Scale analysis and accurate correlations for some Dirichlet problems involving annular disc

This paper presents analytical investigations in order to determine the heat flow through an isothermal annular disc. This kind of problem has no explicit analytical solutions. Our goal aims to develop compact and accurate approximants valid regardless of the value of the ratio between the inner and the outer radii of the annular disc. The principle of this approach is based on the scale analysis to determinate the asymptotic behaviours and the use of an efficient correlation method. Very compact and accurate solutions are thus derived. Comparisons of the results obtained with the proposed solutions with some available numerical data show an excellent agreement (the relative difference is less than 1%).