Boundary Conditions and Evolution of Ballistic Heat Transport

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
F. X. Alvarez ◽  
D. Jou
Keyword(s):  
Thermal Conductivity ◽  
Boundary Conditions ◽  
Heat Transport ◽  
Ballistic Transport ◽  
Theoretical Models ◽  
Effective Size ◽  
Size Dependent ◽  
Fourier Equation

We analyze the effects of boundary conditions on the evolution of ballistic heat transport in four theoretical models and propose that a Fourier equation with an effective size-dependent thermal conductivity is a good candidate for the description of ballistic transport when boundary conditions are suitably imposed.

scholarly journals Thermal Conductivity Calculations for Nanoparticles Embedded in a Base Fluid

2021 ◽  
Vol 11 (4) ◽  
pp. 1459
Author(s):  
Soran M. Mamand
Keyword(s):  
Thermal Conductivity ◽  
Base Fluid ◽  
Theoretical Models ◽  
Simple Method ◽  
Size Dependent ◽  
Nanolayer Thickness ◽  
Embedded Nanoparticles ◽  
Comparison With Experimental Data ◽  
Good Agreement

The Prasher analytical model was used for calculating the thermal conductivity of the embedded nanoparticles of Al2O3, CuO, ZnO, and SiO2 in conventional fluids, such as water and ethylene glycol. The values that were obtained were used in the nanofluid theoretical models for comparison with experimental data, where good agreement was obtained. Liang and Li’s theoretical model was also used to calculate the thermal conductivity of these nanoparticles, where the results agreed with those obtained using the Prasher model. The effect of the liquid nanolayer thickness around the nanoparticles that was used to enhance the effective thermal conductivity of nanofluids was explained. The role of the nanoparticles’ surface specularity parameter, which was size-dependent, was clarified. This theoretical trend provides a simple method for estimating the thermal conductivity of nanoparticles and nanofluids.

scholarly journals Experimental Investigation of Metal-Diamond Thermal Interface Conductance With Different Diamond Surface Terminations

2010 ◽  
Author(s):  
Kimberlee C. Collins ◽  
Gang Chen
Keyword(s):  
Thermal Conductivity ◽  
Heat Transport ◽  
Synthetic Diamond ◽  
Diamond Surface ◽  
Small Scale ◽  
Device Performance ◽  
Thermal Interface ◽  
Single Crystal Diamond ◽  
Heat Spreading ◽  
Resistance To Heat

Synthetic diamond has potential as a heat spreading material due to its uniquely high thermal conductivity. In small-scale devices, interfaces can dominate the resistance to heat transport, and thus play an important role in determining device performance. Here we use transient thermoreflectance techniques to measure the thermal interface conductance at metal-diamond interfaces. We study single crystal diamond samples with various surface terminations. We measure thermal interface conductance values over a range of temperatures from 88 K to 300 K, and find roughly 60 percent higher thermal interface conductance between Al and oxygenated diamond samples as compared to hydrogen terminated samples. The results reported here will be useful for device design and for advancing models of interfacial heat transport.

Study of an Iterative Solution for Boltzmann Transport Equation and Calculation of Thermal Conductivity

2018 ◽  
Vol 777 ◽  
pp. 421-425 ◽  
Author(s):  
Chhengrot Sion ◽  
Chung Hao Hsu
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Numerical Calculation ◽  
Iterative Method ◽  
Transport Equation ◽  
Linear Systems ◽  
Heat Transport ◽  
Boltzmann Transport Equation ◽  
Iterative Solution ◽  
Boltzmann Transport

Many methods have been developed to predict the thermal conductivity of the material. Heat transport is complex and it contains many unknown variables, which makes the thermal conductivity hard to define. The iterative solution of Boltzmann transport equation (BTE) can make the numerical calculation and the nanoscale study of heat transfer possible. Here, we review how to apply the iterative method to solve BTE and many linear systems. This method can compute a sequence of progressively accurate iteration to approximate the solution of BTE.

The Effect of Turbulence on Momentum and Heat Transport in Packed Beds with Low Tube to Particle Diameter Ratio

2018 ◽  
Vol 16 (11) ◽  
Author(s):  
F. I. Molina-Herrera ◽  
C. O. Castillo-Araiza ◽  
H. Jiménez-Islas ◽  
F. López-Isunza
Keyword(s):  
Thermal Conductivity ◽  
Heat Transport ◽  
Mass Flux ◽  
Flow Model ◽  
Particle Diameter ◽  
Packed Bed ◽  
Diameter Ratio ◽  
Packed Beds ◽  
Measured Temperature ◽  
Orthogonal Collocation

Abstract This is a theoretical study about the influence of turbulence on momentum and heat transport in a packed-bed with low tube to particle diameter ratio. The hydrodynamics is given here by the time-averaged Navier-Stokes equations including Darcy and Forchheimer terms, plus a κ-ε two-equation model to describe a 2D pseudo-homogeneous medium. For comparison, an equivalent conventional flow model has also been tested. Both models are coupled to a heat transport equation and they are solved using spatial discretization with orthogonal collocation, while the time derivative is discretized by an implicit Euler scheme. We compared the prediction of radial and axial temperature observations from a packed-bed at particle Reynolds numbers (Rep) of 630, 767, and 1000. The conventional flow model uses effective heat transport parameters: wall heat transfer coefficient (hw) and thermal conductivity (keff), whereas the turbulent flow model includes a turbulent thermal conductivity (kt), estimating hw via least-squares with Levenberg-Marquardt method. Although predictions of axial and radial measured temperature profiles with both models show small differences, the calculated radial profiles of the axial velocity component are very different. We demonstrate that the model that includes turbulence compares well with mass flux measurements at the packed-bed inlet, yielding an error of 0.77 % in mass flux balance at Rep = 630. We suggest that this approach can be used efficiently for the hydrodynamics characterization and design and scale-up of packed beds with low tube to particle diameter ratio in several industrial applications.

Thermal Conductivity of Low Density Polyethylene Foams Part I: Comprehensive Study of Theoretical Models

2019 ◽  
Vol 28 (4) ◽  
pp. 745-754 ◽  
Author(s):  
Hasanzadeh Rezgar ◽  
Azdast Taher ◽  
Doniavi Ali ◽  
Eungkee Lee Richard
Keyword(s):  
Thermal Conductivity ◽  
Theoretical Models ◽  
Low Density Polyethylene ◽  
Low Density ◽  
Comprehensive Study

scholarly journals Thermal Conductive Networks Constructed by Sialon Fibers in-Situ Synthesized in Barium Aluminosilicate Glass-Ceramic

2021 ◽  
Author(s):  
Shaojie Sun ◽  
Xinyu Wang ◽  
Junjie Zhou ◽  
Siqi Zhang ◽  
Kongyu Ge ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Glass Ceramic ◽  
Ceramic Matrix Composite ◽  
Theoretical Models ◽  
Ceramic Materials ◽  
Aluminosilicate Glass ◽  
Complex Shapes ◽  
Barium Aluminosilicate ◽  
Enhanced Thermal Conductivity

Abstract The application of ceramic materials is limited due to the complicated preparation process and intrinsic brittleness. In this work, a pressureless manufacturing route that enables the formation of barium aluminosilicate (BAS) glass-ceramic consisting of internal β-Sialon fibers with enhanced thermal conductivity is developed. By adjusting the carbon source content, composites with different Sialon contents can be easily fabricated. The thermal conductivity of the sample with 3.5 wt.% is improved to 5.845 W/m ∙ K with the Sialon content of 26 wt.% in the composite, which is 112.64 % higher than that of the pure BAS matrix. The theoretical models suggest that the enhanced thermal conductivity is mainly ascribed to the thermal conduction network constructed by Sialon fibers. This work provides a method with industrial application prosperity to fabricate the high temperature ceramic matrix composite of different sizes and complex shapes.

scholarly journals The Kirchhoff Transformation for Convective-radiative Thermal Problemsin Fins

2021 ◽  
Vol 15 ◽  
pp. 12-21
Author(s):  
Jonatas Motta Quirino ◽  
Eduardo Dias Correa ◽  
Rodolfo do Lago Sobral
Keyword(s):  
Thermal Conductivity ◽  
Boundary Conditions ◽  
Thermal Radiation ◽  
Heat Dissipation ◽  
Variable Thermal Conductivity ◽  
Dirichlet Boundary Conditions ◽  
Heat Transfer Analysis ◽  
Temperature Function ◽  
Kirchhoff Transformation ◽  
Comparison Of The Results

- The present work describes the thermal profile of a single dissipation fin, where their surfaces reject heat to the environment. The problem happens in steady state, which is, all the analysis occurs after the thermal distribution reach heat balance considering that the fin dissipates heat by conduction, convection and thermal radiation. Neumann and Dirichlet boundary conditions are established, characterizing that heat dissipation occurs only on the fin faces, in addition to predicting that the ambient temperature is homogeneous. Heat transfer analysis is performed by computational simulations using appropriate numerical methods. The most of solutions in the literature consider some simplifications as constant thermal conductivity and linear boundary conditions, this work addresses this subject. The method applied is the Kirchhoff Transformation, that uses the thermal conductivity variation to define the temperatures values, once the thermal conductivity variate as a temperature function. For the real situation approximation, this work appropriated the silicon as the fin material to consider the temperature function at each point, which makes the equation that governs the non-linear problem. Finally, the comparison of the results obtained with typical results proves that the assumptions of variable thermal conductivity and heat dissipation by thermal radiation are crucial to obtain results that are closer to reality.

scholarly journals Thermal transport properties of decagonal quasicrystals and their approximants

2013 ◽  
Vol 1517 ◽  
Author(s):  
Petar Popčević ◽  
Ante Bilušić ◽  
Kristijan Velebit ◽  
Ana Smontara
Keyword(s):  
Thermal Conductivity ◽  
Electrical Resistivity ◽  
Transport Properties ◽  
Heat Transport ◽  
Thermal Transport ◽  
Strong Relationship ◽  
Decagonal Quasicrystal ◽  
Decagonal Quasicrystals ◽  
Plane Anisotropy ◽  
Out Of Plane

ABSTRACTTransport properties (thermal conductivity, electrical resistivity and thermopower) of decagonal quasicrystal d-AlCoNi, and approximant phases Y-AlCoNi, o-Al13Co4, m-Al13Fe4, m-Al13(Fe,Ni)4 and T-AlMnFe have been reviewed. Among all presented alloys the stacking direction (periodic for decagonal quasicrystals) is the most conductive one for the charge and heat transport, and the in/out-of-plane anisotropy is much larger than the in-plane anisotropy. There is a strong relationship between periodicity length along stacking direction and anisotropy of transport properties in both quasicrystals and their approximants suggesting a decrease of the anisotropy with increasing number of stacking layers.

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