Slender-body theory for transient heat conduction: theoretical basis, numerical implementation and case studies

Abstract

Slender-body theory (SBT) for transient heat transfer from bodies whose lengths are much larger than their radius into a conductive medium is derived. SBT uses matched asymptotic expansions of inner and outer solutions. An analytical inner solution for heat transfer from a circular cross section is matched to an outer solution obtained using Green’s functions. An efficient numerical implementation is obtained based on a judicious choice of the discrete elements used to represent the body and implementation of the fast multipole method (FMM). The SBT requires a one-dimensional spatial discretization only along the axis of the body in contrast to the three-dimensional discretization for finite-element models. Two case studies, heat transfer from two parallel cylinders and heat transfer from a slinky-coil heat exchanger, are used to show the speed and accuracy of the SBT model and its ability to model interacting slender bodies of finite length and bodies with centreline curvature and internal advective heat flow.