Analytical solution for laser short-pulse heating of two-dimensional solids: volumetric and surface heat source considerations

2013 ◽  
Vol 91 (7) ◽  
pp. 522-529
Author(s):  
B.S. Yilbas ◽  
A.Y. Al-Dweik
Keyword(s):  
Analytical Solution ◽  
Heat Source ◽  
Energy Transport ◽  
Pulse Heating ◽  
Short Pulse ◽  
Thermal Response ◽  
Solid Substrate ◽  
Surface Heat ◽  
Heat Sources ◽  
Power Intensity

An analytical solution for lattice temperature distribution in a metallic solid subjected to laser short-pulse heating is presented. The method of similarity solution is adopted for the solution of the diffusive–ballistic energy equation. Volumetric and surface heat sources are each incorporated separately in the analysis. The material thermal response due to both heat sources during the short heating period is analyzed. It is found that a volumetric heat source resulted in smaller temperature increase in the irradiated material than a surface heat source, despite the same laser power intensity being used in both cases. This is attributed to energy transport mechanisms taking place in the solid substrate due to volumetric and surface heat sources.

Analytical solution to laser short-pulse heating of microsized metal wire: volumetric and surface heat source considerations

2012 ◽  
Vol 90 (9) ◽  
pp. 911-918 ◽  
Author(s):  
B.S. Yilbas ◽  
A.Y. Al-Dweik
Keyword(s):  
Analytical Solution ◽  
Heat Source ◽  
Pulse Heating ◽  
Short Pulse ◽  
Thermal Contact ◽  
Lower Surface ◽  
Surface Heat ◽  
Metal Wire ◽  
Fourier Cosine ◽  
Volumetric Heat Source

Analytical solution for laser short-pulse heating of a micro-sized metal wire is presented. In the analysis, volumetric and surface heat sources are incorporated for the same pulse intensity. The volumetric heat source resembles absorption by irradiated field according to Lambert’s Beer law while a surface heat source represents short pulse heating through high intensity thermal contact at the surface. The method of Lie point symmetries is combined with a Fourier cosine transformation to solve the temperature equation with appropriate boundary conditions. It is found that temperature profiles differ significantly for volumetric heat source and surface heat source considerations; in which case, volumetric heat source consideration results in considerably lower surface temperatures than that of the surface heat source consideration.

Laser short-pulse heating with time-varying intensity and thermal stress development in the lattice subsystem

2005 ◽  
Vol 219 (1) ◽  
pp. 73-81 ◽  
Author(s):  
B S Yilbas ◽  
A F M Arif
Keyword(s):  
Thermal Stress ◽  
Lattice Site ◽  
Energy Transport ◽  
Pulse Heating ◽  
Short Pulse ◽  
High Stress ◽  
Surface Region ◽  
Substrate Material ◽  
Temperature Gradients ◽  
Stress Levels

Laser short-pulse heating of solid surfaces results in non-equilibrium energy transport in the region irradiated by the laser beam. Owing to the large temperature gradients in the lattice subsystem, high stress levels develop in the surface region of the substrate material. In the present study, temperature and stress fields in the substrate material are presented for the case of the laser short-pulse heating of gold. Electron kinetic theory and a two-equation heating model are introduced to account for non-equilibrium energy transport during the laser heating pulse. Laser pulses exponentially decaying with time are accommodated in the simulations. It is found that lattice site temperature gradients attain high values inspite of the low magnitude of the lattice site temperature. This, in turn, results in high stress levels in the surface region of the substrate material. Thermal stress is compressive owing to high thermal strain development and low displacement of the surface.

Causes of the 1985-2014 Surface Warming over the Sanjiangyuan Region of the Tibetan Plateau from the Perspective of Energy Transport

2020 ◽  
Author(s):  
Yinglin Tian ◽  
Deyu Zhong
Keyword(s):  
Heat Flux ◽  
Tibetan Plateau ◽  
Heat Source ◽  
Energy Transport ◽  
Longwave Radiation ◽  
Warming Trend ◽  
The Tibetan Plateau ◽  
Heat Sources ◽  
The South ◽  
Downward Longwave Radiation

<p>The Tibetan Plateau (TP), known as the “World Roof”, has significant influences on hydrological and atmospheric circulation at both regional and global scale. As the Sanjiangyuan Region (SJY) supplies water resources to the adjacent river basin and the TP could exert strong thermal forcing on the atmosphere over Asian monsoon region, adequate understand of the climate change over this region and its underlying mechanisms is of great importance. Based on gridded data provided by China Meteorological Administration (CMA), a continuous warming trend higher than that over elsewhere in China has been observed over the TP during 1985-2014, especially in the cold season (0.69 K/decade) and over the SJY (1.0 K/decade). On the basis of ERA interim reanalysis datasets, this paper analyzed the factors facilitating this warming trend in the SJY from the perspective of energy transport. At first, the local processes involved were investigated by calculating partial temperature changes using the surface energy budget equation. Then the horizontal convection of heat was quantified by summing the heat flux across the boundaries of the SJY. Finally, a Lagrangian heat source diagnostic method was developed to identify the major heat source. As the results indicating, among all the local heat sources, the enhanced downward longwave radiation reflected to surface air and the increasing upward longwave radiation emitted by warmer land surface were responsible for the pronounced surface air warming. However, the changes in surface sensible and latent heat fluxes had a reduced warming effect on the surface air. As for the non-local horizontal heat sources, rising horizontal heat flux from the south, west and east boundaries into the SJY contributed to the higher surface temperature of the SJY. In winter season, the heat flows stemmed from the South Himalayan vein into the SJY played a dominant role. Moreover, the higher the temperature over the SJY was, the more inclined this heat source was to Nepal.</p>

scholarly journals Analytical solution of the bioheat equation for thermal response induced by any electrode array in anisotropic tissues with arbitrary shapes containing multiple-tumor nodules

2019 ◽  
Vol 65 (3) ◽  
pp. 284
Author(s):  
E. J. Roca Oria ◽  
L. E. Bergues Cabrales ◽  
And J. Bory Reyes
Keyword(s):  
Analytical Solution ◽  
Initial Temperature ◽  
Electrode Array ◽  
Thermal Response ◽  
Electrochemical Treatment ◽  
Bioheat Transfer ◽  
Heat Sources ◽  
Bioheat Equation ◽  
Multiple Tumor ◽  
Temperature Distributions

The Pennes bioheat transfer equation is the most used model to calculate the temperature induced in a tumor when physical therapies like electrochemical treatment, electrochemotherapy and/or radiofrequency are applied. In this work, a modification of the Pennes bioheat equation to study the temperature distribution induced by any electrode array in an anisotropic tissue containing several nodules (primary or metastatic) with arbitrary shape is proposed. For this, the Green functions approach is generalized to include boundaries among two or more media. The analytical solution we obtain in a very compact way, under quite general suppositions, allows calculating the temperature distributions in the tumor volumes and their surfaces, in terms of heat sources, initial temperature and calorific sources at the boundary of tumors.

Non-equilibrium energy transport and entropy production due to laser short-pulse irradiation

2016 ◽  
Vol 94 (1) ◽  
pp. 130-138 ◽  
Author(s):  
H. Ali ◽  
B.S. Yilbas ◽  
A.Y. Al-Dweik
Keyword(s):  
Laser Pulse ◽  
Entropy Generation ◽  
Energy Transport ◽  
Pulse Heating ◽  
Short Pulse ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Pulse Intensity ◽  
Laser Pulse Intensity ◽  
Nano Size

Laser short-pulse heating of a nano-size wire is considered and entropy generation rate is predicted during the heating pulse. The analytical solution of the heat equation is obtained using the Lie point symmetry for the laser short-pulse heating. The nano-size wire is assumed to be symmetric along its y-axis. Laser pulse intensity is considered to be Gaussian at the irradiated surface while the exponential decay of the laser pulse is incorporated in the time domain. It is found that surface temperature variation in the lattice subsystem almost follows the laser pulse intensity distribution at the surface. Entropy generation rate attains low values along the symmetry axis and it increases considerably in the region of the nano-size wire edges. This behavior is associated with the temperature gradient, which attains high values in the region close to the nano-size wire edge.

Laser short-pulse heating: Three-dimensional consideration

2001 ◽  
Vol 215 (9) ◽  
pp. 1123-1138 ◽  
Author(s):  
B. S. Yilbas
Keyword(s):  
Kinetic Theory ◽  
Energy Transport ◽  
Pulse Heating ◽  
Short Pulse ◽  
Three Dimensional ◽  
Gold Surface ◽  
Equation Model ◽  
Three Dimensions ◽  
Theory Approach ◽  
Energy Transfer Mechanism

Non-equilibrium energy transport takes place in solids once the laser pulse duration reduces to picoseconds or less. It is this energy transfer mechanism that defines the laser interaction process and therefore the rate at which the material is heated through the collisional process. In the present study, laser short-pulse heating of a gold surface is considered. An electron kinetic theory approach is introduced to model the energy transport process in three dimensions. The governing equation of energy transport is solved numerically, and the electron and lattice site temperatures are predicted. In order to validate the electron kinetic theory predictions, a two-equation model is employed to compute the temperature field in the substrate material. It is found that energy transport due to the diffusional process is unlikely during the heating period considered at present. The predictions of electron kinetic theory agree well with the results obtained from the two-equation model.

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