Non-Fourier Heat Conduction in IC Chip

1995 ◽  
Vol 117 (3) ◽  
pp. 174-177 ◽  
Author(s):  
Zeng-Yuan Guo ◽  
Yun-Sheng Xu
Keyword(s):  
Heat Conduction ◽  
Thermal Stress ◽  
Thermal Noise ◽  
Wave Model ◽  
Transient Heat Conduction ◽  
Peak Temperature ◽  
Spatial Difference ◽  
Thermal Reliability ◽  
Fourier Heat Conduction ◽  
Fourier Equation

Instead of the classic Fourier equation based on diffusion, a hyperbolic equation based on a wave model has been used to predict the rapid transient heat conduction in IC chips. The peak temperature, spatial difference, and time variation of temperature, which are critical to thermal reliability of the chip, are given and compared with that obtained from the Fourier equation. Analytical and numerical results show that non-Fourier effects, including the higher peak temperature and thermal stress, greater temperature difference between components, and stronger thermal noise, are significant to IC chip reliability.

Transient Thermal Stress Analysis of the Typical Structures in Turbine Rotor Based on Thermomechanical Analysis

2014 ◽  
Author(s):  
Ning Xu ◽  
Zhansheng Liu ◽  
He Peng
Keyword(s):  
Finite Element ◽  
Heat Conduction ◽  
Thermal Stress ◽  
Thermal Stresses ◽  
Transition Process ◽  
Transient Heat Conduction ◽  
Work Conditions ◽  
Turbine Rotor ◽  
Design Stage ◽  
Turbine Rotors

Thermal stress is one of the most important monitoring parameters in turbine rotors during the transition of work conditions. It has significant influence on the safety and life of turbine rotors. In order to obtain the thermal stress in turbine rotors during the transition process conveniently, the transient heat conduction process in typical structures of turbine rotors is analyzed based on heat conduction equation and finite element simulation. According to thermomechanical principle, thermal stress distributions in the typical structures of turbine rotor are investigated. The solutions of thermal stress in a solid cylinder are derived. A corner formed by shaft and disc is modeled and analyzed by finite element method, and the influences of structure parameters on thermal stresses are studied. The results on thermal stresses in cylinder and corner structures could provide a continent method to estimate thermal stress of turbine rotor on early design stage.

Thermal Stress Associated With Non-Fourier Heat Conduction in Femtosecond Laser Heating of Multilayer Metallic Films

2018 ◽  
Author(s):  
Swarup Bag ◽  
M. Ruhul Amin
Keyword(s):  
Thin Film ◽  
Heat Conduction ◽  
Thermal Stress ◽  
Temperature Distribution ◽  
Pulse Laser ◽  
Laser Heating ◽  
Laser Source ◽  
Phase Lag ◽  
Dual Phase ◽  
Fourier Heat Conduction

In the present work, the deformation behavior in metallic film subjected to ultra-short laser heating is investigated. Static thermo-elastic behavior is predicted for 100 nm thin film of either single layer or multiple layers. The temperature distribution is estimated from dual-phase lag non-Fourier heat conduction model. The maximum temperature after single pulse is achieved 730 K. The temperature profile for this pulse laser is used to compute elastic stress and distortion field following the minimization of potential energy of the system. In the present work, the simulation has been proposed by developing 3D finite element based coupled thermo-elastic model using dual phase lag effect. The experimental basis of transient temperature distribution in ultra-short pulse laser is extremely difficult or nearly impossible, the model results have been validated with literature reported thermal results. Since the temperature distribution due to pulse laser source varies with time, the stress analysis is performed in incremental mode. Hence, a sequentially coupled thermo-mechanical model is developed that is synchronized between thermal and mechanical analysis in each time steps of transient problem. The maximum equivalent stress is achieved 0.3 GPa. Numerical results show that the predicted thermal stress may exceeds the tensile strength of the material and may lead to crack or damage the thin film.

Transient Heat Conduction in Functionally Graded Hollow Cylinders and Spheres

2012 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
Z. T. Chen
Keyword(s):  
Heat Conduction ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase ◽  
Conduction Theory ◽  
Hollow Cylinders ◽  
Fourier Heat Conduction ◽  
Cylinders And Spheres

In the present work, transient heat conduction in functionally graded (FG) hollow cylinders and spheres is investigated based on the non-Fourier heat conduction theories. Since the heat transmission has been observed to propagate at a finite speed for applications with very low temperature, short-pulse thermal-heating, and micro temporal and spatial scales, dual phase lag (DPL) and hyperbolic heat conduction theories are considered in current study instead of the conventional Fourier heat conduction theory. Except the phase lags which are assumed to be constant, all the other material properties of the hollow cylinders and spheres are taken to change continuously along the radial direction according to a power-law formulation with different non-homogeneity indices. The heat conduction equations are written based on the dual phase lag theory which includes the hyperbolic heat conduction theory as well. These equations are applied for axisymmetric hollow cylinders of infinite lengths and spherically symmetric hollow spheres. Using the Laplace transform and Bessel functions, the analytical solutions for temperature and heat flux are obtained in the Laplace domain. The solutions are then converted into the time domain by employing the fast Laplace inversion technique. The exact expression is obtained for the speed of thermal wave in FG cylinders and spheres based on the DPL and hyperbolic heat conduction theories. Finally, the current results are verified with those reported in the literature based on the hyperbolic heat conduction theory.

scholarly journals Modelling and Prediction of Cutting Temperature in the Machining of H13 Hard Steel of Transient Heat Conduction

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3176
Author(s):  
Jingjie Zhang ◽  
Xiangfei Meng ◽  
Jin Du ◽  
Guangchun Xiao ◽  
Zhaoqiang Chen ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Analytical Model ◽  
Cutting Tools ◽  
Cutting Temperature ◽  
Transient State ◽  
Transient Heat Conduction ◽  
Conduction Model ◽  
Cutting Heat ◽  
Fourier Heat Conduction ◽  
Pass Through

Cutting heat conduction undergoes three stages that include intensity transient-state, transient-state, and steady-states. Especially during machining with coated cutting tools, in the conduction process, cutting heat needs to pass through a few micron thick coatings and then flow into the tool body. This heat conduction presents typical non-Fourier heat conduction characteristics. This paper focuses on the cutting temperature in transient heat conduction with a coated tool. A new analytical model to characterize the thermal shock based on the non-Fourier heat conduction was proposed. The distribution of cutting temperature in mono-layer coated tools during the machining was then illustrated. The cutting temperature distribution predicted by the Fourier heat conduction model was employed to compare with that by non-Fourier heat conduction in order to reveal the non-Fourier heat conduction effect in transient heat conduction. The results show that the transient heat conduction analytical model is more suitable for the intensity transient-state and transient-state in the process of cutting heat conduction.

Thermo-Mechanical and Hygro-Mechanical Stress Analyses of an Organic Multilayer Sheet

2007 ◽  
Author(s):  
Toru Ikeda ◽  
Tomonori Mizutani ◽  
Noriyuki Miyazaki
Keyword(s):  
Liquid Crystal ◽  
Heat Conduction ◽  
Thermal Stress ◽  
Liquid Crystal Display ◽  
Mechanical Strain ◽  
Thermal Strain ◽  
Transient Heat Conduction ◽  
Fick’S Law ◽  
Fick's Law ◽  
Liquid Crystal Display Panel

A polarizing plate, which is an important part of a liquid crystal display panel, is made by sandwiching an organic polarizer between protecting films. An organic polarizer is both a hygroscopic and orthotropic material. The hygroscopic swelling and drying shrinkage of the organic polarizer can cause the polarizing plate to crack and the liquid crystal display panel to warp. The diffusion coefficient and Henry’s law coefficient were measured using a thermo-gravimetric analyzer (TGA) under controlled humidity, while the coefficient of moisture expansion (CME) was measured using a thermo-mechanical analyzer (TMA), also under controlled humidity. The thermo-mechanical and hygro-mechanical deformation of a polarizing plate was analyzed using the finite element method (FEM). This analysis was performed as follows. The distribution of the moisture concentration was analyzed according to Fick’s law. The equation of Fick’s law is similar to that of the transient heat conduction, and the FEM for the transient heat conduction was utilized for the transient diffusion analysis. The hygro-mechanical analysis was then carried out in a way similar to the thermal stress analysis. Thermal stress was analyzed separately using the FEM. Finally, the obtained hygro-mechanical strain and stress were added to the thermal strain and stress, respectively. The measured CME of a polarizing plate corresponds to the analyzed CME using the CMEs of a polarizer and protecting films. The warpage of a liquid crystal display panel sometimes causes light leakage along the frame of the display panel due to contact of the display panel with the bezel of the frame. The warpage was analyzed according to the thermo-mechanical strain and the hygro-mechanical strain. The contact between the display panel and the bezel, which causes the light leakage, was estimated.

scholarly journals Thermal shock resistance of solids associated with hyperbolic heat conduction theory

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120754 ◽  
Author(s):  
B. L. Wang ◽  
J. E. Li
Keyword(s):  
Heat Conduction ◽  
Thermal Stress ◽  
Stress Intensity ◽  
Thermal Shock ◽  
Thermal Shock Resistance ◽  
Closed Form Solution ◽  
Hyperbolic Heat Conduction ◽  
Conduction Model ◽  
Fourier Heat Conduction ◽  
Shock Resistance

The thermal shock resistance of solids is analysed for a plate subjected to a sudden temperature change under the framework of hyperbolic, non-Fourier heat conduction. The closed form solution for the temperature field and the associated thermal stress are obtained for the plate without cracking. The transient thermal stress intensity factors are obtained through a weight function method. The maximum thermal shock temperature that the plate can sustain without catastrophic failure is obtained according to the two distinct criteria: (i) maximum local tensile stress criterion and (ii) maximum stress intensity factor criterion. The difference between the non-Fourier solutions and the classical Fourier solution is discussed. The traditional Fourier heat conduction considerably overestimates the thermal shock resistance of the solid. This confirms the fact that introduction of the non-Fourier heat conduction model is essential in the evaluation of thermal shock resistance of solids.

Sign in / Sign up

Export Citation Format

Share Document