The effective thermal conductivity and elongational viscosity of a nondilute suspension of aligned slender rods

Abstract

The effective thermal conductivity and elongational viscosity of a nondilute suspension of infinitely conducting perfectly aligned slender rods of slenderness ratio ε≪1 are determined using an effective medium theory together with a self‐consistent scheme. The expressions thereby obtained cover the range in particle concentration c from infinite dilution c/ε²≪1, to the semidilute regime, c/ε²≫1, but c≪1. In the latter case, the present results agree to leading order with a formula derived by Batchelor [J. Fluid Mech. 4 6, 813 (1971)] even though the analyses employ physical arguments that appear to be quite distinct.