Some Fractional Extensions of the Temperature Field Problem in Oil Strata

This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new integral forms of the solutions are obtained. In each of the different cases the integrands are expressed in terms of a convolution of two special functions of Wright’s type.

On (b,c)-system at finite temperature in thermo field approach

We construct the finite temperature field theory of the two-dimensional ghost-antighost system within the framework of thermo field theory. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Thermal sresses in afinite solid cylinder due to steady temperature variation along the curved and end surface

An exact solution for determining the thermal stresses in a finite short cylinder due to an axisymmetric steady temperature field along the curved surface has been given. It is shown that a part of the solution obtained for this problem can be used to determine the thermal stresses in a finite solid cylinder heated over the end surfaces. Numerical results for a finite cylinder symmetrically heated over a portion on the curved surface and heated over the complete end surfaces have been given.

Oscillatory flow and temperature fields in an open tube with temperature difference across the ends

The oscillating flow and temperature field in an open tube subjected to cryogenic temperature at the cold end and ambient temperature at the hot end is studied numerically. The flow is driven by a time-wise sinusoidally varying pressure at the cold end. The conjugate problem takes into account the interaction of oscillatory flow with the heat conduction in the tube wall. The full set of compressible flow equations with axisymmetry assumption are solved with a pressure correction algorithm. Parametric studies are conducted with frequencies of 5-15 Hz, with one end maintained at 100 K and other end at 300 K. The flow and temperature distributions and the cooldown characteristics are obtained. The frequency and pressure amplitude have negligible effect on the time averaged Nusselt number. Pressure amplitude is an important factor determining the enthalpy flow through the solid wall. The frequency of operation has considerable effect on penetration of temperature into the tube. The density variation has strong influence on property profiles during cooldown. The present study is expected to be of interest in applications such as pulse tube refrigerators and other cryocoolers, where oscillatory flows occur in open tubes. (C) 2011 Elsevier Ltd. All rights reserved.

Transient Temperature Distribution in a Sheet Metal by Low-Energy Laser Scanning

Low-energy laser-heating techniques are widely used in engineering applications such as, thinfilm deposition, surface treatment, metal forming and micro-structural pattern formation. In this paper,under the conditions of ignoring the thermo-mechanical coupling, a numerical simulation on the spatialand temporal temperature distribution in a sheet metal produced by the laser beam scanning in virtue of thefinite element method is presented. Both the three-dimensional transient temperature field and thetemperature evolution as a function of heat penetrating depth in the metal sheet are calculated. Thetemperature dependence of material properties was taken into account. It was shown that, after taking thetemperature dependence of the material absorbance effect into consideration, the temperature change ratealong the scanning direction and the temperature maximum were both increased.

Temperature and composition profile during double-track laser cladding of H13 tool steel

Multi-track laser cladding is now applied commercially in a range of industries such as automotive, mining and aerospace due to its diversified potential for material processing. The knowledge of temperature, velocity and composition distribution history is essential for a better understanding of the process and subsequent microstructure evolution and properties. Numerical simulation not only helps to understand the complex physical phenomena and underlying principles involved in this process, but it can also be used in the process prediction and system control. The double-track coaxial laser cladding with H13 tool steel powder injection is simulated using a comprehensive three-dimensional model, based on the mass, momentum, energy conservation and solute transport equation. Some important physical phenomena, such as heat transfer, phase changes, mass addition and fluid flow, are taken into account in the calculation. The physical properties for a mixture of solid and liquid phase are defined by treating it as a continuum media. The velocity of the laser beam during the transition between two tracks is considered. The evolution of temperature and composition of different monitoring locations is simulated.

Three-dimensional models of mantle convection : influence of phase transitions and temperature-dependent viscosity

Two of the most important questions in mantle dynamics are investigated in three separate studies: the influence of phase transitions (studies 1 and 2), and the influence of temperature-dependent viscosity (study 3).

(1) Numerical modeling of mantle convection in a three-dimensional spherical shell incorporating the two major mantle phase transitions reveals an inherently three-dimensional flow pattern characterized by accumulation of cold downwellings above the 670 km discontinuity, and cylindrical 'avalanches' of upper mantle material into the lower mantle. The exothermic phase transition at 400 km depth reduces the degree of layering. A region of strongly-depressed temperature occurs at the base of the mantle. The temperature field is strongly modulated by this partial layering, both locally and in globally-averaged diagnostics. Flow penetration is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. The amplitude of the geoid is not significantly affected.

(2) Using a simple criterion for the deflection of an upwelling or downwelling by an endothermic phase transition, the scaling of the critical phase buoyancy parameter with the important lengthscales is obtained. The derived trends match those observed in numerical simulations, i.e., deflection is enhanced by (a) shorter wavelengths, (b) narrower up/downwellings (c) internal heating and (d) narrower phase loops.

(3) A systematic investigation into the effects of temperature-dependent viscosity on mantle convection has been performed in three-dimensional Cartesian geometry, with a factor of 1000-2500 viscosity variation, and Rayleigh numbers of 10^5-10^7. Enormous differences in model behavior are found, depending on the details of rheology, heating mode, compressibility and boundary conditions. Stress-free boundaries, compressibility, and temperature-dependent viscosity all favor long-wavelength flows, even in internally heated cases. However, small cells are obtained with some parameter combinations. Downwelling plumes and upwelling sheets are possible when viscosity is dependent solely on temperature. Viscous dissipation becomes important with temperature-dependent viscosity.

The sensitivity of mantle flow and structure to these various complexities illustrates the importance of performing mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.

High resolution direct measurement of temperature distribution in silicon nanophotonics devices.

Following the miniaturization of photonic devices and the increase in data rates, the issues of self heating and heat removal in active nanophotonic devices should be considered and studied in more details. In this paper we use the approach of Scanning Thermal Microscopy (SThM) to obtain an image of the temperature field of a silicon micro ring resonator with sub-micron spatial resolution. The temperature rise in the device is a result of self heating which is caused by free carrier absorption in the doped silicon. The temperature is measured locally and directly using a temperature sensitive AFM probe. We show that this local temperature measurement is feasible in the photonic device despite the perturbation that is introduced by the probe. Using the above method we observed a significant self heating of about 10 degrees within the device.

Equivalent-barotropic definition of tropospheric mean temperature

An equivalent-barotropic (EB) description of the tropospheric temperature field is derived from the geostrophic empirical mode (GEM) in the form of a scalar function Gamma(p, phi), where p is pressure and phi is 300-850-mb thickness. Baroclinic parameter phi plays the role of latitude at each longitudinal section. Compared with traditional Eulerian-mean methods, GEM defines a mean field in baroclinic streamfunction space with a time scale much longer than synoptic variability. It prompts an EB concept that is only based on a baroclinic field. Monthly GEM fields are diagnosed from NCEP-NCAR reanalysis data and account for more than 90% of the tropospheric thermal variance. The circumglobal composite of GEM fields exhibits seasonal, zonal, and hemispheric asymmetries, with larger rms errors occurring in winter and in the Northern Hemisphere (NH). Zonally asymmetric features and planetary deviation from EB are seen in the NH winter GEM. Reconstruction of synoptic sections and correlation analysis reveal that the tropospheric temperature field is EB at the leading order and has a 1-day phase lag behind barotropic variations in extratropical regions.

Stochastic quantization of real-time thermal field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A numerical study of temperature effects on hot wire measurements inside turbulent channel flows

A way to investigate turbulence is through experiments where hot wire measurements are performed. Analysis of the in turbulence of a temperature gradient on hot wire measurements is the aim of this thesis work. Actually - to author's knowledge - this investigation is the first attempt to document, understand and ultimately correct the effect of temperature gradients on turbulence statistics. However a numerical approach is used since instantaneous temperature and streamwise velocity fields are required to evaluate this effect. A channel flow simulation at Re_tau = 180 is analyzed to make a first evaluation of the amount of error introduced by temperature gradient inside the domain. Hot wire data field is obtained processing the numerical flow field through the application of a proper version of the King's law, which connect voltage, velocity and temperature. A drift in mean streamwise velocity profile and rms is observed when temperature correction is performed by means of centerline temperature. A correct mean velocity pro�le is achieved correcting temperature through its mean value at each wall normal position, but a not negligible error is still present into rms. The key point to correct properly the sensed velocity from the hot wire is the knowledge of the instantaneous temperature field. For this purpose three correction methods are proposed. At the end a numerical simulation at Re_tau =590 is also evaluated in order to confirm the results discussed earlier.

Temperature measured in permafrost borehole at ICDP site 5011-3 in El'gygytgyn Crater, 2008-2011

This study focuses on the temperature field observed in boreholes drilled as part of interdisciplinary scientific campaign targeting the El'gygytgyn Crater Lake in NE Russia. Temperature data are available from two sites: the lake borehole 5011-1 located near the center of the lake reaching 400 m depth, and the land borehole 5011-3 at the rim of the lake, with a depth of 140 m. Constraints on permafrost depth and past climate changes are derived from numerical simulation of the thermal regime associated with the lake-related talik structure. The thermal properties of the subsurface needed for these simulations are based on laboratory measurements of representative cores from the quaternary sediments and the underlying impact-affected rock, complemented by further information from geophysical logs and data from published literature. The temperature observations in the lake borehole 5011-1 are dominated by thermal perturbations related to the drilling process, and thus only give reliable values for the lowermost value in the borehole. Undisturbed temperature data recorded over more than two years are available in the 140 m deep land-based borehole 5011-3. The analysis of these observations allows determination of not only the recent mean annual ground surface temperature, but also the ground surface temperature history, though with large uncertainties. Although the depth of this borehole is by far too insufficient for a complete reconstruction of past temperatures back to the Last Glacial Maximum, it still affects the thermal regime, and thus permafrost depth. This effect is constrained by numerical modeling: assuming that the lake borehole observations are hardly influenced by the past changes in surface air temperature, an estimate of steady-state conditions is possible, leading to a meaningful value of 14 ± 5 K for the post-glacial warming. The strong curvature of the temperature data in shallower depths around 60 m can be explained by a comparatively large amplitude of the Little Ice Age (up to 4 K), with low temperatures prevailing far into the 20th century. Other mechanisms, like varying porosity, may also have an influence on the temperature profile, however, our modeling studies imply a major contribution from recent climate changes.

A procedure for the temperature reconstruction in corner domains from Cauchy data

An iterative procedure is proposed for the reconstruction of a stationary temperature field from Cauchy data given on a part of the boundary of a bounded plane domain where the boundary is smooth except for a finite number of corner points. In each step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. Convergence is proved in a weighted L2-space. Numerical results are included which show that the procedure gives accurate and stable approximations in relatively few iterations.

An iterative method for reconstruction of temperature

An iterative method for the reconstruction of a stationary three-dimensional temperature field, from Cauchy data given on a part of the boundary, is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L 2-space is include