Arbitrary Heat Research Articles

ОСОБЕННОСТИ ОПТИМИЗАЦИОННОЙ ЗАДАЧИ НА ПОДБОР МАТЕРИАЛОВ ДЛЯ МИНИМИЗАЦИИ ПОТЕРИ ТЕПЛА ЧЕРЕЗ ПЛОСКУЮ СТЕНКУ

Актуальность. Хранение тепла и его эффективное использование связано с подбором материалов для тепловой изоляции стенок. Такие материалы представлены широким спектром теплофизических свойств и стоимости на рынке. Тогда возникает задача оптимизации, ее решение должно обеспечивать наименьшие потери тепла через стенку при ограниченном выборе материалов с заданными коэффициентами теплопроводности. Вместе с тем при решении оптимизационной задачи могут возникнуть сложности в оценке правильности полученных результатов. Поэтому этот вопрос нуждается в детальном обсуждении. Цель: математическое моделирование стационарных режимов переноса тепла, формулировка минимаксной задачи о потере тепла через стенку, построение области решения минимаксной задачи, анализ полученных результатов и формулировка выводов. Объект: стенка, теплоизоляционные материалы, потоки тепла, условия минимальности, оптимальные решения. Методы: решение минимаксной задачи с применением аналитических методов. Результаты. Сформулирована простая минимаксная задача: дана двухслойная плоская стенка с произвольными коэффициентами теплопроводности и фиксированными толщинами. На правой и левой границах стенки задана постоянная и различная температура. Также задан максимальный тепловой поток через стенку и область возможных значений коэффициентов теплопроводности (т. е. возможные материалы) для каждого слоя стенки. Требуется из этой области найти коэффициенты теплопроводности, обеспечивающие тепловой поток ниже заданного максимального значения. На этом примере показано, что решение поставленной минимаксной задачи может приводить к неверному результату: можно получить или не весь спектр допустимых решений, или задача может не иметь решения. Это означает необходимость строгого отношения к формулировке и методу решения оптимизационных задач для процессов переноса тепла.

Hyperbolic thermal-plasma wave propagation in semiconductor of organic material

Although the thermo-viscoelastic properties of solids have been reported in many articles, no effort has been made to investigate the coupled thermo-viscoelastic and plasma wave behavior of semiconductors based on the photothermal theory. In this work, a new mathematical model of heat and plasma transport has been constructed for semiconductor of viscoelastic material. Some fundamental theorems on the linear coupled and generalized theories can be easily obtained as special cases. A two-dimensional problem is viewed for a half-space of an organic semiconductor plate whose surface is traction free and subjected to an arbitrary time-dependent heat flux. Laplace and Fourier integral transforms are utilized. The carrier density, temperature, thermal stress, and displacement distributions have been obtained through the use of the theoretical model together with plasma and thermo-viscoelastic effects. The inversion technique for Fourier and Laplace transforms is carried out using a numerical technique based on Fourier series expansions. Comparisons are made with the results anticipated through the coupled idea and generalized theory. The influence of the some parameters on all the regarded fields is examined for different theories.

Surface temperature of a multi-layer thermal barrier coated wall subject to an unsteady heat flux

A one-dimensional analytical method of determining the surface temperature of a thermal barrier coated plane wall subjected to an arbitrarily time-varying heat flux was developed. The method allows fast computation, enabling it to be embedded in combustion simulation software to correctly calculate wall heat transfer, which is important for reciprocating engine applications with thin, low thermal inertia coatings that have large temperature swings. The method relies on superposition of the response to successive step changes in heat flux, obtained by discretizing the heat flux history, to compile the solution. The embedded problem of a step-change in heat flux is addressed using the one-dimensional heat diffusion equation in conjunction with the matrix method in the Laplace domain, assuming the lateral conduction is neglected. For a two-layer wall (one coating layer on top of the metal wall) in the limit where kρc of the coating is small relative to that for the wall material, an analytical inversion to the time domain can be derived. For modest values of this parameter or for more than one coating layer, the residue theorem is invoked to invert to the time domain, with the poles and residues found numerically. The analytical inversion, however, provided the impetus for defining a set of non-dimensional parameters that uniquely characterize the surface temperature swing for arbitrary periodic heat flux to the wall. Non-dimensional results are given for a sinusoidially varying surface heat flux.

Large-scalable fabrication of improved Bi–Te-based flexible thermoelectric modules using a semiconductor manufacturing process

Among the several flexible thermoelectric modules in existence, sintered Bi–Te-based modules represent a viable option because of their high output power density and flexibility, which enables the use of arbitrary heat sources. We have fabricated Bi–Te-based modules with a large-scalable fabrication process and improved their output performance. The reduction in the interconnection resistance, using thick electrodes of the flexible printed circuit, significantly improves the module’s output power to 87 mW cm−2 at ΔT = 70 K, which is 1.3-fold higher than a previous prototype module. Furthermore, the establishment of the fabrication for the top electrodes by using the surface mount technology makes it possible to realize a high-throughput manufacturing of the module. Our durability tests reveal that there is no significant change in the internal resistance of the module during 10 000 cycles of mechanical bending test and 1000 cycles of thermal stress test.

Analysis of Non-Fourier Heat Conduction Problem with Suddenly Applied Surface Heat Flux

In literature, the well-acknowledged initial condition is generally used when solving the non-Fourier problems. However, in references, some cases with a suddenly applied heat flux boundary under such an initial condition violate the first law of thermodynamics. This unreasonable situation is first demonstrated in the cases of constant heat flux using the Cattaneo–Vernotte model of a one-dimensional finite medium with the other side being isothermal or insulated. Then it is also demonstrated in the cases of arbitrary heat flux by reduction to absurdity. To adjust the unreasonable situation, an innovative definition of initial condition is proposed to obtain accurate solutions. Besides, the modified cases of a constant heat flux boundary are also discussed in this work with different relaxation time. In those cases, this study, for the first time, discovers that the heat wave can be inversely reflected under the isothermal boundary. Then when is extremely big, the heat flux input may result in a cooling response.

Nanocalorimetry of explosives prepared by inkjet printing

Nanocalorimetry can generate rapid and arbitrary heating profiles for thermal and thermodynamic measurements with high sensitivity, especially for small samples, often at the nanogram mass scale. These features make nanocalorimetry a potentially useful tool for fundamental studies of the behavior of nanogram quantities of explosives during thermal desorption which is the front-end process for many analytical techniques used in screening of these materials in trace residues. Here, inkjet printing was used to reproducibly deposit nanogram quantities of explosives onto the active area of the nanocalorimeters and allowed for an estimation of sample mass based on gravimetric calibration, including cyclotrimethylenetrinitramine (RDX), pentaerythritol tetranitrate (PETN), trinitrotoluene (TNT), and potassium chlorate (PC). Nanocalorimetry results on common explosives demonstrated the measurement capability. We observed both α-RDX and the metastable β-RDX phase using nanocalorimetry, along with the competitive vaporization and decomposition of RDX. Finally, nanocalorimetry coupled mass spectrometry was demonstrated to characterize thermal desorption events during analysis of trace quantities of explosives.

Optimum Operation of Radiation-Balanced Lasers

The operation of radiation-balanced lasers (RBLs) is analyzed for practical considerations of cavity losses, optimum out-coupling, and radial distribution of pump and laser modes. We derive expressions for laser efficiency under arbitrary heat loads, discuss the limitations on high-power scaling imposed by thermal gradients in radiation-balanced disk geometries, and propose potential remedies. The effects of parasitic absorption of the pump and fluorescence are evaluated. The analysis is intended primarily for disk lasers but is also applicable to rod laser geometries.

Analytical solutions of transient heat conduction in multilayered slabs and application to thermal analysis of landfills

The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitrary heat generations is analysed. The boundary conditions are general and include various combinations of Dirichlet, Neumann or Robin boundary conditions at either surface. Moreover, arbitrary heat generations in the slabs are taken into account. The solutions are derived by basic methods, including the superposition method, separation variable method and orthogonal expansion method. The simplified double-layered analytical solution is validated by a numerical method and applied to predicting the temporal and spatial distribution of the temperature inside a landfill. It indicates the ability of the proposed analytical solutions for solving the wide range of applied transient heat conduction problems.

Direct Measurements of the Dynamics of the Electrocaloric Response of Ferroelectrics under Conditions of Arbitrary Heat Transfer

We have a new, effective method for direct measurements of the electrocaloric effect under arbitrary heat transfer conditions. The accuracy and reliability of measurements of the dynamics of changes in the sample temperature are due to the use of photodiode temperature sensors of the mid-IR range with the possibility of their in situ calibration.

The Formation of Electron Heat Flux Over the Sunlit Quiet Polar Cap Ionosphere

AbstractWe consider a new mechanism for the thermal electron heat fluxes formation over the sunlit polar cap in the presence of the potential jumps that are created by the photoelectron escape along the open magnetic field lines. Photoelectrons traveling into the magnetosphere experience small Coulomb collisional scattering, and the low‐energy part of their spectra becomes trapped between the potential jump and upper ionosphere creating the thermal electron energy fluxes that support the formation of electron temperature at the ionospheric altitudes. This mechanism eliminates the need for the customary practice of assuming arbitrary electron heat fluxes at the upper ionospheric boundary in order to explain the measured electron temperature in the topside ionosphere.

Failure modes of soft materials with sharp-hard inhomogeneity under heat flux

This article investigates the failure modes of the structure composed of a soft matrix and a hard line inhomogeneity under uniform remote thermo-mechanical loading. The inhomogeneity is assumed to be thermally permeable and the thermal expansion-induced stretch of the inhomogeneity is incorporated. For arbitrary uniform remote stresses and heat flux, the explicit solution to the full stress field in the matrix is derived by solving the corresponding Riemann-Hilbert problem, and the critical condition for the failure modes of the structure is obtained. The effects of the direction of the remote heat flux and those of the mismatch of thermal expansions on the failure modes of the structure are illustrated via numerical examples. It is shown that the heat-induced failure modes of the structure are distinct at the two tips of the inhomogeneity and are either interface puncture or interface separation depending on the direction of the remote heat flux and the disparity between the thermal expansion coefficients of the inhomogeneity and matrix. In addition, the heat flux-induced stress intensity factors at the inhomogeneity tips are found to be proportional to where a is the half-length of the inhomogeneity, indicating that the failure of the structure may be more sensitive to thermal loading other than mechanical loading.

Efficient temperature field evaluation in wet surface grinding for arbitrary heat flux profile

We consider the heat transfer in surface wet grinding, assuming a constant heat-transfer coefficient over the workpiece surface, as well as the usual heat flux profiles entering into the workpiece given in the literature, i.e. constant, linear, parabolic and triangular. On the one hand, we calculate in the stationary regime, the temperature distribution on the workpiece surface in series form. These series converge only for Biot numbers less than unity. By using convergence acceleration, these series can be computed more rapidly than its equivalent integral form without any appreciable loss of accuracy. Also, we avoid the numerical integration problems found in the expressions given in the literature. Moreover, the expressions found can be used to compute the maximum temperature of the workpiece very rapidly. On the other hand, we have refined some approximations for the relaxation time in wet grinding, and we have derived some new expressions for dry grinding. The relaxation time has been applied to compute the temperature field inside the workpiece in the stationary regime, obtaining a more rapid numerical evaluation without any appreciable loss of precision.

Tidally induced lateral variations of Io's interior

Satellite and recent Earth-based observations of Io's surface reveal a specific spatial pattern of persisting hotspots and sudden high-intensity events. Io's major heat producing mechanism is tidal dissipation, which is thought to be non-uniformly distributed within Io's mantle and asthenosphere. The question arises to what extent Io's non-homogeneous heat production can cause long-wavelength variations in the interior and volcanic activity at the surface. We investigate dissipation patterns resulting from two different initially spherical symmetric visco-elastic rheological structures, which are consistent with geodetic observations. The spatial distributions of the time-averaged tidal heat production are computed by a finite element model. Whereas for the first rheological structure heat is produced only in the upper viscous layer (asthenosphere-heating model), the second rheological structure results in a more evenly distributed dissipation pattern (mixed-heating model) with tidal heating occurring in the deep mantle and the asthenosphere. To relate the heat production to the interior temperature and melt distribution, we use steady-state scaling laws of mantle convection and a simple melt migration model. The resulting long-wavelength thermal heterogeneities strongly depend on the initial tidal dissipation pattern, the thickness of the convective layer, the mantle viscosity, and the ratio between magmatic and convective heat transport. While for the asthenosphere-heating model a strong lateral temperature signal with up to 190 K peak-to-peak difference can remain, convection within a thick convective layer, as for the mixed-heating model, can reduce the lateral temperature variation to <1 K, if the mantle viscosity is sufficiently low. Models with a dominating magma heat transport preserve the long-wavelength pattern of tidal dissipation much better and are favoured, because they are better to explain Io's thick crust. The approach presented here can also be applied to investigate the effect of an arbitrary interior heating pattern on Io's volcanic activity pattern.

Fundamental and Generalized Solutions of the Equations of Motion of a Thermoelastic Half-Plane with a Free Boundary

A coupled thermoelasticity model is used to study the dynamics of a thermoelastic half-plane influenced by nonstationary body forces and heat sources. In space of Laplace transforms with respect to time, Green’s tensor of the boundary value problem for the half-plane with a boundary free of stresses and heat fluxes is constructed. The displacements and the temperature of the medium are determined for arbitrary body forces and heat sources.

Mixed convection heat transfer of water about a vertical surface of variable heat flux with density inversion

Laminar mixed convection boundary layer flow of water about a vertical plate is studied including density inversion effects. The plate surface is subjected to an arbitrary heat flux that is a function of vertical distance from the leading edge. Both aiding and opposing mixed convection situations are considered in the study. The dimensionless forms of stream function and temperature are expanded in terms of perturbation elements and universal functions. The differentials of the heat flux, which are functions of vertical distance, are used as perturbation elements to obtain universal functions. The results for universal functions required to find temperature and velocity profiles are obtained. The obtained universal functions are valid for any arbitrary wall heat flux variation. The universal applicability of results is demonstrated for power-law variation of wall heat flux. The velocity and temperature variation, boundary layer thickness, Nusselt numbers and skin friction coefficient are presented for various values of mixed convection parameter, wall flux power index, for both aiding and opposing mixed convection. For a given combination of Grashof and Reynolds numbers, the heat transfer rates and skin friction coefficient are found to increase almost linearly with wall flux power index, in the parameter range of the study, for both the cases of aiding and opposing mixed convection. The present results of special cases are found to match well with the results available in the literature.

Прямые измерения динамики электрокалорического отклика сегнетоэлектриков в условиях произвольного теплообмена

A new effective method for direct electrocaloric measurements under arbitrary heat exchange conditions is proposed. The accuracy and reliability of the sample temperature measurements in dynamic provided by the use of mid-IR photodiode temperature sensors with the possibility of the in-situ calibration procedure

Stability analysis of the solutions of kinetic equations for modelling of gas flow at arbitrary heat ratio

In the presented paper the stability of the solutions of kinetic equations, which formed the models of ideal compressible gases at arbitrary heat ratio, is investigated. Models are widely used in applications of the lattice Boltzmann method, presented in the literature. The stability analysis is based on the considering of linear approximation and on the transition to the system of ordinary differential equations with complex coefficients. After the computations the stability criteria of the models are formulated for the cases of fixed values of relaxation time. The stability analysis is an important stage of the modelling process, because it may realize some help in choosing of the proper model for using in practical simulations.

A transformation theory for camouflaging arbitrary heat sources

Camouflage devices have attracted intensive research interest for their significant applications. However, most camouflage devices are specifically designed according to target heat sources. Here, by applying the transformation thermotics approach, we develop a coordinate transformation, and design an unspecific camouflage device which can camouflage arbitrary heat sources into a circular one with an anisotropic shell. We verify the ability of our unspecific camouflage device with both steady and transient simulations. We also find the “apparent negative thermal conductivity” under certain conditions without violating the second law of thermodynamics. To ensure the feasibility, we further put forward the effective medium approximation for sample fabrication, and only two natural materials are required. Our results have relevance to the different applications of infrared misleading, uniform heating, and so on; they may also provide guidance to the research on other diffusive fields, such as magnetostatic and electrostatic fields.

Engine-Scalable Rotor Casing Convective Heat Flux Evaluation Using Inverse Heat Transfer Methods

In this paper, we propose a two-step methodology to evaluate the convective heat flux along the rotor casing using an engine-scalable approach based on discrete Green's functions . The first step consists in the use of an inverse heat transfer technique to retrieve the heat flux distribution on the shroud inner wall by measuring the temperature of the outside wall; the second step is the calculation of the convective heat flux at engine conditions, using the experimental heat flux and the Green functions engine-scalable technique. Inverse methodologies allow the determination of boundary conditions; in this case, the inner casing surface heat flux, based on measurements from outside of the system, which prevents aerothermal distortion caused by routing the instrumentation into the test article. The heat flux, retrieved from the inverse heat transfer methodology, is related to the rotor tip gap. Therefore, for a given geometry and tip gap, the pressure and temperature can also be retrieved. In this work, the digital filter method is applied in order to take advantage of the response of the temperature to heat flux pulses. The discrete Green's function approach employs a matrix to relate an arbitrary temperature distribution to a series of pulses of heat flux. In this procedure, the terms of the Green's function matrix are evaluated with the output of the inverse heat transfer method. Given that key dimensionless numbers are conserved, the Green's functions matrix can be extrapolated to engine-like conditions. A validation of the methodology is performed by imposing different arbitrary heat flux distributions, to finally demonstrate the scalability of the Green's function method to engine conditions. A detailed uncertainty analysis of the two-step routine is included based on the value of the pulse of heat flux, the temperature measurement uncertainty, the thermal properties of the material, and the physical properties of the rotor casing.

Mafic High‐Pressure Rocks Are Preferentially Exhumed From Warm Subduction Settings

AbstractThe oceanic crust that enters a subduction zone is generally recycled to great depth. In rare and punctuated episodes, however, blueschists and eclogites derived from subducted oceanic crust are exhumed. Compilations of the maximum pressure‐temperature conditions in exhumed rocks indicate significantly warmer conditions than those predicted by thermal models. This could be due to preferential exhumation of rocks from hotter conditions that promote greater fluid productivity, mobility, and buoyancy. Alternatively, the models might underestimate the forearc temperatures by neglecting certain heat sources. We compare two sets of global subduction zone thermal models to the rock record. We find that the addition of reasonable amounts of shear heating leads to less than 50 °C heating of the oceanic crust compared to models that exclude this heat source. Models for young oceanic lithosphere tend to agree well with the rock record. We test the hypothesis that certain heat sources may be missing in the models by constructing a global set of models that have high arbitrary heat sources in the forearc. Models that satisfy the rock record in this manner, however, fail to satisfy independent geophysical and geochemical observations. These combined tests show that the average exhumed mafic rock record is systematically warmer than the average thermal structure of mature modern subduction zones. We infer that typical blueschists and eclogites were exhumed preferentially under relatively warm conditions that occurred due to the subduction of young oceanic lithosphere or during the warmer initial stages of subduction.