the soft-core DY potential are in good agreement with the experiments, including the lattice constant and compression curve. The lattice constant versus temperature relationship for ${\mathrm{C}}_{76}$ and ${\mathrm{C}}_{84}$ solids calculated from the DY potential is qualitatively in accordance with experimental data as same as the Girifalco potential. The compression curve of the ${\mathrm{C}}_{84}$ solid calculated from the DY potential deviates from and is softer than the experimental data available. The reason for deviation is discussed, and it is concluded that the influence of compressibility of fullerene molecules to thermophysical quantities is important at high-pressure conditions.

Effect of Basis Sets on the Selection of the Level of Theory Toward the Development of Quantum-Based Force Field Equation for Ionic Liquids

The chemical industry is under considerable pressure to replace many of the volatile organic compounds. Volatile organic compounds are a major contributor to air pollution, but out of necessity, they are still frequently used in many chemical and industrial processes. A new class of solvents, referred to as ionic liquids, may offer at least a partial solution to the pollution problem caused by volatile organic compounds. Ionic liquids are generally considered "green" solvents because of their environment-friendly properties. However, the main problem that hinders the chemical industry from using ionic liquids is that, compared to conventional organic solvents, relatively little is known about their thermodynamic and transport properties. Since there are large possible combinations of ionic liquids, it would be very expensive if the study were conducted in the laboratory. The more appropriate approach in studying the properties of ionic liquids is to engage in a computational method, which uses a computer software that evaluates ionic liquids' thermophysical quantities via quantum mechanical and molecular mechanical simulations. In this study, a computer simulation, with the aid of SPARTAN '02 software, is used to study the effect of basis sets on the selection of the appropriate level of theory, which would be employed later in developing a quantum-based force field equation for predicting the properties of ionic liquids. Using the Hartree-Fock self-consistent filled (HF-SCF) molecular orbital model with different basis sets, a single point energy calculations were carried out for the chosen ionic liquid. With the exception of the minimal basis set, the SCF total energies for the other basis sets agree with each other in terms of magnitude. The SCF total energy is not affected as the basis set varies from minimal to split valence and as it polarizes. The most appropriate basis set was found to be 6-31G*. Keywords: Basis sets, Hartree-Fock, ionic liquids, force field equation, level of theory, and SPARTAN '02.

Impact of polymer film thickness and cavity size on polymer flow during embossing: toward process design rules for nanoimprint lithography

This paper presents continuum simulations of polymer flow during nanoimprint lithography (NIL). The simulations capture the underlying physics of polymer flow from the nanometer to millimeter length scale and examine geometry and thermophysical process quantities affecting cavity filling. Variations in embossing tool geometry and polymer film thickness during viscous flow distinguish different flow driving mechanisms. Three parameters can predict polymer deformation mode: cavity width to polymer thickness ratio, polymer supply ratio and capillary number. The ratio of cavity width to initial polymer film thickness determines vertically or laterally dominant deformation. The ratio of indenter width to residual film thickness measures polymer supply beneath the indenter which determines Stokes or squeeze flow. The local geometry ratios can predict a fill time based on laminar flow between plates, Stokes flow, or squeeze flow. A characteristic NIL capillary number based on geometry-dependent fill time distinguishes between capillary- or viscous-driven flows. The three parameters predict filling modes observed in published studies of NIL deformation over nanometer to millimeter length scales. The work seeks to establish process design rules for NIL and to provide tools for the rational design of NIL master templates, resist polymers and process parameters.

Effect of thermophysical quantities on the natural convection flow of gases over a vertical cone

The laminar steady nonsimilar natural convection flow of a gases over an isothermal vertical cone has been investigated where the thermal conductivity, dynamic viscosity and specific heat at constant pressure are assumed to have a power-law variation with absolute temperature. The density is taken as inversely proportional to the absolute temperature, whereas the Prandtl number is assumed to be constant. The nonlinear coupled parabolic partial differential equations have been solved numerically by using an implicit finite-difference scheme. The variable gas properties significantly affects the heat transfer and skin friction. The heat transfer and skin friction decrease with increasing wall temperature ratio and the streamwise distance. The heat transfer increases with suction, but decreases with injection.

Non-contact measurements of thermophysical properties of niobium at high temperature

Four thermophysical properties of both solid and liquid niobium have been measured using the vacuum version of the electrostatic levitation furnace developed by the National Space Development Agency of Japan. These properties are the density, the thermal expansion coefficient, the constant pressure heat capacity, and the hemispherical total emissivity. For the first time, we report these thermophysical quantities of niobium in its solid as well as in liquid state over a wide temperature range, including the undercooled state. Over the 2340 K to 2900 K temperature span, the density of the liquid can be expressed as ρL (T) = 7.95 × 103 − 0.23 (T − T m)(kg · m−3) with T m = 2742 K, yielding a volume expansion coefficient αL(T) = 2.89 × 10−5 (K−1). Similarly, over the 1500 K to 2740 K temperature range, the density of the solid can be expressed as ρs(T) = 8.26 × 103 − 0.14(T − T m)(kg · m−3), giving a volume expansion coefficient αs(T) = 1.69 × 10−5 (K−1). The constant pressure heat capacity of the liquid phase could be estimated as C PL(T) = 40.6 + 1.45 × 10−3 (T − T m) (J · mol−1 · K−1) if the hemispherical total emissivity of the liquid phase remains constant at 0.25 over the temperature range. Over the 1500 K to 2740 K temperature span, the hemispherical total emissivity of the solid phase could be rendered as eTS(T) = 0.23 + 5.81 × 10−5 (T − T m). The enthalpy of fusion has also been calculated as 29.1 kJ · mol−1.