A new 1-D composite lumped model facilitates the algebraic calculation of local temperatures, mean temperatures, and total heat transfer in simple bodies

Abstract

Estimates of spatio-temporal temperatures and total heat transfer in simple bodies (large plate, long cylinder and sphere) have been done in the past with the help of charts and recently by way of algebraic correlation equations; both avenues are valid for large times mostly, i.e., dimensionless times or Fourier numbers τ ≥ 0.2. The imposing time restriction comes from the utilization of the truncated ‘one-term series’ because the Fourier infinite series diverge for very short times approaching zero. The central goal of this technical paper is to predict the mean, surface and center temperatures, as well as the total heat transfer in those simple bodies by implementing a 1-D composite lumped analysis united to a sound physics-based computational procedure. The effortless combined methodology is new. It brings forth a handful of compact algebraic equations covering the full gamma of Biot numbers (0 < Bi < 100) and all dimensionless times, 0 < τ < ∞.