Boundary Condition Effect on Thermoelectric Coefficients

2013 ◽  
Vol 743-744 ◽  
pp. 116-119 ◽  
Author(s):  
Chun Lei Wang ◽  
Wen Bin Su ◽  
Hua Peng ◽  
Yuan Hu Zhu ◽  
Jian Liu ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Boundary Conditions ◽  
High Performance ◽  
Figure Of Merit ◽  
Chemical Potential ◽  
Thermoelectric Device ◽  
Chemical Potential Difference ◽  
Condition Effect ◽  
Physical Boundary

nfluence of physical boundary conditions on the thermoelectric transportation coefficients has been analyzed starting form Onsager equations. Four boundary conditions have been considered: electric short, i.e, the chemical potential difference is zero; electric open, or electric current free; isothermal, i.e., no temperature difference; adiabatic, or heat flux free. Four kinds of thermoelectric equations have been derived with different boundary conditions. It was found that the influence of boundary cannot be ignored when figure-of-merit is near and larger than 1.0. This results could be useful in designing thermoelectric device with high performance thermoelectric materials.

On Effects of Temperature Boundary Conditions on Heat Transfer in Turbulent Low-Prandtl-Number Flows

2020 ◽  
Author(s):  
Ivan Otic
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Flux Boundary Condition ◽  
Large Eddy ◽  
Heat Flux Boundary Condition ◽  
Effects Of Temperature

Abstract One important issue in understanding and modeling of turbulent heat transfer is the behavior of fluctuating temperature close to the wall. Common engineering computational approach assumes constant heat flux boundary condition on heated walls. In the present paper constant heat flux boundary condition was assumed and effects of temperature fluctuations are investigated using large eddy simulations (LES) approach. A series of large eddy simulations for two geometries is performed: First, forced convection in channels and second, forced convection over a backward facing step. LES simulation data is statistically analyzed and compared with results of direct numerical simulations (DNS) from the literature which apply three cases of heat flux boundary conditions: 1. ideal heat flux boundary condition, 2. non-ideal heat flux boundary condition, 3. conjugate heat transfer boundary condition. For low Prandtl number flows LES results show that, despite very good agreement for velocities and mean temperature, predictions of temperature fluctuations may have strong deficiencies if simplified boundary conditions are applied.

Nodal Topology in Compact Thermal Models

2007 ◽  
Author(s):  
D. H. Greisen ◽  
V. P. Manno
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Area Ratio ◽  
System Level ◽  
Thermal Models ◽  
Single Boundary

Compact Thermal Models (CTMs) utilize a few connected thermal nodes to represent the thermal characteristics of electronic packages. These models are preferable to highly discretized models in preliminary design and system level analysis because of their computational efficiency. Surface heat flux non-uniformities often make it necessary to subdivide the package surfaces into multiple CTM nodes. This division is often quantified as the surface area ratio. This work assesses CTM performance sensitivity to area ratio changes and variation in heat transfer coefficient boundary conditions. CTMs for benchmark TQFP and BGA packages are developed using an admittance matrix approach. While optimum area ratios are identified, a direct correlation between these optimal values and the heat flux distributions computed from fully-discretized models was not obtained. CTM performance was found to be sensitive to changes in the heat transfer coefficient used to generate the CTM parameter values. A critical generating heat transfer coefficient was determined such that the resulting CTM, when optimized for a single boundary condition, was relatively accurate over the whole set of boundary conditions considered. This single boundary condition also provided an upper bound for error. This finding could be significant in future CTM development procedures.

Site-Specific and On-Demand High Heat-Flux Cooling Using Superlattice Based Thin-Film Thermoelectrics

2009 ◽  
Author(s):  
Ihtesham Chowdhury ◽  
Ravi Prasher ◽  
Kelly Lofgreen ◽  
Sridhar Narasimhan ◽  
Ravi Mahajan ◽  
...  
Keyword(s):  
Thin Film ◽  
Heat Flux ◽  
Thermal Management ◽  
High Performance ◽  
High Heat ◽  
Thermoelectric Device ◽  
High Heat Flux ◽  
General Will ◽  
Site Specific ◽  
Fully Integrated

We have recently reported the first ever demonstration of active cooling of hot-spots of >1 kW/cm2 in a packaged electronic chip using thin-film superlattice thermoelectric cooler (TEC) cooling technology [1]. In this paper, we provide a detailed account of both experimental and theoretical aspects of this technological demonstration and progress. We have achieved cooling of as much as 15°C at a location on the chip where the heat-flux is as high as ∼1300 W/cm2, with the help of a thin-film TEC integrated into the package. To our knowledge, this is the first demonstration of high heat-flux cooling with a thin-film thermoelectric device made from superlattices when it is fully integrated into a usable electronic package. Our results, which validate the concept of site-specific micro-scale cooling of electronics in general, will have significant potential for thermal management of future generations of microprocessors. Similar active thermal management could also be relevant for high-performance solid-state lasers and power electronic chips.

scholarly journals Investigation of the Wall Scalar Fluctuations Effect on Passive Scalar Turbulent Fields at Several Prandtl Numbers by Means of Direct Numerical Simulations

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Bruno Chaouat ◽  
Christophe Peyret
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Plane Channel ◽  
Passive Scalar ◽  
Wall Region ◽  
Turbulent Heat ◽  
The Mean ◽  
Prandtl Numbers

Abstract We investigate the effect of the wall-scalar fluctuations on passive scalar turbulent fields for a moderate Reynolds number Rτ = 395 and for several Prandtl numbers ranging from the very low value Pr = 0.01 to the high value Pr = 10 by means of direct numerical simulation (DNS) simulations. Several cases of plane channel flows are considered. Case I is a channel flow heated on both walls with a constant imposed heat flux qw. We consider for this case two different types of boundary conditions. For the first one, the isoscalar boundary condition θw = 0 is imposed at the wall implying that its fluctuation and therefore its rms scalar fluctuations θrms=⟨θ′θ′⟩ is zero at the wall whereas in the second type, θw is not prescribed to a fixed value so that it is fluctuating in time at the wall leading to nonzero rms fluctuations. In this latter case, as the heat flux is maintained constant in time at the wall, the fluctuating heat flux q′w reduces to zero at the wall. For illustration purpose, in addition to case I, we also consider case II, which is a plane channel heated only from one wall but cooled from the other one at the same rate taking into account of the freestream scalar boundary condition at the wall θ′w≠0 with q′w=0. The distributions of the mean scalar field, root-mean-square fluctuations, turbulent heat flux, correlation coefficient, turbulent Prandtl number, and Nusselt number are examined in detail. Moreover, some insights into the flow structure of the scalar fields are provided. As a result of interest, it is found that the mean scalar field ⟨θ⟩ is not affected by the scalar fluctuations at the wall. But owing to the different boundary conditions applied at the wall, significant differences in the evolution of the rms scalar fluctuations θrms are observed in the immediate vicinity of the wall. Surprisingly, the maximum rms intensity remains almost unchanged in the near wall region whatever the type of boundary condition is applied at the wall. In addition, the turbulent heat fluxes that play a major role in heat transfer are found to be independent of the wall scalar fluctuations. This study demonstrates that the impact of the wall scalar fluctuations is appreciable mainly in the near wall region. This outcome must be taken into account when simulating industrial flows with thermal boundary conditions involving different fluid/solid combinations.

Effects of thermal boundary conditions on rotating Rayleigh-Bénard convection with implications on geophysical and astrophysical systems

2021 ◽  
Author(s):  
Janet Peifer ◽  
Onno Bokhove ◽  
Steve Tobias
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Biot Number ◽  
Thermal Flux ◽  
Thermal Boundary Condition ◽  
Actual Condition ◽  
Fixed Temperature ◽  
Thermal Boundary Conditions ◽  
Core Dynamics

<p>Rayleigh-Bénard convection (RBC) is a fluid phenomenon that has been studied for over a century because of its utility in simplifying very complex physical systems. Many geophysical and astrophysical systems, including planetary core dynamics and components of weather prediction, are modeled by including rotational forcing in classic RBC. Our understanding of these systems is confined by experimental and numerical limits, as well as theoretical assumptions. </p><p>The role of thermal boundary condition choice on experimental studies of geophysical and astrophysical systems has been often been overlooked, which could account for some lack of agreement between experimental and numerical models as well as the actual flows. The typical thermal boundary conditions prescribed at the top and the bottom of a convection system are fixed temperature conditions, despite few real geophysical systems being bounded with a fixed temperature. A constant heat flux is generally more applicable for real large-scale geophysical systems. However, when this condition is applied in numerical systems, the lack of fixed temperature can cause a temperature drift. In this study, we seek to minimize temperature drifting by applying a fixed temperature condition on one boundary and a fixed thermal flux on the other.</p><p>Experimental boundary conditions are also often assumed to be a fixed temperature. However, the actual condition is determined by the ratio of the height and thermal conductivity of the boundary material to that of the contained fluid, known as the Biot number. The relationship between the Biot number and thermal boundary condition behavior is defined by the Robin, or 'thin-lid', boundary condition such that low Biot number boundaries are essentially fixed thermal flux and high Biot number boundaries are essentially fixed temperature. </p><p>This study seeks to strengthen the link between numerical and experimental models and geophysical flows by investigating the effects of thermal boundary conditions and their relationship to real-world processes. Both fixed temperature and fixed flux boundary conditions are considered. In addition, the Robin boundary condition is studied at a range of Biot numbers spanning from fixed temperature to fixed flux, allowing intermediate conditions to be investigated. Each system is studied at increasingly rapid rotation rates, corresponding to decreasing Ekman numbers as low as Ek=10<sup>-5</sup> Heat transport is analyzed using the Nusselt number, Nu, and the form of the solution is described by the number of convection rolls and time-dependency. Further investigations will analyze Nu and fluid movement within a system with heterogeneous heat flux condition on the  sidewall boundary conditions, which is useful in the study of planetary core dynamics. The results of this study have implications for improvements in modeling geophysical systems both experimentally and numerically. </p>

Boundary Conditions and Integrated Sensors in Microchannel Convective Heat Transfer

2006 ◽  
Author(s):  
Man Lee ◽  
Luthur Siu Lin Cheung ◽  
Yi-Kuen Lee ◽  
Yitshak Zohar
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Pressure Sensors ◽  
Uniform Heat Flux ◽  
Phase Flow ◽  
Convective Boiling ◽  
Flux Boundary Condition ◽  
Heat Flux Boundary Condition ◽  
Temperature And Pressure

A microchannel heat sink, integrated with pressure and temperature microsensors, is fabricated to study convective boiling under uniform heat flux boundary condition. Utilizing a wafer bond and etch back technology, the heat source, temperature and pressure sensors are separated from the fluid flow by a membrane only 1.5μm in thickness; thus, allowing good control of the thermal boundary conditions. Temperature and pressure distributions for various power levels and flow rates are measured while, simultaneously, the flow patterns are recorded. Single-phase flow results, compared with numerical simulations, confirm that the heat flux boundary condition is indeed nearly uniform. The sensor arrays, particularly for two-phase flow, provide the spatial and temporal dependence of both the temperature and pressures fields.

scholarly journals Realizing a 14% single-leg thermoelectric efficiency in GeTe alloys

2021 ◽  
Vol 7 (19) ◽  
pp. eabf2738
Author(s):  
Zhonglin Bu ◽  
Xinyue Zhang ◽  
Bing Shan ◽  
Jing Tang ◽  
Hongxia Liu ◽  
...  
Keyword(s):  
High Performance ◽  
Figure Of Merit ◽  
High Efficiency ◽  
Phonon Scattering ◽  
Waste Heat ◽  
Chemical Diffusion ◽  
Thermoelectric Device ◽  
Thermoelectric Efficiency ◽  
Good Service ◽  
Thermoelectric Figure

GeTe alloys have recently attracted wide attention as efficient thermoelectrics. In this work, a single-leg thermoelectric device with a conversion efficiency as high as 14% under a temperature gradient of 440 K was fabricated on the basis of GeTe-Cu2Te-PbSe alloys, which show a peak thermoelectric figure of merit (zT) > 2.5 and an average zT of 1.8 within working temperatures. The high performance of the material is electronically attributed to the carrier concentration optimization and thermally due to the strengthened phonon scattering, the effects of which all originate from the defects in the alloys. A design of Ag/SnTe/GeTe contact successfully enables both a prevention of chemical diffusion and an interfacial contact resistivity of 8 microhm·cm2 for the realization of highly efficient devices with a good service stability/durability. Not only the material’s high performance but also the device’s high efficiency demonstrated the extraordinariness of GeTe alloys for efficient thermoelectric waste-heat recovery.

Mathematical Model of the Cooling of a Plastic, Thermoformed Part

2010 ◽  
Author(s):  
Thomas M. Aidich ◽  
Tien-Chien Jen ◽  
Yi-Hsin Yen
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Boundary Condition ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Cooling Cycle ◽  
Transient Conduction

This paper presents research into the mechanism involved in the cooling of a plastic thermoformed part after it is formed onto a mold. The intent of this research is to develop a simple and practical mathematical model useful to small thermoforming companies without a large engineering staff that describes the transient heat conduction of the cooling process. The model should also be able to predict the temperature distribution within the thickness of the part during the cooling. This mathematical model, which began with simplified boundary conditions, was then compared to experimental cooling data and modified accordingly to properly fit that data and the actual boundary conditions of the cooling part. The research began by examining the cooling of a series of high molecular weight polyethylene thermoformed side panels for plastic, portable restrooms. These parts where chosen for this preliminary research because of their very simple, flat geometric shape that lends them to being modeled as simple plane walls in transient conduction. The shape of the parts also leads to near constant thickness over the vast majority of the part. Using the model of a plane wall in transient conduction, the governing partial differential equation was solved for two possible boundary conditions on the mold side of the part: constant imposed surface temperature and constant imposed surface heat flux. These two solutions were then compared to experimental data gathered on the temperature profile of the free surface of the part during a production environment. After the experimental data and simple mathematical models were compared the necessary changes to the assumed mold side boundary condition was made to adjust the mathematical model to the experimental data. The research found that the use of simple boundary conditions at the mold side of the part is incorrect. Neither the constant imposed surface temperature nor the imposed surface heat flux boundary conditions fit the data. Initial analysis of the experimental data showed that a time of 30 seconds into the cooling cycle an apparent change in that boundary condition occurs for the part and mold used to gather the data. Further analysis showed that the boundary condition begins as a constant surface heat flux and then changes to an imposed surface temperature that decays exponentially to the initial mold surface temperature. Using this boundary condition, a revised mathematical was developed that match the experimental data very well. The error of the new model compared to the experimental was less than 1.5% for all times during the cooling cycle.

scholarly journals A flexible micro-thermoelectric device from carbon nanotube-epitaxially grown (Bi,Sb)2Te3 nanocrystal

2021 ◽  
Author(s):  
Qun Jin ◽  
Yang Zhao ◽  
Xuehao Long ◽  
Song Jiang ◽  
Ziqiang Wang ◽  
...  
Keyword(s):  
Thermal Management ◽  
High Performance ◽  
Figure Of Merit ◽  
Open Circuit ◽  
Single Wall Carbon Nanotubes ◽  
Thermoelectric Device ◽  
Potential Applications ◽  
Flexible Thermoelectric ◽  
Growth Approach ◽  
Average Figure

Abstract Flexible thermoelectric (TE) materials have attracted increasing interest due to their potential applications in energy harvesting and high-spatial-resolution thermal management. However, a high-performance flexible micro-TE device (TED) compatible with the modern electronics fabrication process has not yet been developed. Here we report a general van der Waals epitaxial growth approach to fabricating a freestanding and flexible hybrid comprised of single-wall carbon nanotubes and highly ordered (Bi,Sb)2Te3 nanocrystals. High power factors ranging from ~1,680 to ~1,020 µW m−1 K−2 in the temperature range of 300-480 K, combined with a strongly depressed thermal conductivity yield an average figure of merit of ~0.81. A prototype flexible micro-TED module consisting of two p-n hybrids was then fabricated, which demonstrated an unprecedented open circuit voltage of ~22.7 mV and a power density of ~0.36 W cm−2 under a ~30 K temperature difference, and a net cooling temperature of ~22.4 K and a heat absorption density of ~92.5 W cm−2.

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

1970 ◽  
Vol 28 ◽  
pp. 360-361
Author(s):  
John W. Coleman
Keyword(s):  
Boundary Conditions ◽  
High Performance ◽  
Force Fields ◽  
Optical Design ◽  
Direct Conversion ◽  
Design Engineering ◽  
Design Data ◽  
Scalar Potentials ◽  
Geometric Elements ◽  
At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

Sign in / Sign up

Export Citation Format

Share Document