Conductive heat transport across rough surfaces and interfaces between twoconforming media

Conductive heat transport across an isothermal three-dimensional irregular surface into a semi-infinite conductive medium and heat transport across th e interface between two semi-infinite conductive media are considered by as ymptotic and numerical methods. The temperature profile far from the surfac e or interface varies in a linear manner with respect to distance normal to the mean position of the surface or interface, and is displaced by a const ant with respect to the linear profile corresponding to the flat geometry. The displacement constant amounts to a macroscopic temperature drop or disc ontinuity that depends on the geometry of the irregularities and on the med ia conductivities. An asymptotic expansion for the jump is derived by the m ethod of domain perturbation for small-amplitude, doubly-periodic corrugati ons, and an integral formulation is developed for finite-amplitude corrugat ions. Numerical results based on the boundary element method for three-dime nsional wavy corrugations with square or hexagonal pattern show that the as ymptotic results are accurate when the ratio of the vertical span to the wa velength of the corrugations is less than roughly 0.5. Illustrations of the flux distribution over the corrugated surfaces show explicitly a considera ble enhancement or reduction at the crests or troughs, even for moderate-am plitude irregularities. (C) 2001 Elsevier Science Ltd. All rights reserved.