scholarly journals Analytical solution for two dimensional time-dependent heat conduction in a multilayer sphere with heat sources using eigenfunction expansion method

2016 ◽  
Vol 7 (3) ◽  
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Eigenfunction Expansion ◽  
Expansion Method ◽  
Time Dependent ◽  
Heat Sources ◽  
Two Dimensional ◽  
Eigenfunction Expansion Method ◽  
Multilayer Sphere

scholarly journals Exact Analytical Solution for 3D Time-Dependent Heat Conduction in a Multilayer Sphere with Heat Sources Using Eigenfunction Expansion Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Nemat Dalir
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Eigenfunction Expansion ◽  
Radial Direction ◽  
Exact Analytical Solution ◽  
Internal Heat ◽  
Expansion Method ◽  
Time Dependent ◽  
Heat Sources ◽  
Eigenfunction Expansion Method

An exact analytical solution is obtained for the problem of three-dimensional transient heat conduction in the multilayered sphere. The sphere has multiple layers in the radial direction and, in each layer, time-dependent and spatially nonuniform volumetric internal heat sources are considered. To obtain the temperature distribution, the eigenfunction expansion method is used. An arbitrary combination of homogenous boundary condition of the first or second kind can be applied in the angular and azimuthal directions. Nevertheless, solution is valid for nonhomogeneous boundary conditions of the third kind (convection) in the radial direction. A case study problem for the three-layer quarter-spherical region is solved and the results are discussed.

Interactions of a horizontal flexible membrane with oblique incident waves

1998 ◽  
Vol 367 ◽  
pp. 139-161 ◽  
Author(s):  
I. H. CHO ◽  
M. H. KIM
Keyword(s):  
Eigenfunction Expansion ◽  
Numerical Solutions ◽  
Domain Boundary ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Source Distribution ◽  
Two Dimensional ◽  
Flexible Membrane ◽  
Eigenfunction Expansion Method ◽  
Incident Waves

The interaction of oblique monochromatic incident waves with a horizontal flexible membrane is investigated in the context of two-dimensional linear hydro-elastic theory. First, analytic diffraction and radiation solutions for a submerged impermeable horizontal membrane are obtained using an eigenfunction expansion method. Secondly, a multi-domain boundary element method (BEM) is developed to confirm the analytic solutions. The inner solution based on a discrete membrane dynamic model and simple-source distribution over the entire fluid boundaries is matched to the outer solution based on an eigenfunction expansion. The numerical solutions are in excellent agreement with the analytic solutions. The theoretical prediction was then compared to a series of experiments conducted in a two-dimensional wave tank at Texas A&M University. The measured reflection and transmission coefficients reasonably follow the trend of predicted values. Using the computer program developed, the performance of surface-mounted or submerged horizontal membrane wave barriers is tested with various system parameters and wave characteristics. It is found that the horizontal flexible membrane can be an effective wave barrier if properly designed.

Heat Conduction Across Corrugated Thermal Interface

2007 ◽  
Author(s):  
Bozhi Yang ◽  
Wenjun Liu
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
High Performance ◽  
Fem Simulation ◽  
Expansion Method ◽  
Thermal Interface Material ◽  
Thermal Interface ◽  
Eigenfunction Expansion Method ◽  
First Time

This paper presents the analytical solution of the heat conduction across a corrugated thermal interface material with rectangular straight fin arrangement. Domain decomposition and eigenfunction expansion method were used to study the thermal diffusion in such geometry for the first time. The temperature field solved from the analytical method agrees well with FEM simulation. The total heat transfer rate across the corrugated interface and thermal boundary resistance were derived analytically also. Results have shown that the effective thermal resistance across the interface can be significantly reduced with the corrugated TIM geometry. The analytical solution in the paper can provide insight into geometry effect on the heat transfer enhancement, and is a very useful complement to experimental work and numerical simulation in designing high-performance corrugated thermal interface.

The Quasi-Static Analysis for Two-Dimensional Thin Plates

2011 ◽  
Vol 255-260 ◽  
pp. 166-169
Author(s):  
Li Chen ◽  
Yang Bai
Keyword(s):  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Solution Space ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Elastic Plates ◽  
Various Boundary Conditions ◽  
Eigenfunction Expansion Method ◽  
Concentration Phenomena

The eigenfunction expansion method is introduced into the numerical calculations of elastic plates. Based on the variational method, all the fundamental solutions of the governing equations are obtained directly. Using eigenfunction expansion method, various boundary conditions can be conveniently described by the combination of the eigenfunctions due to the completeness of the solution space. The coefficients of the combination are determined by the boundary conditions. In the numerical example, the stress concentration phenomena produced by the restriction of displacement conditions is discussed in detail.

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