Heat diffusion in geometry

2016 ◽  
pp. 1-14
Author(s):  
Gerhard Huisken
Keyword(s):  
Heat Diffusion

Heat Diffusion in an Optical Logic Gate Array on Silicon-on-Sapphire

1997 ◽  
Vol 7 (3) ◽  
pp. 739-748
Author(s):  
H. Gualous ◽  
A. Koster ◽  
D. Pascal ◽  
S. Laval
Keyword(s):  
Logic Gate ◽  
Heat Diffusion ◽  
Optical Logic ◽  
Optical Logic Gate ◽  
Gate Array

Fault Localization and Functional Testing of ICs by Lock-in Thermography

2002 ◽  
Author(s):  
O. Breitenstein ◽  
J.P. Rakotoniaina ◽  
F. Altmann ◽  
J. Schulz ◽  
G. Linse
Keyword(s):  
Spatial Resolution ◽  
Electronic Device ◽  
Imaging Techniques ◽  
Heat Diffusion ◽  
Acquisition Time ◽  
Temperature Modulation ◽  
Heat Sources ◽  
Ir Camera ◽  
Free Running ◽  
Lock In

Abstract In this paper new thermographic techniques with significant improved temperature and/or spatial resolution are presented and compared with existing techniques. In infrared (IR) lock-in thermography heat sources in an electronic device are periodically activated electrically, and the surface is imaged by a free-running IR camera. By computer processing and averaging the images over a certain acquisition time, a surface temperature modulation below 100 µK can be resolved. Moreover, the effective spatial resolution is considerably improved compared to stead-state thermal imaging techniques, since the lateral heat diffusion is suppressed in this a.c. technique. However, a serious limitation is that the spatial resolution is limited to about 5 microns due to the IR wavelength range of 3 -5 µm used by the IR camera. Nevertheless, we demonstrate that lock-in thermography reliably allows the detection of defects in ICs if their power exceeds some 10 µW. The imaging can be performed also through the silicon substrate from the backside of the chip. Also the well-known fluorescent microthermal imaging (FMI) technique can be be used in lock-in mode, leading to a temperature resolution in the mK range, but a spatial resolution below 1 micron.

scholarly journals Inductive Thermography as Non-Destructive Testing for Railway Rails

2021 ◽  
Vol 11 (3) ◽  
pp. 1003
Author(s):  
Christoph Tuschl ◽  
Beate Oswald-Tranta ◽  
Sven Eck
Keyword(s):  
Eddy Current ◽  
Electrical Discharge Machining ◽  
Rolling Contact ◽  
Heat Diffusion ◽  
Non Destructive Testing ◽  
Destructive Testing ◽  
Ir Camera ◽  
Advantages And Disadvantages ◽  
Average Crack ◽  
Non Destructive

Inductive thermography is a non-destructive testing method, whereby the specimen is slightly heated with a short heating pulse (0.1–1 s) and the temperature change on the surface is recorded with an infrared (IR) camera. Eddy current is induced by means of high frequency (HF) magnetic field in the surface ‘skin’ of the specimen. Since surface cracks disturb the eddy current distribution and the heat diffusion, they become visible in the IR images. Head checks and squats are specific types of damage in railway rails related to rolling contact fatigue (RCF). Inductive thermography can be excellently used to detect head checks and squats on rails, and the method is also applicable for characterizing individual cracks as well as crack networks. Several rail pieces with head checks, with artificial electrical discharge-machining (EDM)-cuts and with a squat defect were inspected using inductive thermography. Aiming towards rail inspection of the track, 1 m long rail pieces were inspected in two different ways: first via a ‘stop-and-go’ technique, through which their subsequent images are merged together into a panorama image, and secondly via scanning during a continuous movement of the rail. The advantages and disadvantages of both methods are compared and analyzed. Special image processing tools were developed to automatically fully characterize the rail defects (average crack angle, distance between cracks and average crack length) in the recorded IR images. Additionally, finite element simulations were used to investigate the effect of the measurement setup and of the crack parameters, in order to optimize the experiments.

scholarly journals Thermal weakening friction during seismic slip: an efficient numerical scheme for heat diffusion

2020 ◽  
Author(s):  
Stefan Nielsen ◽  
Elena Spagnuolo ◽  
Marie Violay ◽  
Giulio Di Toro
Keyword(s):  
Numerical Scheme ◽  
Heat Diffusion ◽  
Seismic Slip

scholarly journals Short-time heat diffusion in compact domains with discontinuous transmission boundary conditions

2015 ◽  
Vol 26 (01) ◽  
pp. 59-110 ◽  
Author(s):  
Claude Bardos ◽  
Denis Grebenkov ◽  
Anna Rozanova-Pierrat
Keyword(s):  
Asymptotic Expansion ◽  
Boundary Conditions ◽  
Order Term ◽  
Heat Content ◽  
Resistance Coefficient ◽  
Small Time ◽  
Heat Diffusion ◽  
Heat Problem ◽  
Short Time ◽  
Mathematical Justification

We consider a heat problem with discontinuous diffusion coefficients and discontinuous transmission boundary conditions with a resistance coefficient. For all bounded (ϵ, δ)-domains Ω ⊂ ℝn with a d-set boundary (for instance, a self-similar fractal), we find the first term of the small-time asymptotic expansion of the heat content in the complement of Ω, and also the second-order term in the case of a regular boundary. The asymptotic expansion is different for the cases of finite and infinite resistance of the boundary. The derived formulas relate the heat content to the volume of the interior Minkowski sausage and present a mathematical justification to the de Gennes' approach. The accuracy of the analytical results is illustrated by solving the heat problem on prefractal domains by a finite elements method.

Mapping Thickness Dependent Thermal Conductivity of GaN

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Elbara Ziade ◽  
Jia Yang ◽  
Gordie Brummer ◽  
Denis Nothern ◽  
Theodore Moustaks ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Pump Beam ◽  
Continuous Wave ◽  
High Electron Mobility Transistors ◽  
Heat Diffusion ◽  
Phase Lag ◽  
High Electron ◽  
Heat Diffusion Equation ◽  
Phase Images ◽  
Gan Film

Frequency domain thermoreflectance (FDTR) is used to create quantitative maps of thermal conductivity and thickness for a thinning gallium nitride (GaN) film on silicon carbide (SiC). GaN was grown by molecular beam epitaxy on a 4H-SiC substrate with a gradient in the film thickness found near the edge of the chip. The sample was then coated with a 5 nm nickel adhesion layer and a 85 nm gold transducer layer for the FDTR measurement. A piezo stage raster scans the sample to create phase images at different frequencies. For each pixel, a periodically modulated continuous-wave laser (the red pump beam) is focused to a Gaussian spot, less than 2 um in diameter, to locally heat the sample, while a second beam (the green probe beam) monitors the surface temperature through a proportional change in the reflectivity of gold. The pump beam is modulated simultaneously at six frequencies and the thermal conductivity and thickness of the GaN film are extracted by minimizing the error between the measured probe phase lag at each frequency and an analytical solution to the heat diffusion equation in a multilayer stack of materials. A scanning electron microscope image verifies the thinning GaN. We mark the imaged area with a red box. A schematic of the GaN sample in our measurement system is shown in the top right corner, along with the two fitting properties highlighted with a red box. We show the six phase images and the two obtained property maps: thickness and thermal conductivity of the GaN. Our results indicate a thickness dependent thermal conductivity of GaN, which has implications of thermal management in GaN-based high electron mobility transistors.

Sign in / Sign up

Export Citation Format

Share Document