Thermal Diffusion Field Research Articles

Magnetized dissipative Soret-Dufour effects on Walter’s-B fluid flow over a stretching sheet with nonuniform heat source/sink and thermal radiation under chemical reaction

The main motivation behind this numerical analysis is to disclose the salient magneto-thermo characteristic features of two-dimensional viscous incompressible magnetized Soret and Dufour effects on the boundary layer flow of Walter’s-B fluid over a stretching sheet under the influence of viscous dissipation. The novel physical effects such as nonuniform heat source/sink and magnetic Ohmic heating are included in the governing equations. Further, prescribed surface temperature condition is introduced in the boundary conditions to describe the thermal transport features. However, the deployed non-Newtonian Walter’s-B fluid rheology model finds its innumerable applications in numerous areas of science and engineering including electronic cooling, polymer processing, nuclear reactor cooling, extraction of polymer sheet, plastic sheet drawing, chemical engineering, metallurgy, injection molding and many more. Therefore, authors have motivated with these applications and advantageous of considered fluid model. Hence, an effort is made to describe the dynamic characteristic features of non-Newtonian Walter’s-B rheology model about a stretching sheet. However, present physical flow model produces highly nonlinear coupled two-dimensional partial differential equations and which are not acquiescent to available analytical methods. Owing to this, a robust MATLAB-based BVP4C technique is deployed to produce the appropriate numerical solutions through suitable similarity transformations. The graphical representations of velocity, temperature and concentration profiles along with skin-friction coefficient, Nusselt and Sherwood numbers are presented. Magnifying magnetic number decays the velocity profile and enhances the thermal and concentration fields. Rising viscoelastic parameter diminishes the thermal and concentration fields and magnifies the velocity field. Rising the radiation parameter diminish the thermal field. Magnifying Soret number raises the concentration field. Rising the space and temperature dependent heat source/sink coefficient amplifies the thermal diffusion field. Magnifying Dufour and Eckert numbers amplifies the thermal field. Finally, the guarantee and accuracy of the investigated problem is presented through a comparison with previous studies.

A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step

A Finite-Volume based POD-Galerkin reduced order modeling strategy for steady-state Reynolds averaged Navier–Stokes (RANS) simulation is extended for low-Prandtl number flow. The reduced order model is based on a full order model for which the effects of buoyancy on the flow and heat transfer are characterized by varying the Richardson number. The Reynolds stresses are computed with a linear eddy viscosity model. A single gradient diffusion hypothesis, together with a local correlation for the evaluation of the turbulent Prandtl number, is used to model the turbulent heat fluxes. The contribution of the eddy viscosity and turbulent thermal diffusivity fields are considered in the reduced order model with an interpolation based data-driven method. The reduced order model is tested for buoyancy-aided turbulent liquid sodium flow over a vertical backward-facing step with a uniform heat flux applied on the wall downstream of the step. The wall heat flux is incorporated with a Neumann boundary condition in both the full order model and the reduced order model. The velocity and temperature profiles predicted with the reduced order model for the same and new Richardson numbers inside the range of parameter values are in good agreement with the RANS simulations. Also, the local Stanton number and skin friction distribution at the heated wall are qualitatively well captured. Finally, the reduced order simulations, performed on a single core, are about 105 times faster than the RANS simulations that are performed on eight cores.

Measuring Thermal Diffusivity of Dilute Nanofluids Using Interferometry-Based Inverse Heat Transfer Approach

Measurement of thermophysical properties of nanofluids is essential to understand the heat transfer performance of nanoparticles suspended in base fluids. In this direction, as a definite advancement over the conventional methods, laser interferometry has been employed to study the dependence of thermal diffusivity of dilute nanofluids on increasing volume concentration of nanoparticles using the principles of inverse heat transfer. Two types of nanofluids, namely, and with de-ionized water as the base fluid, have been considered for this analysis. The experimental configuration consists of a layer of working fluid (water or nanofluid) contained between two differentially heated horizontal walls of a rectangular cavity. Temperature potential is applied to the fluid layer by raising the temperature of the upper horizontal wall of the cavity with respective to the lower one. Transient evolution of the thermal diffusion field (from top plate to the lower horizontal wall) has been recorded in the form of interferograms at various time instants. As the forward model, the transient form of heat diffusion equation has been analytically solved for a guessed value of thermal diffusivity. Finally, the experimentally determined temperature field has been compared with the analytical solution, and following the principles of inverse heat transfer, the thermal diffusivity of the working fluid has been calculated. The methodology developed has first been benchmarked by determining the thermal diffusivity of the base fluid, that is, water, and thereafter it has been employed to determine the corresponding thermophysical properties of the dilute nanofluids. Results showed an increase in the thermal diffusivity of dilute nanofluids as a function of increasing volume concentration of the nanofluids.

Upscaling the Steam-Assisted-Gravity-Drainage Model for Heterogeneous Reservoirs

Summary The effects of heterogeneities in the rock and fluid properties on the governing equations in modeling the steam-assisted-gravity-drainage (SAGD) process are investigated using a spectrum-based upscaling approach. In this approach, heterogeneity is included by assigning random perturbation fields to permeability and thermal diffusivity that hold the assumption of first and second orders of stationarity. Heat and mass-transport parameters and dependent variables (e.g., temperature and viscosity) that are affected by heterogeneity are represented by their mean and perturbations around the mean values. Substituting the perturbed variables and coefficients into the basic governing equations (heat-diffusion and Darcy equations) results in new sets of stochastic partial-differential equations that include mean and perturbation. Mean equations are essentially upscaled new governing equations that include the autocorrelations and cross correlations between different perturbed quantities. The cross correlations are derived by applying the Fourier-Stieltjes transform. Verification and validation of the developed results for the heat-diffusion equation are performed using numerical simulations with synthetic heterogeneities. The upscaled equations embrace the heterogeneity in permeability and thermal diffusivity and can predict the flow rate and shape of the steam chamber. The upscaled model is compared with the homogeneous model, developed by Butler (1991), to quantify the effects of heterogeneities in permeability and thermal diffusivity on the SAGD efficiency. A case is studied by assigning harmonic distribution to the perturbations of thermal diffusivity and permeability. Different cases with different relationships between permeability and thermal-diffusivity fields are considered to investigate their effects on the oil flow rate. The results show that local perturbations decrease the oil flow rate. Furthermore, steam-chamber growth is retarded in a reservoir with local perturbations compared with homogeneous reservoirs. The developed model can be used in the initial stages of SAGD development projects for long-range planning as a guide to find the upper and lower limits of production in reservoirs with heterogeneities.

Understanding the temperature dependence of thermo-physical properties of nanofluid suspensions using non-intrusive dynamic measurements

Thermal diffusivity dependence on temperature and concentration of aqueous colloidal suspensions of Al2O3 in deionized water has been investigated by conducting transient heat transfer experiments. The study has been performed in a purely non-intrusive manner using Mach Zehnder interferometry. Through the dependence of refractive index on temperature, the time sequence of recorded interferograms has been used to generate highly sensitive data of evolving temperature distribution in the thermal diffusion field. Determination of thermal diffusivity from temperature-position data has been carried out by the method of least square. In comparison with deionized water, substantial enhancement in thermal diffusivity with increasing temperature and concentration of nanofluid suspension of Al2O3 is observed through the time sequence of the recorded interferograms as well as through analytical measurements. Additionally, the measurement of ζ-potential, pH and effective viscosity of dilute Al2O3 suspension at various temperatures explains the possible mechanisms at micro-scale levels that are responsible for such an anomalous behaviour of thermal diffusivity. The competing interaction of these factors reveals dependence of thermal diffusivity on particle cluster formation and thereby in the resultant stability of the suspension. The experimental findings indicate that, at specific size and shape, the higher conductivity of solid alumina particles and their cluster formation plays a major role in enhancing the thermophysical properties of the nanofluid Al2O3 suspension over the considered range of temperature and concentration. Also, a reasonably close agreement of the obtained trends of thermal diffusivity values with those reported in the literature and clear visualization of enhancement in thermal transport through interferograms signifies the importance of the proposed non-intrusive measurement technique for reliable measurement of thermal properties of nanofluids.

Pulsed flying spot with the logarithmic parabolas method for the estimation of in-plane thermal diffusivity fields on heterogeneous and anisotropic materials

A novel thermal non-destructive technique based on a Pulsed Flying Spot is presented here by considering in-plane logarithmic processing of the relaxing temperature field around the heat source spot. Recent progress made in optical control, lasers, and infrared cameras permits the acquisition of 2D temperature fields and localized thermal excitation on a small area instead of the entire recorded image. This study focuses on a new method based on spatial logarithm analysis of a temperature field to analyse and measure different parameters, such as the in-plane thermal diffusivity and localization of the spot. In this paper, this method is presented and the first results of heterogeneous anisotropic materials are depicted. The in-plane thermal diffusivity is estimated with an error lower than 4%, and the initial location of the heating spot is determined.

The effect of two-dimensional shear flow on the stability of a crystal interface in a supercooled melt

A model is developed based on the time-related thermal diffusion equations to investigate the effects of two-dimensional shear flow on the stability of a crystal interface in the supercooled melt of a pure substance. Similar to the three-dimensional shear flow as described in our previous paper, the two-dimensional shear flow can also be found to reduce the growth rate of perturbation amplitude. However, compared with the case of the Laplace equation for a steady-state thermal diffusion field, due to the existence of time partial derivatives of the temperature fields in the diffusion equation the absolute value of the gradients of the temperature fields increases, therefore destabilizing the interface. The circular interface is more unstable than in the case of Laplace equation without time partial derivatives. The critical stability radius of the crystal interface increases with shearing rate increasing. The stability effect of shear flow decreases remarkably with the increase of melt undercooling.

Experimental Observation and Computer Simulations of 3D Triplet Structures in Diffusion Limited Growth of Xenon Crystals

Changes of growth morphologies are induced by a perturbation of the thermal diffusion field in the surrounding melt of a growing xenon crystal. Apart from the dendritic morphology, seaweed and doublon morphologies and for the first time transitions from dendritic to triplet structures (first predicted by T. Abel, E. Brener, and H. Müller-Krumbhaar [Phys. Rev. E 55, 7789 (1997)10.1103/PhysRevE.55.7789] were observed experimentally. With 3D phase-field simulations it was possible to reproduce the experimental procedure and to verify that triplet structures can grow in a stable way even in the presence of anisotropic surface free energy as found for experimental substances.

Simultaneous velocity and diffusivity mapping in the case of 3-D transient heat diffusion: heat pulse thermography and IR image sequence analysis

A non uniform heat pulse is used as a non intrusive marker on opaque liquids or highly deformable solid media, in order to estimate both the full velocity and thermal diffusivity fields from thermal image processing. The difficult issue of identifying both the local transport and diffusion properties is addressed by adopting two different inverse approaches. First, a new specific version of the Total Least Squares (TLS) method is implemented, yielding both sensitivity analysis and confidence estimation, with no prior knowledge of the measurement noise variance. A second strategy is proposed from an iterative Digital Image Correlation (DIC) approach, yielding an hybrid DIC/TLS method. Both methods are first validated on simulated data,and calibrated with homogenous materials under uniform displacement. Two different grids are used in order to analyze the effect of the spatial period of the heat pulse on the retrieved parameters. Then, the effective velocity and thermal diffusivity fields are retrieved from an experimental bench in the case of a moving Thermisorel® sample. The Fine grid is found to yield better estimation results than the coarse grid. Thermal diffusivity mapping obtained with the TLS method is more trusted.

Visualization of a Thermal Diffusion Field around a Single Ice Crystal Growing in Supercooled Water under a Short-term Microgravity Condition

Visualization of a Thermal Diffusion Field around a Single Ice Crystal Growing in Supercooled Water under a Short-term Microgravity Condition

811 確率密度関数法による円管内乱流中の熱拡散場の数値シミュレーションの試み

811 確率密度関数法による円管内乱流中の熱拡散場の数値シミュレーションの試み

Crack instabilities of a heated glass strip.

Recently, Yuse and Sano [Nature (London) 362, 329 (1993)] have observed that a crack traveling in a glass strip submitted to a nonuniform thermal diffusion field undergoes numerous instabilities. We study two cases of quasistatic crack propagation. The crack extension condition in straight propagation is determined. An asymptotic analysis of the elastic free energy is introduced and scaling laws are derived. A linear stability analysis of the straight propagation is performed, based on the assumption that the crack tip propagation deviates from the centered straight one as soon as it is submitted to a ``physical'' singular shear stress. It is shown that a straight propagation can become unstable after which a wavy instability appears. The condition for instability as well as the selected wavelength is calculated quantitatively. The results are compared with experiments and the agreement is favorable.

Subcritical-supercritical bifurcation crossover in directional solidification.

The Mullins-Sekerka planar-cellular instability in directional solidification should be subcritical when the partition coefficient k0.45 and latent heat is ignored. However, Merchant and Davis [Phys. Rev. Lett. 63, 573 (1989)] predicted that as the solute concentration is reduced, the increasingly important thermal diffusion field would lead to a crossover from a subcritical to a supercritical bifurcation. We have performed directional solidification experiments on a series of succinonitrile samples containing different concentrations of Coumarin 152, and have found preliminary evidence for the predicted crossover at a concentration ${\mathit{C}}_{\mathit{t}}$ \ensuremath{\sim} 0.1%.

Dynamics of Interfacial Pattern Formation

A phenomenological model of dendritic solidification incorporating interfacial kinetics, crystalline anisotropy, and a local approximation for the dynamics of the thermal diffusion field is proposed. The preliminary results are in qualitative agreement with natural dendritelike pattern formation.