Effective heat conductivity of a composite with hexagonal lattice of perfectly conducting circular inclusions: An analytical solution

Abstract

Paper is devoted to the effective stationary heat conductivity for the fibre composite materials. We are aimed on getting on analytical expression for effective thermal conductivity coefficient. Asymptotic homogenization approach, based on the multiple scale perturbation method, is used. This allows to reduce the original boundary value problem in multiply connected domain to the sequence of boundary value problems in simply connected domains. These problems include: the local problem for the periodically repeated cell and homogenized problem with effective coefficient. It is shown that for densely packed and high contrast fibre composites, the cell problem can be solved analytically. For this aim, lubrication approach (asymptotics of thin layer) has been employed. We also generalise obtained solution to the case of medium‐sized inclusions in the framework of the Padé approximants.

Thermal performance of a longitudinal fin under the influence of magnetic field using Sumudu transform method with pade approximant (STM‐PA)

“…A strong tool for managing boundary value problems on infinite or semi-infinite domains is the combination of the series solutions with the Pade approximants. The ratio of two polynomials formed from the coefficients of a function's Taylor series expansion is known as a Pade approximant (See [36], [37], and [38]).…”