Heat conduction across an array of cylinders

Heat transport through an infinite medium across a one-dimensional array of cylinders consisting of another conductive material is considered with the objective of assessing the effective thermal conductivity of the cylinder band. The formulation accounts for the thermal contact resistance of the interface between two materials in imperfect contact. The effective conductivity is expressed in terms of the displacement of the temperature profile far from the cylinder band with respect to that prevailing in a homogeneous medium. Integral representations involving single-layer potentials are developed to describe the temperature field in the presence of the cylinders, pertinent integral equations are derived, and numerical results based on a boundary-element method are presented to illustrate the effect of the cylinder size and conductivity ratios on the effective conductivity of the array.