Nonlinear Temperature Profile Research Articles

Gradient on Rayleigh–Bénard – Marangoni – Magnetoconvection in a Micropolar Fluid with Maxwell – Cattaneo Law

The effect of non-uniform temperature gradient on the onset of Rayleigh-Bénard-Marangoni- Magneto-convection in a Micropolar fluid with Maxwell-Cattaneo law is studied using the Galerkin technique. The eigen value is obtained for rigid-free velocity boundary combination with isothermal and adiabatic condition on the spin-vanishing boundaries. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. One linear and five non-linear temperature profiles are considered and their comparative influence on onset is discussed. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (Second Sound) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed.

On thermal diffusion separation in binary mixtures with variable transport coefficients

The stationary heat transfer and Soret separation of a binary mixture between parallel plates with different constant temperatures is studied allowing for variable transport properties. The mixture is described by non-linear one-dimensional equations of heat and mass transfer, where the density, thermal conductivity, and Soret coefficient depend on temperature and concentration. A general procedure for integrating these equations is proposed. The problem is reduced to the ordinary differential equation of first order, which describes the trajectory of the system in the concentration–temperature plane, and implicit dependence of temperature on space coordinate. It is shown that the solution for concentration is unique if the density and thermal conductivity do not depend on concentration. Analytical solutions of the problem are derived in a number of cases, while the most general case is treated numerically. The non-linear temperature and concentration profiles in different binary mixtures (aqueous solutions, colloidal suspensions, polymer blend) are constructed and analyzed. A procedure for extracting the dependence of Soret coefficient on temperature and concentration from the experimentally measured thermal and compositional profiles is suggested.

Daily temperature grids for Austria since 1961—concept, creation and applicability

AbstractCurrent interest into past climate change and its potential role for changes in the environment call for spatially distributed climate datasets of high temporal resolution and extending over several decades. To foster such research, we present a new gridded dataset of daily minimum and maximum temperature covering Austria at 1-km resolution and extending back till 1961 at daily time resolution. To account for the complex and highly variable thermal distributions in this high-mountain region, we adapt and employ a recently published interpolation method that estimates nonlinear temperature profiles with altitude and accounts for the non-Euclidean spatial representativity of station measurements. The spatial analysis builds upon 150 station series in and around Austria (homogenised where available), all of which extend over or were gap-filled to cover the entire study period. The restriction to (almost) complete records shall avoid long-term inconsistencies from changes in the station network. Systematic leave-one-out cross-validation reveals interpolation errors (mean absolute error) of about 1 °C. Errors are relatively larger for minimum compared to maximum temperatures, for the interior of the Alps compared to the flatland and for winter compared to summer. Visual comparisons suggest that valley-scale inversions and föhn are more realistically captured in the new compared to existing datasets. The usefulness of the presented dataset (SPARTACUS) is illustrated in preliminary analyses of long-term trends in climate impact indices. These reveal spatially variable and eventually considerable changes in the thermal climate in Austria.

On the thermodynamics of melting sea ice versus melting freshwater ice

AbstractWe examine the melting of sea ice versus freshwater ice in laboratory experiments and with one-dimensional model simulations. Our primary aim is to investigate the vertical partitioning of heat between thinning and internal phase changes. In agreement with our general understanding of the two ice types, we find that freshwater ice quickly starts thinning and then keeps a constant melt rate for constant external heat input. In contrast, sea ice starts thinning later but then thins faster than freshwater ice. This temporal evolution is caused by the substantial amount of heat that is used for internal phase changes in sea ice. Those internal phase changes give rise to a nonlinear temperature profile in the sea ice during the entire melting period, whereas freshwater ice quickly reaches its melting temperature throughout its entire thickness. Infrared imagery provides additional insights into the surface temperature of both ice types during melting. We find that, during melting, sea ice can have a mean surface temperature several tenths of a degree above 0°C because of meltwater-filled millimetre-scale dimples at the ice surface.

Fluid motion and energy transfer within burning liquid fuel pools of various thicknesses

The burning characteristics and thermal-flow structures within laboratory-scale pool fires have previously been shown to be dependent on the pool’s bottom temperature and the pool wall material. Relatively unexplored are the effects of the thickness of liquid fuel in the pool without ullage. These effects are explored experimental here using a 90mm diameter quartz pool burning methanol in a quiescent environment for a range of bottom boundary temperature (i.e., −4°C to 50°C). Three pools with fuel depth of 6, 12 and 18mm were examined in terms of overall burning rate, flame height, and cross-sectional maps of mean temperature and in-plane 2-D velocity. It was shown that the burning rate and flame height for a specified pool bottom temperature increased with increasing pool depth, and shallower pools were more sensitive to pool bottom boundary temperature. Generally, the pool showed a distinct two-layer thermal structure with a near uniform upper layer, and a lower layer with a non-linear temperature gradient. The uniform layer was coincidental with a pair of standing counter-rotating vortices keeping this fluid well-mixed, while the lower layer had only a slow upward velocity associated with maintaining the liquid level. For the deepest pool, the thicknesses of the well-mixed and lower layers were essentially fixed, and the investigation showed that its velocity and non-dimensional temperature structures were independent of the bottom temperature. This independence was used to identify a regime of thick-pools, which allow the liquid to be modeled with relative simplicity. For shallow pools (i.e., thin-pools), the thicknesses of these layers were dependent on the bottom temperature. Mechanisms for this behavior were proposed. Lastly, an energy analysis of the liquid beneath the well-mixed layer was able to explain the non-linear temperature profiles in that region as being a combination of vertical conduction and advection energy transfer.

On the stability of internally heated natural convection due to the absorption of radiation in a laterally confined fluid layer with a horizontal throughflow

This study focuses on the marginal stability of the natural convection flow induced by the absorption of radiation. Non-uniform internal heating associated with the absorption of radiation following Beer’s law and the absorption and re-emission of residual radiation by the bottom boundary wall lead to a nonlinear base temperature profile that evolves with time. A horizontal throughflow and lateral confinement are incorporated in the analysis, and two forms of convective instability, i.e. longitudinal and transverse rolls, are investigated. It is shown that the formation of longitudinal rolls, with their axes parallel to the throughflow direction, is not affected by the presence of the throughflow. For transverse rolls, with their axes perpendicular to the throughflow direction, however, the throughflow is shown to have a stabilising effect, with the critical Rayleigh number increasing with the increasing throughflow Reynolds number. It follows that longitudinal rolls are the preferred form of instability in laterally unconfined domains for any nonzero Reynolds number and in confined domains if the Reynolds number is greater than a critical value. The value of the critical Reynolds number, which separates the preferred mode of instability, is found to rapidly reduce with increasing lateral extent and approaches zero for a normalised lateral extent greater than 2.0. The lateral confinement is also shown to have a stabilising effect for both longitudinal and transverse rolls, with the critical Rayleigh number increasing with the reducing lateral extent. It is shown that the lateral confinement only substantially affects the wave number of the rolls with their axes parallel to the confining walls but not the rolls with their axes perpendicular to the confining walls.

Vacuum thermochromatography: diffusion approximation, evaluation of desorption energy

The recent report (I. Zvara Vacuum thermochromatography: physical principles and Monte Carlo simulation 2014 Report JINR E6-2014-1, Dubna) concerned Monte Carlo (MC) approach to understanding the vacuum thermochromatography in cylindrical columns by simulating migration histories of a great many molecules. Their paths consist of random variable steps, each of them being followed by adsorption for a random time. The same problem is considered here using the diffusion approximation to random walks. The appropriate diffusion equation is for the fraction of the total retention time spent by the adsorbate “in flight”; it monotonously decreases with time and distance. Meanwhile, the related fraction due to the adsorption time rapidly grows with the inverse temperature and so with distance. The product of the two factors yields a peaking distribution, which well fits that from the MC simulation. Like the latter, the diffusion approach does not yield any explicit formula for the peak as a function of the experimental variables. Yet, we did find such a formula in a semi-theoretical way, when aiming at the two factors’ structure. It accurately enough fits the MC profiles, provides much faster calculations than the two above tools, and is reasonably versatile in accounting for many possible variables. It, for example, greatly enhances accurate evaluation of the experimental data with very poor statistics, like those met in the VTC studies of the heaviest known elements. The here illustrated Bayesian approach to the latter problem requires calculation of the peaks for many desorption energies to find the prior likelihoods of the particular experimental data. This gives the posterior probability density and so the credible intervals of required levels for the sought for energy values. Considered are also peculiarities of treating the VTC data when the column has a non-linear temperature profile, non-circular cross section, or heterogeneous surface.

Effective Thermal Conductivity of Soda‐Lime Silicate Glassmelts with Different Iron Contents Between 1100°C and 1500°C

This study presents a simple method for retrieving the effective thermal conductivity of semitransparent glassmelts from measured temperature profiles. Effective thermal conductivity of molten glass at high temperature is an important thermophysical property that affects the glassmelting and forming processes and thus the quality of the final glass products. In semitransparent glassmelts, heat is transferred by both conduction and radiation. In the limiting case of optically thick glassmelts, typically featuring high iron content, thermal radiation can be treated as a diffusion process. The total heat flux can be expressed as the sum of a phononic and a radiative heat fluxes based on Fourier's law. For weakly absorbing glassmelts, the temperature profile may be strongly nonlinear particularly neat container walls due to the contribution from emission and absorption. Steady‐state measurement techniques, such as the linear heat flux method, have been developed to measure glassmelt effective thermal conductivity at high temperatures. However, they typically use only three temperatures measurements and assume linear temperature profile in the glassmelt. The new retrieval method addresses these drawbacks particularly for weakly absorbing glassmelts featuring nonlinear temperature profiles. It is demonstrated with experimental data collected for soda‐lime silicate glasses with iron content ranging from 0.008 to 1.1 wt% and temperatures between 1100°C and 1550°C.

A Stepped-Bar Apparatus for Thermal Resistance Measurements

A stepped-bar apparatus has been designed and constructed to characterize the thermal resistance of materials using steady-state heat transfer techniques. The design of the apparatus is a modification of the ASTM D5470 standard where reference bars of equal cross-sectional area are used to extrapolate surface temperatures and heat flux across a sample of unknown thermal resistance. The design modification involves intentionally oversizing the upper reference bar (URB) of the apparatus to avoid contact area uncertainty due to reference bar misalignment, which is difficult to account for, as well as the high cost that can be associated with equipping the apparatus with precise alignment controls (e.g., pneumatic alignment). Multidimensional heat transfer in the upper reference bar near the sample interface is anticipated using numerical modeling. The resulting nonlinear temperature profile in the upper reference bar is accounted for by fitting a second order regression line through thermocouple readings near the sample interface. The thermal resistances of commercially available thermal gap pads and thermal pastes were measured with the stepped-bar apparatus; the measured values were in good agreement with published results, and exhibited a high degree of reproducibility. The measurement uncertainty of both the standard and stepped-bar apparatus decrease with increased thermocouple precision. Notably, the uncertainty due to reference bar misalignment with the standard apparatus becomes more pronounced as thermocouple precision and the number of thermocouples increases, which suggests that the stepped-bar apparatus would be especially advantageous for enabling accurate, high-precision measurements of very low thermal resistances.

Computational Modeling of Temperature, Flow, and Crystallization of Mold Slag During Double Hot Thermocouple Technique Experiments

A three-dimensional finite-difference model has been developed to study heat transfer, fluid flow, and isothermal crystallization of mold slag during double hot thermocouple technique (DHTT) experiments. During the preheating stage, temperature in the middle of the mold slag sample was found to be significantly [~350 K (~77 °C)] lower than near the two thermocouples. During the quenching stage, the mold slag temperature decreases with the cooled thermocouple. The temperature across the mold slag achieves a steady, nonlinear temperature profile during the holding stage; the insulating effect of the crystallizing layer in the middle of the slag sample causes the high temperature region to become hotter, while the lower temperature mold slag becomes cooler. Fluid flow is driven by Marangoni forces along the mold slag surface from the hotter region to the cooler region, and then recirculates back through the interior. Slag velocities reach 7 mm/s. Crystallization is predicted to start in the middle of the slag sample first and then grows toward both thermocouples, which matches well with observations of the DHTT experiment.

Effect of Non-Uniform Temperature Gradient on the Onset of Rayleigh–Bénard–Magnetoconvection in Micropolar Fluid with Maxwell–Cattaneo Law

The effect of non-uniform temperature gradient on the onset of Rayleigh-Bénard magnetoconvection in a Micropolar fluid with Maxwell-Cattaneo law is studied using the Galerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal condition on the spin-vanishing boundaries. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. One linear and five non-linear temperature profiles are considered and their comparative influence on onset of convection is discussed. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (Second Sound) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed.

Molecular dynamics simulation study on heat transport in monolayer graphene sheet with various geometries

Using non-equilibrium molecular dynamics (MD) simulations, we study heat transport in monolayer graphene sheet. We show that the thermal transport in monolayer graphene sheet exhibits a strong length dependence on thermal conductivity, reaching 2360 W/mK at 2.8 μm. By modeling a two-dimensional heat spread type of heat conduction mimicking the experimental probing using the excitation laser light focused on a graphene, the isotropic nature of heat flow in graphene is revealed, which is in support of recent experimental probing. The T−1 dependence of thermal conductivity is observed at temperatures above room temperature. A peak value at 300 K is observed with further decreasing T, in good agreement with that of carbon nanotubes reported experimentally. Thermal conductivity of graphene nanoribbons (GNRs) strongly depends on the ribbon width, which is attributed to arise from the surface phonon scattering. Furthermore, the nonlinear temperature profile is revealed for asymmetric GNRs. A fitting approach for the MD obtained temperature profile based upon the analytic solution is proposed to obtain the thermal conductivity of GNRs of asymmetric geometry. These findings shed light on tuning thermal properties of GNRs with geometry optimizations.

NH3/H2O 혼합냉매를 사용한 압축/흡수식 히트펌프 시스템의 흡수기 최적화에 관한 실험적 연구

본 연구는 암모니아/물 혼합냉매를 이용한 압축/흡수식하이브리드 히트펌프 개발에 관한 연구이다. 히트펌프 사이클은 증기압축식과흡수식을 혼합한 개념으로 이단압축기, 흡수기, 재생기, 과열냉각기, 용액열교환기(SHX), 용액펌프, 정류기, 기액분리기 등으로 구성되어 있다. 압축/흡수식 히트펌프는 상변화열교환과정에서 높은 온도구배를 이용하여 90℃ 이상의 고온을 제조하기 위한 목적으로 고안되었다. 특히 흡수기에서의 응축과정은 비열변화로 인하여 온도변화에 비선형성이 뚜렷한데, 시스템 성능 최적화를 위하여는 흡수기의 설계가 중요하다. 본 연구에서는 다수의 판형열교환기로 흡수기를 구성하였는데 열교환기의 용량, 형태, 배치에 따른 성능특성을 실험적으로 관찰하였다.

Optimal design of nonlinear temperature programmed reduction experiments

AbstractWe propose the application of nonconstant temperature gradients to improve the quality of temperature programmed reduction (TPR) experiments with respect to parameter estimation and model discrimination. This leads to TPR experiments with nonlinear temperature profiles (N‐TPR). To determine optimal profiles for the temperature gradient, optimal control problems are set up and solved numerically. The results show that N‐TPR experiments can be significantly better than traditional linear TPR experiments for many different scenarios. To implement these results in practice, we develop and demonstrate reduced optimization problem formulations, which can be solved faster and more reliably than the original formulation, with very similar results. © 2011 American Institute of Chemical Engineers AIChE J, 2011

Temperature Gradient and Curling Stresses in Concrete Pavement with and without Open-Graded Friction Course

Curling stresses of concrete pavement can be very damaging, and reducing the temperature swings would be very beneficial. This study includes a field instrumentation effort with pavement temperature sensors to quantify the thermal behavior of concrete pavement with and without an open-graded asphalt rubber friction course. The study shows a nonlinear temperature profile across slab thickness, with a large change in temperature between day and night at the top of the concrete slab, and little change at the bottom of the slab. Adding an open-graded friction course over the concrete pavement reduces the temperature fluctuation between day and night as a result of the aeration effect, which is increased by traffic. A three-dimensional (3D) finite-element analysis with a nonlinear temperature gradient shows that adding the friction course reduces the curling stresses in the summer. Furthermore, since traffic increases the aeration effect, sections without traffic show lower effect of friction course on reducin...

On errors in thermal conductivity measurements of suspended and supported nanowires using micro-thermometer devices from low to high temperatures

For micro-thermometer devices developed for thermal conductivity measurements of nanowires, it is found using finite element analysis that radiation heat transfer can cause nonlinear temperature profiles in the long supporting beams of the thermometers when the sample stage temperature is considerably higher or lower than room temperature. Although the nonlinearity alone does not introduce errors in the measured thermal conductance, it can cause errors in the measured temperature coefficient of resistance of the thermometers and needs to be minimized with additional radiation shields. For a design where the sample is supported on a silicon dioxide bridge between two micro-thermometers, the numerical analysis reveals that a two-dimensional temperature distribution can cause a 25% error in the sample thermal conductance obtained from a one-dimensional heat conduction analysis for a high-thermal-conductance thin film sample covering only the center part of the oxide bridge. This systematic error is reduced considerably for a low-thermal-conductance nanowire sample. However, care must be taken to ensure that the random uncertainties in the two measured thermal conductance values of the bridge with and without the nanowires are much smaller than the thermal conductance of the nanowires.

Internal thermal coupling in direct-flow coaxial vacuum tube collectors

Abstract This investigation covers the impact of low flow rates on the efficiency of coaxial vacuum tube collectors. Measurements show an efficiency reduction of 10% if reducing the flow rate from 78 kg/m2 h to 31 kg/m2 h for a collector group with 60 parallel vacuum tubes with a coaxial flow conduit at one-sided connection. For a more profound understanding a model of the coaxial tube was developed which defines the main energy fluxes including the internal thermal coupling. The tube simulations show a non-linear temperature profile along the tube with the maximum temperature in the outer pipe. Due to heat transfer to the entering flow this maximum is not located at the fluid outlet. The non-linearity increases with decreasing flow rates. The experimentally determined flow distribution allows simulating the measured collector array. The simulation results confirm the efficiency decrease at low flow rates. The flow distribution has a further impact on efficiency reduction, but even at an ideal uniform flow, a considerable efficiency reduction at low flow rates is to be expected. As a consequence, low flow rates should be prevented for coaxial tube collectors, thus restricting the possible operation conditions. The effect of constructional modifications like diameter or material variations is presented. Finally the additional impact of a coaxial manifold design is discussed.

Simplified Nonlinear Temperature Curling Analysis for Jointed Concrete Pavements

The assumption of a linear temperature change through the slab depth has been overwhelmingly used in pavement analysis since Westergaard proposed a curling solution for rigid pavements. However, the actual temperature profiles through the slab thickness are primarily nonlinear. These nonlinear temperature profiles produce stresses that can be divided into three components: a uniform temperature stress, an equivalent linear curling stress, and a nonlinear self-equilibrating stress. It is the self-equilibrating stress component that often goes unaccounted for in concrete pavement stress prediction and can significantly affect the tensile stress magnitude and critical location. This paper presents a solution for a piecewise method and proposes a simplified method termed NOLA, or nonlinear area, that easily captures the effect of temperature nonlinearity on rigid pavement responses. The proposed NOLA method enables the use of a three-dimensional temperature frequency distribution that allows simple postprocessing of rigid pavement curling stress solutions derived from a linear temperature assumption. The impact of accounting for self-equilibrating stresses in terms of projected fatigue damage levels and critical cracking locations is also explored using a mechanistic-based rigid pavement analysis program called RadiCAL.

Darcy–Forchheimer Flow With Viscous Dissipation in a Horizontal Porous Layer: Onset of Convective Instabilities

Parallel Darcy–Forchheimer flow in a horizontal porous layer with an isothermal top boundary and a bottom boundary, which is subject to a third kind boundary condition, is discussed by taking into account the effect of viscous dissipation. This effect causes a nonlinear temperature profile within the layer. The linear stability of this nonisothermal base flow is then investigated with respect to the onset of convective rolls. The third kind boundary condition on the bottom boundary plane may imply adiabatic/isothermal conditions on this plane when the Biot number is either zero (adiabatic) or infinite (isothermal). The solution of the linear equations for the perturbation waves is determined by using a fourth order Runge–Kutta scheme in conjunction with a shooting technique. The neutral stability curve and the critical value of the governing parameter R=GePe2 are obtained, where Ge is the Gebhart number and Pe is the Péclet number. Different values of the orientation angle between the direction of the basic flow and the propagation axis of the disturbances are also considered.

Effect of linear and non-linear components in the temperature dependences of thermoelectric properties on the cooling performance

The relative cooling of performance of ϕ / ϕ 0 for a thermoelectric (TE) element was derived analytically by taking the linear and non-linear components in the temperature ( T z ) dependences of TE properties into the thermal rate equations (TRE) on the assumption that all of the TE properties are expressed by a quadratic function of T z at a position z along a TE element and the temperature profile along a TE element is linear or non-linear, where ϕ and ϕ 0 are the coefficients of performance (COP) derived from the new and conventional TRE, respectively. The linear and non-linear components in the T z -dependences of TE properties were estimated experimentally for Bi–Te alloys. When a TE element has a linear temperature profile, ϕ / ϕ 0 estimated using the linear and/or non-linear components in the T z -dependences of their TE properties increases with an increase of Δ T and reached great values of 1.3–1.6 at ZT = 1 under the condition of T = 300 K and Δ T = 80 k . As a result, it was found that the linear component in the electrical resistivity ρ and the non-linear one in the Seebeck coefficient α have a significant effect on ϕ / ϕ 0 . When ϕ / ϕ 0 was estimated for a non-linear temperature profile of a module fabricated using these Bi–Te alloys, however, it was slightly lower than that obtained for a linear temperature profile. The formulas obtained for ϕ and ϕ / ϕ 0 are applicable even for the practical TE coolers and refrigerators with a strong non-linearity in the temperature profile.