Non-axisymmetric Temperature Distribution Research Articles

Gravitational radiation from thermal mountains on accreting neutron stars: sources of temperature non-axisymmetry

ABSTRACTThe spin distribution of accreting neutron stars in low-mass X-ray binary systems shows a concentration of pulsars well below the Keplerian break-up limit. It has been suggested that their spin frequencies may be limited by the emission of gravitational waves, due to the presence of large-scale asymmetries in the internal temperature profile of the star. These temperature asymmetries have been demonstrated to lead to a non-axisymmetric mass distribution, or ‘mountain’, that generates gravitational waves at twice the spin frequency. The presence of a toroidal magnetic field in the interior of accreting neutron stars has been shown to introduce such anisotropies in the star’s thermal conductivity, by restricting the flow of heat orthogonal to the magnetic field and establishing a non-axisymmetric temperature distribution within the star. We revisit this mechanism, extending the computational domain from (only) the crust to the entire star, incorporating more realistic microphysics, and exploring different choices of outer boundary condition. By allowing a magnetic field to permeate the core of the neutron star, we find that the likely level of temperature asymmetry in the inner crust (ρ ∼ 1013 g cm−3) can be up to 3 orders of magnitude greater than the previous estimate, improving prospects for one day detecting continuous gravitational radiation. We also show that temperature asymmetries sufficiently large to be interesting for gravitational wave emission can be generated in strongly accreting neutron stars if crustal magnetic fields can reach ∼1012 G.

The influence of the length of heat sources on the external border on the temperature distribution in profiled polar-orthotropic ring plates taking into account there heat exchange with the external environment

We study the influence of N extended heat sources at external boundaries on the nonaxisymmetric temperature distribution on profiled polar-orthotropic ring plates and take into account heat exchange with the external environment. The solution of the stationary heat conduction problem for anisotropic annular plates of a random profile is resolved through the solution of the corresponding Volterra integral equation of the second kind. The formula of a temperature calculations in anisotropic annular plates of an random profile is given. The exact solution of stationary heat conductivity problem for a reverse conical polar-orthotropic ring plate is recorded. The temperature distribution in such anisotropic plate from N extended heat sources at its outer border is more complex than in the case of temperature distribution from N point heat sources at their external border.

Soot temperature measurement within 3D flame by light-field imaging based on wave optics theory

Light-field imaging technique provides a new approach to non-intrusive temperature measurement, which can achieve 3D measurement via single detector equipment. We consider wave characteristics of radiation rays in the light-field imaging model in this work. We propose an improved light-field imaging model of an emitting and absorbing medium by combining wave optics theory and radiation transfer process in semitransparent media. The combination of Fresnel diffraction theory and phase conversion principles of the lens provides a theoretical basis for a description of radiation ray propagation in space and across the lens. The point spread function of the light-field camera can be calculated and used to attain a light-field image in accordance with the convolution imaging model. The light-field image of the flame is regarded as input to reconstruct the soot temperature field of a 3D flame. Inverse problem is formulated as a linear optimization problem and solved by Landweber algorithm. Simulated reconstruction results show that axisymmetric and non-axisymmetric temperature distribution can be reconstructed successfully, thereby verifying the applicability of the presented method. The effect of the measurement noise and the Tikhonov regularization on the reconstructed quality of the temperature are investigated as well. The results show that the temperature can be reconstructed with acceptable accuracy under different noise levels. Tikhonov regularization method is proven available in this problem.

Evaluation of anisotropic tangential conduction in printed-circuit-board heated-thin-foil heat flux sensors

The effect of the tangential conduction contribution in a thermally anisotropic heated-thin-foil heat flux sensor is examined. A parameter to assess the degree of importance of tangential conduction in the sensor is defined and evaluated in order to justify the need of tangential conduction corrections. Printed circuit boards (PCBs) are typical examples of sensors with anisotropic thermal conduction properties, due to the different conductance values in the directions either parallel or orthogonal to the copper tracks which are placed onto a fiberglass substrate. A parametric study on PCBs with different tracks coverage fraction and copper-to-fiberglass heat conductance ratio is carried out. A revised heated-thin-foil formulation, including a correction for anisotropic thermal properties of the PCB, is experimentally tested. The selected thermo-fluid-dynamic test case is the convective heat transfer of a normally impinging round jet for which axisymmetric maps of the Nusselt number are expected. The anisotropic tangential conduction results in non-axisymmetric temperature distributions. Consequently, if anisotropy is not properly accounted for, non-axisymmetric Nusselt number maps are obtained. The anisotropic conduction effects are shown to be weakly sensitive to the copper tracks coverage fraction while strongly dependent on a parameter called degree of anisotropy, which accounts for the copper-to-fiberglass heat-conductance ratio. Anisotropic conduction effects are found to be almost negligible in PCBs with low values of the degree of anisotropy and/or low values of the tangential conduction degree of importance. Accounting for the anisotropic tangential conduction in the heated-thin-foil formulation allows minimizing the differences between the Nusselt number profiles measured in the directions parallel and orthogonal to the copper tracks. For all the considered PCBs, differences after correction are found to be below the measurement uncertainty expected for an equivalent thermally-isotropic sensor. The proposed approach also allows reducing below the measurement uncertainty the spread between the Nusselt number values measured with all the considered printed circuit boards, providing measurements practically independent of the sensor characteristics.

Efficient and robust method for simultaneous reconstruction of the temperature distribution and radiative properties in absorbing, emitting, and scattering media

A rapid computational method called generalized sourced multi-flux method (GSMFM) was developed to simulate outgoing radiative intensities in arbitrary directions at the boundary surfaces of absorbing, emitting, and scattering media which were served as input for the inverse analysis. A hybrid least-square QR decomposition–stochastic particle swarm optimization (LSQR–SPSO) algorithm based on the forward GSMFM solution was developed to simultaneously reconstruct multi-dimensional temperature distribution and absorption and scattering coefficients of the cylindrical participating media. The retrieval results for axisymmetric temperature distribution and non-axisymmetric temperature distribution indicated that the temperature distribution and scattering and absorption coefficients could be retrieved accurately using the LSQR–SPSO algorithm even with noisy data. Moreover, the influences of extinction coefficient and scattering albedo on the accuracy of the estimation were investigated, and the results suggested that the reconstruction accuracy decreased with the increase of extinction coefficient and the scattering albedo. Finally, a non-contact measurement platform of flame temperature field based on the light field imaging was set up to validate the reconstruction model experimentally.

Control of Interface Shape by Non-Axisymmetric Solution Convection in Top-Seeded Solution Growth of SiC Crystal

We achieved the convex growth interface shape in top-seeded solution growth of SiC applying non-axisymmetric solution convection induced by non-axisymmetric temperature distribution. The detailed solution flow, temperature distribution and carbon concentration distribution were calculated by 3-dimensional numerical analysis. In the present case, the solution flow below the crystal was unidirectional and the supersaturation was increased along the solution flow direction. By the rotation of the crystal in the unidirectional flow and the temperature distribution, we successfully obtained the crystal with the convex growth interface shape.

Algebraic tomographic reconstruction of two-dimensional gas temperature based on tunable diode laser absorption spectroscopy

Based on tunable diode laser absorption spectroscopy, the combustion gas temperature distribution was reconstructed using the algebraic iterative reconstruction technique. The effects of the projected angle and number of rays on the temperature reconstruction results for both fan beam and parallel beam were investigated. The flow field information was shown in detail. The reconstruction quality increased with increased ray number for both parallel- and fan-beam projections. The trend tended to be smooth when the total number of beams exceeded 100. A virtual ray method combined with the reconstruction algorithms was proposed. The virtual ray method is effective to improve the accuracy of reconstruction results for the symmetric and non-axisymmetric temperature distributions. Moreover, the temperature reconstruction of an infrared gas-field furnace is demonstrated, showing the virtual ray method can be applied to the combustion diagnostics.

Convective heat transfer for viscoelastic fluid in a curved pipe

In this paper, fully developed convective heat transfer of viscoelastic flow in a curved pipe under the constant heat flux at the wall is investigated analytically using a perturbation method. Here, the curvature ratio is used as the perturbation parameter and the Oldroyd-B model is applied as the constitutive equation. In the previous studies, the Dirichlet boundary condition for the temperature at the wall has been used to simplify the solution, but here exactly the non-homogenous Neumann boundary condition is considered to solve the problem. Based on this solution, the non-axisymmetric temperature distribution of Dean flow is obtained analytically and the effect of flow parameters on the flow field is investigated in detail. The current analytical results indicate that increasing the Weissenberg number, viscosity ratio, curvature ratio, and Prandtl number lead to the increase of the heat transfer in the Oldroyd-B fluid flow.

Extension of Stoney’s Formula to Arbitrary Temperature Distributions in Thin Film/Substrate Systems

Abstract Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states that are assumed to remain uniform over the entire film/substrate system. By considering a circular thin film/substrate system subject to nonuniform and nonaxisymmetric temperature distributions, we derive relations between the film stresses and temperature, and between the plate system’s curvatures and the temperature. These relations featured a “local” part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a “nonlocal” part that reflects the effect of temperature of other points on the location of scrutiny. Most notably, we also derive relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary nonuniformities. These relations also feature a “nonlocal” dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. Finally, it is shown that the interfacial shear tractions between the film and the substrate are related to the gradients of the first curvature invariant and can also be inferred experimentally.

Liquid Crystal Thermography on the Fluid Solid Interface of Rotating Systems

Liquid crystal thermography is an effective method widely employed in transient and steady-state heat transfer experiments with excellent spatial resolution and good accuracy. Most of the past studies in liquid crystal thermography deal with stationary conditions. The present investigation deals with the influence of rotation on the color response of encapsulated liquid crystals attached to a flat rotating surface. A general methodology developed for the application of thermochromic liquid crystals in rotating systems is described for the first time. The investigation is performed for a rotational speed range from 0 to 7500 rpm using two different coatings displaying red at 30° and 45°C, under stationary conditions. Local liquid crystal color on the surface of a rotating disk is correlated with local temperature as measured by a non-intrusive infrared sensor at various rotational speeds. An immediate observation from the present study is that the color response (hue) of encapsulated liquid crystals is not altered by either the centrifugal acceleration of the rotating environment or the aerodynamic friction force at the rotating disk-air interface. Present investigation also shows that when a stroboscope light is introduced, the color response is not significantly altered due to additional periodic illumination. A complete and general experimental methodology including rotating surfaces with non-axisymmetric temperature distribution is presented. Results from the current liquid crystal technique agree well with the theoretical adiabatic temperature rise of a free rotating disk as predicted by an analytical method.

Natural and forced convection of molten silicon during Czochralski single crystal growth

Natural and/or forced convection of molten silicon during Czochralski single crystal growth was directly observed using X-ray radiography with solid tracers for various crystal and crucible rotation speeds, and temperature distribution in a crucible holder. Downflow attributed to natural convection in the center of a crucible which had been simulated by numerical calculation was scarcely observed with and without crucible rotation. Numerical simulation of the molten silicon was carried out by a packaged code of “FLUENT”; in the calculation, measured non-axisymmetric temperature distribution in a crucible holder was adopted. Unidirectional flow with and without crucible rotations can be qualitatively explained by the numerical simulation with non-axisymmetric temperature distribution in the crucible holder. The particle path attributed to natural convection near the solid-liquid interface was suppressed downward with increase in crystal rotation speed. The phenomena can be explained by a generation of forced convection beneath the rotating crystal.

Direct observation by X-ray radiography of convection of boric oxide in the GaAs liquid encapsulated czochralski growth

Convection of molten boric oxide (B 2O 3) encapsulant during liquid encapsulated Czochralski single crystal growth of GaAs was directly observed by X-ray radiography. The melt flow pattern was monitored using a solid tracer method. The observed flow pattern was axisymmetric, and the flow was steady. The flow of the molten B 2O 3 was more stable than that of molten silicon. The flow velocity of the molten boric oxide with and without single crystal were about 0.03 and 0.3 mm/s, respectively. Numerical simulation of the molten B 2O 3 natural convection using commercially available code “FLUENT” was also performed. Three-dimensional calculation was carried out employing observed non-axisymmetric temperature distribution in a crucible holder. The calculated data was able to explain the steady and axisymmetric flow observed even in the non-axisymmetric temperature distribution.

A chemical and isotopic study of hibonite-rich refractory inclusions in primitive meteorites

The ion microprobe has been used to determine the concentrations of a number of trace elements (including all 14 stable rare earth elements) and the isotopic compositions of Ca and Mg in seven hibonite-rich refractory inclusions. Hibonite in every inclusion analyzed shows the effect of REE partitioning with other solid or liquid phases, in which hibonite is enriched in light over heavy REE compared to other coexisting phases. This partitioning causes Cl chondritenormalized enrichments to drop by factors of 4 to 22 from lanthanum to lutetium. Fractionations due to gas-solid partitioning of REE are sometimes superimposed on the pattern produced by partitioning between condensed phases. Two inclusions, HAL and DH-H1, show evidence for formation in extremely oxidizing environments and their Ca is mass fractionated in favor of the heavy isotopes by 7 and 12%./amu, respectively. Two corundum-hibonite inclusions show evidence of extremely high temperature gas-solid fractionation, such that the more volatile light REE are depleted as a group relative to the more refractory heavy REE. These inclusions both have Ca that is mass fractionated in favor of the light isotopes. Hibonite preserves the largest nuclear isotope anomalies in Ti found to date ( Fahey et al. 1985a; Hinton el al., 1987b), but there does not seem to be a simple relationship between chemical composition, isotopic mass fractionation and the sign and magnitude of nuclear isotopic anomalies in hibonite-rich inclusions. One possibility for producing a variety of chemical compositions and degrees of mass fractionation while preserving nuclear isotope anomalies is by multiple cycles of condensation and evaporation in a turbulent protoplanetary accretion disk ( Morfill, 1983; Morfill and R. N. Clayton, 1986a,b). These cycles could also occur in a presolar nebula with large non-axisymmetric temperature and pressure distributions ( Boss, 1988). Nuclear anomalies are most likely to be preserved in hibonite because hibonite is the most refractory major phase to occur commonly in meteorites.

Three-dimensional simulations of the Czochralski bulk flow

Abstract Six numerical simulations of 3-dimensional time-dependent flow in the presence of a non-axisymmetric temperature distribution at the crucible wall are described. All simulated cases have in common the presence of temperature oscillations and/or time periodic flow. It is also shown that the crucible rotation is needed in order to symmetrize the temperature field in the vicinity of the solid-liquid interface.

Thermoelastic Analysis of Nonaxisymmetrically Heated Thick Cylindrical Shells

The thermoelastic problem of a thick cylinder subjected to nonaxisymmetric temperature distribution is considered. The temperature distribution may be harmonic or non-harmonic. The problem is formulated in terms of the in-plane displacements u and v and a solution is obtained by using Fourier series method. Two examples corresponding to a steady state and transient thermal distributions are solved. The steady-state case is compared to an exact solution and the transient problem is compared to a finite element solution. The transient problem considered is that of a solar superheater during startup after the departure of a cloud cover. The problem has applications in the conventional fossil-fired steam generators as well.