Parabolic and Hyperbolic Two-Temperature Models of Microscopic Heat Transfer. Comparison of Numerical Solutions

2012 ◽  
Vol 706-709 ◽  
pp. 1454-1459 ◽  
Author(s):  
Ewa Majchrzak
Keyword(s):  
Heat Transfer ◽  
Metal Film ◽  
Numerical Solutions ◽  
Thin Metal Film ◽  
Ultrafast Laser ◽  
Microscale Heat Transfer ◽  
The Finite Difference Method ◽  
Energy Equations ◽  
Transfer Problems ◽  
Two Temperature

The paper deals with the microscale heat transfer problems. In particular, the ultrafast laser heating of thin metal film is considered. The problem is described by so-called two-temperature models consisting of two equations concerning the electron and lattice temperatures. Energy equations are supplemented by two additional ones determining the dependencies between electrons (phonons) heat flux and electrons (phonons) temperature gradient. According to the form of above dependencies one obtains the parabolic or hyperbolic heat transfer models discussed here. The problems have been solved using the finite difference method. In the final part of the paper the results of computations and the comparison of solutions obtained are presented.

scholarly journals Homotopy Perturbation Method

2017 ◽  
pp. 24-61
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Wide Range ◽  
Transfer Problems

The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

Use of a Zener Approximation for Heat Transfer Analyses of Quasi One-Dimensional Welding Problems

2018 ◽  
Vol 941 ◽  
pp. 2313-2318
Author(s):  
Jerry E. Gould
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
One Dimensional ◽  
Copper Electrodes ◽  
Wide Range ◽  
Linear Friction ◽  
Diffusion Transfer ◽  
Cooling Behavior ◽  
Transfer Problems ◽  
Analytical Approaches

Most welding methods in use today involve heating and subsequent cooling of the substrates for joining. Not surprisingly, understanding of associated thermal cycles implicit with the various processes has been a key facet of welding research. While the tools are available for sophisticated numerical solutions, much insight can be gained from simplified analytical approaches. A wide range of joining technologies in use today can be addressed by nominal one-dimensional heat transfer analyses. These include, for example, resistance spot, flash-butt, and linear friction welding. In addressing heat transfer problems, the mathematical constructs for heat transfer are analogous to those for mass (diffusion) transfer. Not surprisingly, one dimensional heat transfer problems can be greatly simplified by adapting the Zener approximation from mass transfer. The work described here employs the Zener approximation to address the direct spot welding of aluminum to steel. The Zener approximation is used to understand heat flow progressively from the steel into the aluminum and finally the copper electrodes. The results are used to understand weld morphology and implicit cooling behavior

Unsteady Hydromagnetic Generalized Couette Flow of a Non-Newtonian Fluid With Heat Transfer Between Parallel Porous Plates

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Hazem Ali Attia ◽  
Mohamed Eissa Sayed-Ahmed
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Fluid Motion ◽  
Casson Fluid ◽  
Lower Plate ◽  
Plate Temperature ◽  
Electrically Conducting ◽  
Energy Equations ◽  
External Uniform Magnetic Field ◽  
Newtonian Behavior

The unsteady magnetohydrodynamics flow of an electrically conducting viscous incompressible non-Newtonian Casson fluid bounded by two parallel nonconducting porous plates is studied with heat transfer considering the Hall effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate is suddenly set into motion and simultaneously suddenly isothermally heated to a temperature other than the lower plate temperature. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions are studied.

Effect of thin metal film and micro structure of surface on condensation heat transfer

2017 ◽  
Vol 2017.23 (0) ◽  
pp. 503
Author(s):  
Tomohito NISHIMURA ◽  
Yuki MIKOSHIBA ◽  
Hiroyasu OHTAKE ◽  
Koji HASEGAWA
Keyword(s):  
Heat Transfer ◽  
Metal Film ◽  
Thin Metal Film ◽  
Thin Metal ◽  
Condensation Heat Transfer ◽  
Micro Structure

A SMOOTHED FEM (S-FEM) FOR HEAT TRANSFER PROBLEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 1340001 ◽  
Author(s):  
B. Y. XUE ◽  
S. C. WU ◽  
W. H. ZHANG ◽  
G. R. LIU
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Three Dimensions ◽  
Mesh Free ◽  
Theoretical Investigations ◽  
Mesh Free Methods ◽  
Standard Finite Element Method ◽  
Gradient Smoothing ◽  
Transfer Problems ◽  
Super Convergence

By smoothing, via various ways, the compatible strain fields of the standard finite element method (FEM) using the gradient smoothing technique, a family of smoothed FEMs (S-FEMs) has been developed recently. The S-FEM possesses the advantages of both mesh-free methods and the standard FEM and works well with triangular and tetrahedral background cells and elements. Intensive theoretical investigations have shown that the S-FEM models can achieve numerical solutions for many important properties, such as the upper bound solution in strain energy, free from volumetric locking, insensitive to the distortion of the background cells, super-accuracy and super-convergence in displacement or stress solutions or both. Engineering problems, including complex heat transfer problems, have also been analyzed with better accuracy and efficiency. This paper presents the general formulation of the S-FEM for thermal problems in one, two and three dimensions. To examine our formulation, some computational results are compared with those obtained using other established means.

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