scholarly journals AN ANALYTICAL TEMPERATURE SOLUTION ANALYSIS FOR A MULTILAYER HEAT CONDUCTION PROBLEM

2014 ◽  
Vol 13 (2) ◽  
pp. 89
Author(s):  
G. C. Oliveira ◽  
A. P. Fernandes ◽  
G. Guimarães
Keyword(s):  
Heat Conduction ◽  
Green Function ◽  
Analytical Solution ◽  
Heat Conduction Problem ◽  
Direct Method ◽  
Function Solution ◽  
Solution Equation ◽  
Temperature Solution ◽  
The Green Function ◽  
A Direct Method

This paper presents a method of obtaining an analytic temperature solution for a two-layer heat conduction problem. Obtaining the temperature analytical solution for a multilayer heat conduction problem is not a direct method. The way to indentify the eigenvalues and to derive the Green function solution equation requires a different treatment since there are more than one domain to solve. This work presents a solution of a thermal twolayer problem based on Green’s functions.

Effects of Thermo-Physically Initial Properties on Inverse Heat Conduction Problem

2013 ◽  
Vol 284-287 ◽  
pp. 733-737
Author(s):  
Sung Deok Hong ◽  
Mi Gyung Cho ◽  
Chan Soo Kim ◽  
Cheol Ho Bai ◽  
Sung Yull Hong ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Conduction Problem ◽  
Damping Ratio ◽  
Initial Guess ◽  
Convergence Time ◽  
Theoretical Equation ◽  
Inverse Heat Conduction ◽  
Marquardt Algorithm ◽  
Infinite Slab

The Levenberg-Marguardt algorithm is used to study effects on convergence for inverse heat conduction in the unsteady state. In this model, the finite volume method is usedto obtain anestimated temperature, which is necessary for minimizing inverse error. To validate the model, constant thermal conductivity (k) and heat capacity (ρCpC) are identified from a semi-infinite slab subjected to constant heat flux. These properties are inserted into the theoretical equation for a semi-infinite slab, and an analytical solution is obtained by solving the theoretical equation including the two identified properties. The analytical solution and the identified resultare in very good agreement. Three simulations were performed to investigate the sensitivity of computation time and conversion to initial thermo-physical values by changing three different damping ratios of the Levenberg-Marquardt algorithm. Our results show that agood initial guessallowsgood convergence, but convergence time decreases as the value of damping ratio decreases.A poor initial guess results in more convergence time, and causes divergence when a small damping ratio is used. Once the simulation converges, our model shows that results areobtained within an error of 0.01%.

Nonhomogeneous Dual-Phase-Lag Heat Conduction Problem: Analytical Solution and Select Case Studies

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Simon Julius ◽  
Boris Leizeronok ◽  
Beni Cukurel
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Generation ◽  
Integral Transform ◽  
Heat Conduction Problem ◽  
Relaxation Times ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase

Finite integral transform techniques are applied to solve the one-dimensional (1D) dual-phase heat conduction problem, and a comprehensive analysis is provided for general time-dependent heat generation and arbitrary combinations of various boundary conditions (Dirichlet, Neumann, and Robin). Through the dependence on the relative differences in heat flux and temperature relaxation times, this analytical solution effectively models both parabolic and hyperbolic heat conduction. In order to demonstrate several exemplary physical phenomena, four distinct cases that illustrate the wavelike heat conduction behavior are presented. In the first model, following an initial temperature spike in a slab, the thermal evolution portrays immediate dissipation in parabolic systems, whereas the dual-phase solution depicts wavelike temperature propagation—the intensity of which depends on the relaxation times. Next, the analysis of periodic surface heat flux at the slab boundaries provides evidence of interference patterns formed by temperature waves. In following, the study of Joule heating driven periodic generation inside the slab demonstrates that the steady-periodic parabolic temperature response depends on the ratio of pulsatile electrical excitation and the electrical resistivity of the slab. As for the dual-phase model, thermal resonance conditions are observed at distinct excitation frequencies. Building on findings of the other models, the case of moving constant-amplitude heat generation is considered, and the occurrences of thermal shock and thermal expansion waves are demonstrated at particular conditions.

Green Function Solutions for the Transient Motion of Water Sections

2002 ◽  
Vol 46 (02) ◽  
pp. 99-120
Author(s):  
D. S. Holloway ◽  
M. R. Davis
Keyword(s):  
Green Function ◽  
Computational Algorithm ◽  
Liquid Surface ◽  
Domain Boundary ◽  
Analytic Solutions ◽  
Function Solution ◽  
Fixed Frame ◽  
Strip Theory ◽  
High Froude Number ◽  
The Green Function

A time-domain boundary element method based on a Green function solution is derived for two-dimensional motions in the presence of a free liquid surface. Particular attention is given to the numerical evaluation of the required Green functions with regard to accuracy and speed of solution by choice of a computational algorithm appropriate to the domain of particular computations. The method is validated with reference to analytic solutions for submerged and floating cylinders in steady, transient and periodic motion. The intended application of the method is in the computation of wave response of slender ships at high Froude number by a fixed frame strip theory where the Green function obviates the necessity to panel the free surface with elements.

Multilayer analytical solution for heat conduction problem: Application of coated tools

2015 ◽  
Author(s):  
Gabriela Costa de Oliveira ◽  
Ana Paula Fernandes ◽  
Gilmar Guimarães ◽  
Sidney Ribeiro da Silveira
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Conduction Problem ◽  
Coated Tools
Sign in / Sign up

Export Citation Format

Share Document