Maximum Temperature Rise in the Reacted Zone of Electrochemical Devices for Space Applications

A model to predict the temperature rise in the reacted zone of discharging electrochemical devices has been developed. The model assumes that electrode kinetics are fast and concentration gradients are negligible. In the reacted zone, a thermal boundary layer grows, and its thickness is proportional to the reacted zone thickness. In the model, the temperature rise is predicted using the one-dimensional heat diffusion equation for a porous medium. The effective heat capacity per unit volume and effective thermal conductivity are defined as a function of electrode porosity. The instantaneous power per unit area dissipated in the reacted zone is used as a source term in the heat diffusion equation. With fixed parameters such as discharge current density, charge capacity per unit volume, electrode electrical conductivity, electrode porosity, and thermophysical properties of the pore-space fluid and electrode, the transient temperature distribution in the reacted zone is derived in closed-form. Subsequently, the maximum electrode temperature is readily obtained, and the maximum electrode temperature at complete discharge is derived. A new dimensionless parameter, the electro-thermal number, emerges as one of the most important parameters controlling the discharge time and maximum temperature rise.

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Sub-Continuum Simulations of Heat Conduction in Silicon-on-Insulator Transistors

10.1115/imece1999-1061 ◽

1999 ◽

Author(s):

Per G. Sverdrup ◽

Y. Sungtaek Ju ◽

Kenneth E. Goodson

Keyword(s):

Diffusion Equation ◽

Free Path ◽

Temperature Rise ◽

Mean Free Path ◽

Channel Length ◽

Silicon On Insulator ◽

Heat Diffusion ◽

Boltzmann Transport ◽

Heat Diffusion Equation ◽

Silicon Devices

Abstract The temperature rise in compact silicon devices is predicted at present by solving the heat diffusion equation based on Fourier’s law. The validity of this approach needs to be carefully examined for semiconductor devices in which the region of strongest electronphonon coupling is narrower than the phonon mean free path, Λ, and for devices in which Λ is comparable to or exceeds the dimensions of the device. Previous research estimated the effective phonon mean free path in silicon near room temperature to be near 300 nm, which is already comparable with the minimum feature size of current generation transistors. This work numerically integrates the phonon Boltzmann transport equation (BTE) within a two-dimensional Silicon-on-Insulator (SOI) transistor. The BTE is coupled with the classical heat diffusion equation, which is solved in the silicon dioxide layer beneath a transistor with a channel length of 400 nm. The sub-continuum simulations yield a peak temperature rise that is 159 percent larger than predictions using only the classical heat diffusion equation. This work will facilitate the development of simpler calculation strategies, which are appropriate for commercial device simulators.

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Sub-Continuum Simulations of Heat Conduction in Silicon-on-Insulator Transistors

Journal of Heat Transfer ◽

10.1115/1.1337651 ◽

2000 ◽

Vol 123 (1) ◽

pp. 130-137 ◽

Cited By ~ 104

Author(s):

Per G. Sverdrup ◽

Y. Sungtaek Ju ◽

Kenneth E. Goodson

Keyword(s):

Heat Conduction ◽

Diffusion Equation ◽

Free Path ◽

Temperature Rise ◽

Mean Free Path ◽

Channel Length ◽

Silicon On Insulator ◽

Heat Diffusion ◽

Boltzmann Transport ◽

Heat Diffusion Equation

The temperature rise in sub-micrometer silicon devices is predicted at present by solving the heat diffusion equation based on the Fourier law. The accuracy of this approach needs to be carefully examined for semiconductor devices in which the channel length is comparable with or smaller than the phonon mean free path. The phonon mean free path in silicon at room temperature is near 300 nm and exceeds the channel length of contemporary transistors. This work numerically integrates the two-dimensional phonon Boltzmann transport equation (BTE) within the silicon region of a silicon-on-insulator (SOI) transistor. The BTE is solved together with the classical heat diffusion equation in the silicon dioxide layer beneath the transistor. The predicted peak temperature rise is nearly 160 percent larger than a prediction using the heat diffusion equation for the entire domain. The disparity results both from phonon-boundary scattering and from the small dimensions of the region of strongest electron-phonon energy transfer. This work clearly shows the importance of sub-continuum heat conduction in modern transistors and will facilitate the development of simpler calculation strategies, which are appropriate for commercial device simulators.

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Modeling temperature rise in multi-track reciprocating frictional sliding

Proceedings of the Institution of Mechanical Engineers Part J Journal of Engineering Tribology ◽

10.1177/1350650120988230 ◽

2021 ◽

pp. 135065012098823

Author(s):

Thierry A Blanchet

Keyword(s):

Temperature Rise ◽

Peclet Number ◽

Maximum Temperature ◽

Uniform Heat Flux ◽

Heat Accumulation ◽

Stroke Length ◽

Péclet Number ◽

Maximum Temperature Rise ◽

Rectangular Patch ◽

Accumulation Effect

As in various manufacturing processes, in sliding tests with scanning motions to extend the sliding distance over fresh countersurface, temperature rise during any pass is bolstered by heating during prior passes over neighboring tracks, providing a “heat accumulation effect” with persisting temperature rises contributing to an overall temperature rise of the current pass. Conduction modeling is developed for surface temperature rise as a function of numerous inputs: power and size of heat source; speed and stroke length, and track increment of scanning motion; and countersurface thermal properties. Analysis focused on mid-stroke location for passes of a square uniform heat flux sufficiently far into the rectangular patch being scanned from the first pass at its edge that steady heat accumulation effect response is adopted, focusing on maximum temperature rise experienced across the pass' track. The model is non-dimensionalized to broaden the applicability of the output of its runs. Focusing on practical “high” scanning speeds, represented non-dimensionally by Peclet number (in excess of 40), applicability is further broadened by multiplying non-dimensional maximum temperature rise by the square root of Peclet number as model output. Additionally, investigating model runs at various non-dimensional speed (Peclet number) and reciprocation period values, it appears these do not act as independent inputs, but instead with their product (non-dimensional stroke length) as a single independent input. Modified maximum temperature rise output appears to be a function of only two inputs, increasing with decreasing non-dimensional values of stroke length and scanning increment, with outputs of models runs summarized compactly in a simple chart.

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Fast Fluid Thermodynamics Simulation by Solving Heat Diffusion Equation

International Journal of Computer Graphics & Animation ◽

10.5121/ijcga.2021.11401 ◽

2021 ◽

Vol 11 (04) ◽

pp. 1-11

Author(s):

Wanwan Li

Keyword(s):

Diffusion Equation ◽

Real Time ◽

Stokes Equations ◽

Fluid Simulation ◽

Heat Diffusion ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Heat Diffusion Equation ◽

Acceleration Techniques ◽

Speed Up

In mechanical engineering educations, simulating fluid thermodynamics is rather helpful for students to understand the fluid’s natural behaviors. However, rendering both high-quality and realtime simulations for fluid dynamics are rather challenging tasks due to their intensive computations. So, in order to speed up the simulations, we have taken advantage of GPU acceleration techniques to simulate interactive fluid thermodynamics in real-time. In this paper, we present an elegant, basic, but practical OpenGL/SL framework for fluid simulation with a heat map rendering. By solving Navier-Stokes equations coupled with the heat diffusion equation, we validate our framework through some real-case studies of the smoke-like fluid rendering such as their interactions with moving obstacles and their heat diffusion effects. As shown in Fig. 1, a group of experimental results demonstrates that our GPU-accelerated solver of Navier-Stokes equations with heat transfer could give the observers impressive real-time and realistic rendering results.

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Braking performance of a novel frictional-magnetic compound disc brake for automobiles

Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering ◽

10.1177/0954407018791056 ◽

2018 ◽

Vol 233 (10) ◽

pp. 2443-2454 ◽

Cited By ~ 1

Author(s):

Yan Yin ◽

Jiusheng Bao ◽

Jinge Liu ◽

Chaoxun Guo ◽

Tonggang Liu ◽

...

Keyword(s):

Magnetic Field ◽

Temperature Rise ◽

Friction Material ◽

Maximum Temperature ◽

Interface Temperature ◽

Disc Brake ◽

Braking Performance ◽

Maximum Temperature Rise ◽

Disc Brakes ◽

Braking Torque

Disc brakes have been applied in various automobiles widely and their braking performance has vitally important effects on the safe operation of automobiles. Although numerous researches have been conducted to find out the influential law and mechanism of working condition parameters like braking pressure, initial braking speed, and interface temperature on braking performance of disc brakes, the influence of magnetic field is seldom taken into consideration. In this paper, based on the novel automotive frictional-magnetic compound disc brake, the influential law of magnetic field on braking performance was investigated deeply. First, braking simulation tests of disc brakes were carried out, and then dynamic variation laws and mechanisms of braking torque and interface temperature were discussed. Furthermore, some parameters including average braking torque, trend coefficient and fluctuation coefficient of braking torque, average temperature, maximum temperature rise, and the time corresponding to the maximum temperature rise were extracted to characterize the braking performance of disc brakes. Finally, the influential law and mechanism of excitation voltage on braking performance were analyzed through braking simulation tests and surface topography analysis of friction material. It is concluded that the performance of frictional-magnetic compound disc brake is prior to common brake. Magnetic field is greatly beneficial for improving the braking performance of frictional-magnetic compound disc brake.

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Heat-balance integral to fractional (half-time) heat diffusion sub-model

Thermal Science ◽

10.2298/tsci1002291h ◽

2010 ◽

Vol 14 (2) ◽

pp. 291-316 ◽

Cited By ~ 29

Author(s):

Jordan Hristov

Keyword(s):

Diffusion Equation ◽

Heat Balance ◽

Integral Method ◽

Time Derivative ◽

Heat Diffusion ◽

Half Time ◽

Heat Diffusion Equation ◽

Parabolic Profile ◽

Heat Balance Integral Method ◽

The Heat Balance

The fractional (half-time) sub-model of the heat diffusion equation, known as Dirac-like evolution diffusion equation has been solved by the heat-balance integral method and a parabolic profile with unspecified exponent. The fractional heat-balance integral method has been tested with two classic examples: fixed temperature and fixed flux at the boundary. The heat-balance technique allows easily the convolution integral of the fractional half-time derivative to be solved as a convolution of the time-independent approximating function. The fractional sub-model provides an artificial boundary condition at the boundary that closes the set of the equations required to express all parameters of the approximating profile as function of the thermal layer depth. This allows the exponent of the parabolic profile to be defined by a straightforward manner. The elegant solution performed by the fractional heat-balance integral method has been analyzed and the main efforts have been oriented towards the evaluation of fractional (half-time) derivatives by use of approximate profile across the penetration layer.

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