Anisotropic Thermal Diffusivity Research Articles

Effect of Anisotropic Properties on Defect Detection by Pulse Phase Thermography

The influence of anisotropic thermal diffusivities on non-destructive testing of CFRP laminates using pulse phase thermography (PPT) was studied analytically. The results show that the optimum frequency for maximizing detectable depths of defects increases concomitantly with the increase in the ratio of the thermal diffusivities in the through-thickness direction to that in the in-plane direction . Furthermore, the phase difference between sound and defective areas decreases significantly with decreased . These predicted tendencies were verified through experiments. Experimental results also demonstrated that defects of 10 mm in diameter can be detected up to around 5 mm depth in CFRP with lower but only to around 1 mm in CFRP with higher

Computational studies of LXR molecular interactions reveal an allosteric communication pathway

The liver X receptor, LXRα, is an important regulator of genes involved in metabolism and inflammation. The mechanism of communication between the cofactor peptide and the ligand in the ligand-binding pocket is a crucial and often discussed issue for the nuclear receptors (NRs), but such allosteric signaling pathways are difficult to detect and the transmission mechanism remains elusive. Here, we apply the anisotropic thermal diffusion method to the LXRα with bound coactivator and ligand. We detected a possible communication pathway between the coactivator peptide and the ligand. The signal is transmitted both through the receptor backbone and side chains. A key signaling residue is the first leucine in the cofactor peptide recognition motif LXXLL, which is conserved within the NR cofactors, suggesting a general mechanism for allosteric signaling. Furthermore, we studied the LXR receptor and cofactor molecular interactions in detail using molecular dynamics simulations. The protein-protein interaction patterns in the complexes of nine different cofactor peptides and holo-LXRα were characterized, revealing the importance of the receptor-cofactor charge clamp interaction. Specific, but infrequently occurring interactions were observed toward the cofactor peptide C-terminal residues. Thus, additional specificity between LXRα and its cofactors is likely to be found in molecular interactions outside the cofactor peptide or in other biological factors.

Anisotropic thermal properties of talc under high temperature and pressure

The anisotropic thermal conductivity and diffusivity of talc were simultaneously measured up to 5.3 GPa and 900 K using the pulse transient method. Although significant anisotropy was observed in the thermal conductivity of talc, the average thermal conductivity is comparable to that of olivine and roughly three times greater than that of antigorite. From the ratio of the thermal conductivity to the thermal diffusivity, the heat capacity of talc was evaluated. The pressure derivative of heat capacity was found to be positive, which is related to the anomaly of thermal expansivity of talc above 50 °C at atmospheric pressure.

Anisotropic turbulent thermal diffusion and thermal convection in a rapidly rotating fluid sphere

Estimates of the molecular values of magnetic, viscous and thermal diffusion suggest that the state of the Earth’s core is turbulent and that complete numerical simulation of the geodynamo is not realizable at present. Large eddy simulation of the geodynamo with modelling of the sub-grid scale turbulence must be used. Current geodynamo models effectively model the sub-grid scale turbulence with isotropic diffusivities larger than the molecular values appropriate for the core. In the Braginsky and Meytlis (1990) picture of core turbulence the thermal and viscous diffusivities are enhanced up to the molecular magnetic diffusivity in the directions of the rotation axis and mean magnetic field. We neglect the mean magnetic field herein to isolate the effects of anisotropic thermal diffusion, enhanced or diminished along the rotation axis, and explore the instability of a steady conductive basic state with zero mean flow in the Boussinesq approximation. This state is found to be more stable (less stable) as the thermal diffusion parallel to the rotation axis is increased (decreased), if the transverse thermal diffusion is fixed. To examine the effect of simultaneously varying the diffusion along and transverse to the rotation axis, the Frobenius norm is used to control for the total thermal diffusion. When the Frobenius norm of the thermal diffusion tensor is fixed, it is found that increasing the thermal diffusion parallel to the rotation axis is destabilising. This result suggests that, for a fixed total thermal diffusion, geodynamo codes with anisotropic thermal diffusion may operate at lower modified Rayleigh numbers.

A fast semi-implicit method for anisotropic diffusion

Simple finite differencing of the anisotropic diffusion equation, where diffusion is only along a given direction, does not ensure that the numerically calculated heat fluxes are in the correct direction. This can lead to negative temperatures for the anisotropic thermal diffusion equation. In a previous paper we proposed a monotonicity-preserving explicit method which uses limiters (analogous to those used in the solution of hyperbolic equations) to interpolate the temperature gradients at cell faces. However, being explicit, this method was limited by a restrictive Courant–Friedrichs–Lewy (CFL) stability timestep. Here we propose a fast, conservative, directionally-split, semi-implicit method which is second order accurate in space, is stable for large timesteps, and is easy to implement in parallel. Although not strictly monotonicity-preserving, our method gives only small amplitude temperature oscillations at large temperature gradients, and the oscillations are damped in time. With numerical experiments we show that our semi-implicit method can achieve large speed-ups compared to the explicit method, without seriously violating the monotonicity constraint. This method can also be applied to isotropic diffusion, both on regular and distorted meshes.

Heat Maps for Intramolecular Communication in an RNP Enzyme Encoding Glutamine

Allosteric signaling within large ribonucleoproteins modulates both catalytic function and biological specificity, but the spatial extent and quantitative magnitudes of long-distance free-energy couplings have yet to be well characterized. Here, we employ pre-steady-state kinetics to generate a comprehensive mapping of intramolecular communication in the glutaminyl-tRNA synthetase:tRNA(Gln) complex. Alanine substitution at 29 positions across the protein-RNA interface reveals distinct coupling amplitudes for glutamine binding and aminoacyl-tRNA formation on the enzyme, respectively, implying the existence of multiple signaling pathways. Structural models suggest that long-range signal propagation from the tRNA anticodon is dynamically driven, whereas shorter pathways are mediated by induced-fit rearrangements. Seven protein contacts with the distal tRNA vertical arm each weaken glutamine binding affinity across distances up to 40 Å, demonstrating that negative allosteric coupling plays a key role in enforcing the selective RNA-amino acid pairing at the heart of the genetic code.

A Physically Consistent Path-Weighted Diffusivity Function for Modeling of Drop-by-Drop Liquid Metal Deposition

A physically consistent path-weighted diffusivity function is derived for parametric representation of heat diffusion patterns occurring within a volume of material where in there exists inhomogeneous or anisotropic thermal diffusivity. A physically consistent parametric representation of energy deposition processes, where there exists spatially dependent thermal diffusivity, provides for more optimal inverse analysis of such processes. The path-weighted diffusivity function presented here further extends an inverse analysis approach presented previously. The general functional characteristics of the path-weighted diffusivity function derived are examined via a prototype simulation of drop-by-drop liquid metal deposition upon a material characterized by anisotropic thermal diffusivity. The results of this simulation are compared with previous simulations concerning path-weighted thermal diffusivity. The parametric representations presented, which are constructed using path-weighted sums of analytic basis functions, are examined from the perspective of discrete numerical methods. This perspective provides a foundation for the development of control algorithms for process optimization with respect to achieving specific microstructures within a fabricated structure.

Numerical Simulation of Fusion Zone Shape of Lotus-type Porous Iron by Laser Welding

The effect of direction of unidirectional pores on the fusion zone shape, which produced by laser welding, of lotus-type porous iron was investigated through the numerical simulation of temperature distribution. Three-dimensional heat-transfer analyses, which take into account the thermal properties of the lotus-type porous iron depending on the direction and volume fraction of unidirectional pores, were performed by the ABAQUS FE code with user-defined subroutines. These results indicated that the lotus-type porous iron has little anisotropy of melting property. The calculated shape of weld fusion zone is in good agreement with the cross-sectional view obtained by experiments. In order to clarify the reason of these results, anisotropy of thermal diffusivity in the lotus-type porous copper, magnesium, and iron used and anisotropy of laser energy absorption coefficient for these metals were estimated. As a result, the lotus-type porous iron used has a little difference of thermal diffusivity and laser energy absorption coefficient due to its low thermal conductivity, low porosity, large average pore diameters, and high laser absorption coefficient of base metal.

A thermographic technique for the simultaneous estimation of in-plane and in-depth thermal diffusivities of TBCs

Absolute values and anisotropy of thermo-physical and mechanical properties of TBC are significantly affected by the microstructure. The thermal properties as a function of the specific microstructure along the different directions are therefore worth studying. In the present work a thermographic technique able to estimate in a single experiment both in-plane and in-depth thermal diffusivities of TBC has been described and the results obtained on three different freestanding APS TBC samples will be compared with the in-plane elastic modulus as measured by the three-point bending test. Depending on the microstructure and on the heat propagation direction, TBC thermal diffusivity in the range of 3–7 × 10 − 7 m 2 s − 1 has been found. The technique allows measuring the thermal diffusivity along two orthogonal directions highlighting, when present, any anisotropic in-plane structure. An analytical model has been applied to semi-quantitatively estimate both in-depth and in-plane thermal diffusivities of the three samples starting from quantitative image analysis characterization of sample micrographs obtained by scanning electron microscopy. The agreement between model and experimental data resulted quite satisfactory. The model accounts for the anisotropy of thermal diffusivity observed in some samples.

Growth and anisotropic thermal properties of biaxial Ho:YAlO3 crystal

Ho : YAlO 3 (YAP) crystal with large size and good optical quality has been grown by the Czochralski method. Thermal properties of the as-grown Ho:YAP crystal have been investigated by measuring the temperature-dependent, anisotropic thermal expansion, specific heat, thermal diffusion, and thermal conductivity. The results show that Ho:YAP crystal possesses a large anisotropic thermal expansion and good thermal conductivity. The calculated average thermal expansion coefficients along a, b, and c axis are αa=9.18×10−6/K, αb=1.94×10−6/K, and αc=7.61×10−6/K from 293.15 to 770.15 K. The thermal conductivities along a, b, and c axis are up to 11.6, 9.9, and 12.3 W m−1 K−1 at 298.15 K. Compared with Ho: Y3Al5O12 (YAG), Ho:YAP crystal has a larger thermal conductivity along a axis from 298.15 to 568.15 K.

Penetrative convection in anisotropic porous media with variable permeability

The onset of penetrative convection in an anisotropic porous medium, for fluids with quadratic density law, is studied. In particular, the effects of anisotropic permeability and thermal diffusivity have been taken into account.

Penetrative convection via internal heating in anisotropic porous media

Penetrative convection in an anisotropic porous medium is simulated via internal heating. We consider both internal heat sources and sinks, where the porous medium has constant anisotropic thermal diffusivity and non-homogeneous permeability. Both linear instability and global nonlinear energy stability analyses are performed. By adopting a differential constraint approach, the nonlinear stability boundaries are shown to be sharp when compared with the linear instability thresholds. In contrast, it is shown that adopting a standard energy analysis does not yield sharp results.

Path-Weighted Diffusivity Functions for Parameterization of Heat Deposition Processes

General parameterizations are constructed for spatial modulation of heat diffusion patterns according to energy deposition characteristics occurring within a volume of material where there exist inhomogeneous or anisotropic thermal diffusivity. These parameterizations are formulated in terms of path-weighted diffusivity functions. The construction of a general parameterization of energy deposition processes where spatially dependent thermal diffusivity exists is necessary for their inverse analysis. The structure of such a parameterization follows from the concepts of model and data spaces that imply the existence of an optimal parametric representation for a given class of inverse problems. Accordingly, the optimal parametric representation is determined by the characteristics of the available data, which, in principle, can contain both experimental measurements and numerical simulation data. Parameterizations for spatial modulation of heat diffusion follow from the observation that many different types of energy deposition processes can be represented by weighted sums of basis functions whose general forms are that of spatially modulated diffusion. The parameterizations presented are constructed according to a specific definition of the inverse heat deposition problem that provides a rigorous foundation for a highly flexible and general parameterization of energy deposition processes, which is essential for their inverse analysis.

Spectral element spatial discretization error in solving highly anisotropic heat conduction equation

This paper describes a study of the effects of the overall spatial resolution, polynomial degree and computational grid directionality on the accuracy of numerical solutions of a highly anisotropic thermal diffusion equation using the spectral element spatial discretization method. The high-order spectral element macroscopic modeling code SEL/HiFi has been used to explore the parameter space. It is shown that for a given number of spatial degrees of freedom, increasing polynomial degree while reducing the number of elements results in exponential reduction of the numerical error. The alignment of the grid with the direction of anisotropy is shown to further improve the accuracy of the solution. These effects are qualitatively explained and numerically quantified in 2- and 3-dimensional calculations with straight and curved anisotropy.

Downstream heat flux profile versus midplane T profile in tokamaks

The relationship between the midplane scrape-off-layer (SOL) electron temperature profile and the parallel heat flux profile at the divertor in tokamaks is investigated. A model is applied that takes into account anisotropic thermal diffusion in rectilinear geometry with constant density. Eigenmode analysis is applied to the simplified problem with rectangular geometry and constant, but highly anisotropic, thermal diffusivities. A nonlinear solution is also found for the more realistic problem with anisotropically temperature-dependent thermal diffusivities. Numerical solutions are developed for both cases, with spatially dependent heat flux emerging from the plasma, and geometry that includes a model for the divertor leg. For both constant and temperature-dependent thermal diffusivities, it is found that, below about one-half of its peak, the heat flux profile shape at the divertor, compared to the midplane temperature profile shape, is robustly described by the scaling of the simplest two-point model. However, the physical processes are not those assumed in the simplest two-point model, nor is the numerical coefficient relating q∥div to Tmpχ∥mp∕L∥ as predicted in that model. For realistic parameters, the peak in the heat flux, moreover, can be reduced by a factor of 2 or more relative to the two-point model scaling that fits the remaining profile. For temperature profiles in the SOL region above the x-point set by marginal stability, the heat flux profile to the divertor can be largely decoupled from the prediction of the two-point model. These results suggest opportunities and caveats for data interpretation and possibly favorable outcomes for divertor configurations with extended field lines.

Towards physically realizable and hyperbolic moment closures for kinetic theory

The numerical prediction of continuum and non-equilibrium flows by using fully hyperbolic and realizable mathematical descriptions that follow from moment closures of gas kinetic theory is reviewed. A brief review is first given of some of the current capabilities and limitations of moment closures for predicting a range of continuum and non-equilibrium flow. Next, an extended but hyperbolic Gaussian closure for diatomic gases that does not account for heat-transfer effects, as well as a regularized version of this closure that incorporates anisotropic thermal-diffusion effects via the inclusion of higher order terms having an elliptic nature, are both reviewed and applied to a number of canonical flow problems. The numerical results for the Gaussian closures clearly demonstrate the capabilities and potential of moment closures and purely hyperbolic treatments. Following these reviews, a somewhat novel hierarchy of physically realizable and hyperbolic moment closures is considered and described. This alternative hierarchy is based on modifications to the more common maximum-entropy hierarchies, so as to ensure the validity and integrability of the approximate distribution function for all values of the velocity moments that are physically realizable. The predictive capabilities of this new closure hierarchy are then explored by considering numerical solutions of the closures for a one-dimensional kinetic equation with a relaxation-time collision operator and by comparing the closure solutions to discrete numerical solutions of this simplified kinetic equation. The study concludes with a brief summary of the findings and a discussion of the potential of the physically realizable and hyperbolic moment closures for application to fully three-dimensional physics.

Nonisothermal Model for the Direct Isotropic/Smectic-A Liquid-Crystalline Transition

An extension to a high-order model for the direct isotropic/smectic-A liquid-crystalline phase transition was derived to take into account thermal effects including anisotropic thermal diffusion and latent heat of phase ordering. Multiscale multitransport simulations of the nonisothermal model were compared to isothermal simulation, showing that the presented model extension corrects the standard Landau-de Gennes prediction from constant growth to diffusion-limited growth under shallow quench/undercooling conditions. Nonisothermal simulations, where metastable nematic preordering precedes smectic-A growth, were also conducted, and novel nonmonotonic phase-transformation kinetics were observed.

A Numerical Simulation to Propose a Flash Method for In Situ Detection of the Thermal Diffusivity of Anisotropic Thin Film Materials

Strong anisotropy of thermal diffusivity is frequently observed in thin film materials. We propose an in situ experimental method to remotely measure radial and axial components of the thermal diffusivity. The method is based on the traditional laser flash technique but is specialized to also highly challenging experimental situations such as sample manufacture and use phase when thin films may be exposed to very high pressures or temperatures and to high temperature gradients. The method requires laser pulses of very short duration and fast measurement of transient temperature excursions in only radial directions on the surface of the thin film samples. The accuracy of the method is checked by comparison with results from a finite element calculation for a graphite sheet with high anisotropic conductivity that simulates a thermo-physical experiment.

Thermal diffusivity of aromatic polyimide thin films by temperature wave analysis

The heat transport properties of aromatic polyimide thin films have become more important in the use for the electric insulation in the microelectronic devices with highly integrated circuits. The various kinds of measuring methods have been applied to obtain the anisotropic thermal conductivity and thermal diffusivity of thin films, however, if the specimens are soft and transparent, the conventional methodology requires highly advanced technology in preparing the specimens for the measurement and the results obtained vary widely. The purpose of this study is to apply the temperature wave analysis (TWA) method to measure the thermal diffusivity of thin films and spin-coated layers of aromatic polyimide in the thickness direction at various temperatures. The TWA is an absolute method to determine the thermal diffusivity by using the phase shift of temperature wave. We have performed measurements on the five different chemical structures of aromatic polyimide, including polyimide isoindoloquinazolinedione (PIQ), pyromellitic dianhydride and 4,4′-oxydianiline (PMDA/ODA), 3,3′,4,4′,-biphenyltetracarboxylic dianhydride and p-phenylenediamine (BPDA/PPDA), 3,3′,4,4′-biphenyltetracarboxylic dianhydride and 4,4′-oxydianiline (BPDA/ODA), and 3,3′,4,4′-benzophenonetetracarboxylic dianhydride and 3,3′-diaminobenzophenone (BTDA/DAB). As a result, thermal diffusivity of thin films in a thickness range from 0.1 to 300 μm at a temperature range from 10 to 570 K is obtained. The thickness dependence of thermal diffusivity of spin-coated layers of PIQ exhibits a good coincidence with the tendency of molecular anisotropy observed by attenuated total reflection Fourier transform infrared spectroscopy. In the low temperature below 20 K the amorphous PMDA/ODA film exhibits a substantial increase, which can be understood by considering the phonon mean free path of amorphous systems as first noted by Kittel for inorganic glasses. The glass transition of BTDA/DAB is observed as a rapid decrease of thermal diffusivity. The results indicate the availability of TWA for the present needs of accurate but simple measuring technique to determine the thermal diffusivity of thin polymer films, which is strongly dependent on the chemical and anisotropic structures.

Anisotropy and symmetry in porous media convection

The linear and nonlinear stability analysis of the motionless state (conduction solution) and of a vertical throughflow in an anisotropic porous medium is performed. In particular, the effect of a nonhomogeneous porosity and a constant anisotropic thermal diffusivity have been taken into account.