TY - JOUR
TI - Simple and accurate correlations for some problems of heat conduction with nonhomogeneous boundary conditions
AU - Laraqi Najib
AU - Chahour Elkhansaa
AU - Monier-Vinard Eric
AU - Fahdi Nouhaila
AU - Zerbini Clémence
AU - Nguyen Minh-Nhat
JN - Thermal Science
PY - 2017
VL - 21
IS - 1
SP - 125
EP - 132
PT - Article
AB - Heat conduction in solids subjected to non-homogenous boundary conditions  leads to singularities in terms of heat flux density. That kind of issues can  be also encountered in various scientists’ fields as electromagnetism,  electrostatic, electrochemistry and mechanics. These problems are difficult  to solve by using the classical methods such as integral transforms or  separation of variables. These methods lead to solving of dual integral  equations or Fredholm integral equations, which are not easy to use. The  present work addresses the calculation of thermal resistance of a finite  medium submitted to conjugate surface Neumann and Dirichlet conditions, which  are defined by a band-shape heat source and a uniform temperature. The  opposite surface is subjected to a homogeneous boundary condition such  uniform temperature, or insulation. The proposed solving process is based on  simple and accurate correlations that provide the thermal resistance as a  function of the ratio of the size of heat source and the depth of the medium.  A judicious scale analysis is performed in order to fix the asymptotic  behaviour at the limits of the value of the geometric parameter. The  developed correlations are very simple to use and are valid regardless of the  values of the defined geometrical parameter. The performed validations by  comparison with numerical modelling demonstrate the relevant agreement of the  solutions to address singularity calculation issues.