Prediction of the Effective Thermal Diffusivity of Discretely Inhomogeneous Media

2009 ◽  
Author(s):  
Daniel W. Mackowski ◽  
Mario Ramos
Keyword(s):  
Wave Propagation ◽  
Thermal Diffusivity ◽  
Addition Theorem ◽  
Inhomogeneous Media ◽  
Spherical Particles ◽  
Effective Thermal Diffusivity ◽  
Effective Medium Model ◽  
The Matrix ◽  
Sphere Radius ◽  
Definition Of

An extended definition of the effective thermal diffusivity is posed via an analogy to acoustic and EM wave propagation in discretely inhomogeneous media. Specifically, the propagation of a periodic, plane thermal wave of frequency ω, through an inhomogeneous medium consisting of spherical particles embedded in a continuous matrix, is theoretically examined. An exact solution for the time–harmonic conduction equation, for the multiple sphere system, is developed by use of the scalar wave harmonic functions and the addition theorem for the harmonics. An effective medium model, which is based on the Quasi–Crystalline approximation (QCA) for acoustic and EM wave propagation, is developed, and a formulation for the frequency–dependent effective thermal diffusivity is derived. In the limit of x = Rω/α0→0, where R is the sphere radius and α0 the matrix thermal diffusivity, it is shown that formulation reduces to that derived from a static model.

Heat transfer across sheared suspensions: role of the shear-induced diffusion

2013 ◽  
Vol 724 ◽  
pp. 527-552 ◽  
Author(s):  
Bloen Metzger ◽  
Ouamar Rahli ◽  
Xiaolong Yin
Keyword(s):  
Thermal Diffusivity ◽  
Volume Fraction ◽  
Spherical Particles ◽  
Transient Temperature ◽  
Particle Diffusion ◽  
Driving Mechanism ◽  
Average Particle ◽  
Particle Rotation ◽  
Effective Thermal Diffusivity ◽  
Couette Cell

AbstractSuspensions of non-Brownian spherical particles undergoing shear provide a unique system where mixing occurs spontaneously at low Reynolds numbers. Through a combination of experiments and simulations, we investigate the effect of shear-induced particle diffusion on the transfer of heat across suspensions. The influence of particle size, particle volume fraction and applied shear are examined. By applying a heat pulse to the inner copper wall of a Couette cell and analysing its transient temperature decay, the effective thermal diffusivity of the suspension, $\alpha $, is obtained. Using index matching and laser-induced fluorescence imaging, we measured individual particle trajectories and calculated their diffusion coefficients. Simulations that combined a lattice Boltzmann technique to solve for the flow and a passive Brownian tracer algorithm to solve for the transfer of heat are in very good agreement with experiments. Fluctuations induced by the presence of particles within the fluid cause a significant enhancement (${\gt }200\hspace{0.167em} \% $) of the suspension transport properties. The effective thermal diffusivity was found to be linear with respect to both the Péclet number ($\mathit{Pe}= \dot {\gamma } {d}^{2} / {\alpha }_{0} \leq 100$) and the solid volume fraction ($\phi \leq 40\hspace{0.167em} \% $), leading to a simple correlation $\alpha / {\alpha }_{0} = 1+ \beta \phi \mathit{Pe}$ where $\beta = 0. 046$ and ${\alpha }_{0} $ is the thermal diffusivity of the suspension at rest. In our Couette cell, the enhancement was found to be optimum for a volume fraction, $\phi \approx 40\hspace{0.167em} \% $, above which, due to steric effects, both the particle diffusion motion and of the effective thermal diffusion dramatically decrease. No such correlation was found between the average particle rotation and the thermal diffusivity of the suspension, suggesting that the driving mechanism for enhanced transport is the translational particle diffusivity. Movies are available with the online version of the paper.

Prediction of the Effective Thermal Conductivity of Discretely Inhomogeneous Media

2013 ◽  
Author(s):  
Mario Ramos-Negrete ◽  
Daniel W. Mackowski
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Effective Conductivity ◽  
Mathematical Formulation ◽  
Addition Theorem ◽  
Inhomogeneous Media ◽  
Spherical Particles ◽  
High Harmonics ◽  
Exact Calculations ◽  
Number Of Particles

An exact mathematical formulation and associated parallel computational scheme is developed by use of regular harmonics and the addition theorem for the harmonics to calculate the effective thermal conductivity of discretely inhomogeneous media consisting of spherical particles embedded in a continuous matrix. Exact calculations of the temperature field and heat transfer (with high harmonics orders of sphere interactions) are performed in various particulate configurations in which the number of particles is sufficiently large to represent a continuous inhomogeneous medium. Effective medium principles are applied to determine the effective conductivity of the medium. Reported experimental results in the literature are compared with the results from our analytical formulation.

About definition of the local entropy rate of production in experiment of pulse electric heating

2020 ◽  
pp. 29-34
Author(s):  
Alexandr V. Kostanovskiy ◽  
Margarita E. Kostanovskaya
Keyword(s):  
Thermal Diffusivity ◽  
Electric Heating ◽  
Thermal Capacity ◽  
Entropy Rate ◽  
Initial Time ◽  
Local Entropy ◽  
Linear Mode ◽  
Electric Capacity ◽  
Definition Of ◽  
Pulse Electric

Work is devoted to studying of a linear mode thermodynamic – a mode which is actively investigated now. One of the main concepts of a linear mode – local entropy rate of production. The purpose of given article consists in expansion of a circle of problems for which it is possible to calculate a local entropy rate of production, namely its definition, using the experimental “time-temperature” curves of heating/cooling. “Time-temperature” curves heating or cooling are widely used in non-stationary thermophysical experiments at studying properties of substances and materials: phase transitions of the first and second sort, a thermal capacity, thermal diffusivity. The quantitative substantiation of the formula for calculation of the local entropy rate of production in which it is used thermogram (change of temperature from time) which is received by a method of pulse electric heating is resulted. Initial time dependences of electric capacity and temperature are measured on the sample of niobium in a microsecond range simultaneously. Conformity of two dependences of the local entropy rate of production from time is shown: one is calculated under the known formula in which the brought electric capacity is used; another is calculated, using the thermogram.

scholarly journals Modelling of torsional wave propagation in a two-layer anisotropic inhomogeneous media

2021 ◽  
Vol 1849 (1) ◽  
pp. 012013
Author(s):  
Tapas Ranjan Panigrahi ◽  
Sumit Kumar Vishwakarma ◽  
Dinesh Kumar Majhi
Keyword(s):  
Wave Propagation ◽  
Inhomogeneous Media ◽  
Torsional Wave

Effects of thermal oxidation on the effective thermal diffusivity of titanium alloys

2014 ◽  
Vol 47 (38) ◽  
pp. 385306 ◽  
Author(s):  
A Somer ◽  
F Camilotti ◽  
G F Costa ◽  
A R Jurelo ◽  
A Assmann ◽  
...  
Keyword(s):  
Thermal Diffusivity ◽  
Titanium Alloys ◽  
Thermal Oxidation ◽  
Effective Thermal Diffusivity

scholarly journals Infinite Matrix Products and the Representation of the Matrix Gamma Function

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
J.-C. Cortés ◽  
L. Jódar ◽  
Francisco J. Solís ◽  
Roberto Ku-Carrillo
Keyword(s):  
Gamma Function ◽  
Infinite Product ◽  
Infinite Matrix ◽  
Convergence Results ◽  
Matrix Products ◽  
The Matrix ◽  
Definition Of

We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.

Effect of Precursors on Transmittance and Microstructure of Mullite Ceramics

2009 ◽  
Vol 620-622 ◽  
pp. 429-432 ◽  
Author(s):  
Gui Min Zhang ◽  
Zheng Yi Fu ◽  
Yu Cheng Wang ◽  
Hao Wang ◽  
Wei Min Wang ◽  
...  
Keyword(s):  
Spray Drying ◽  
Ethanol Solution ◽  
Spherical Particles ◽  
Plasma Sintering ◽  
The Matrix ◽  
Conventional Drying ◽  
Spark Plasma ◽  
Mean Size ◽  
Dta Curves ◽  
Equiaxed Grains

Two different kinds of mullite precursors with composition 3Al2O3•2SiO2 (3:2) were prepared by conventional drying ethanol solution and spray-drying aqueous solution of aluminum nitrate nanohydrate and tetraethoxysilane, respectively. The results of scanning electron microscope (SEM) indicate that one powder consists of irregular particles with size of 1-10μm, the other powder is made of inhomogeneously sized hollow spherical particles with mean size of 0.5-5μm. The TG-DTA curves indicate the hollow spherical particles are unfavorable to eliminate the decomposed products. After the precursors were sintered by Spark Plasma Sintering at 1450°C for 10min, the microstructures of the former are made of fine equiaxed grains with sizes of around 0.5μm, the latter consist of elongated grains distributed in the matrix of fine grains with imhomogenous size of 0.5~10μm due to the liquid phase forming. The different microstructures lead to the former sintered body is transparent, while, the sample from spray-drying is opaque.

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