Algebraic Evaluation of Temperatures and Heat Transfer Rates in Simple Bodies with a 1-D Composite Lumped Model. Its Connection to the Heisler/Gröber Charts

Abstract

Calculations of temperature histories and heat transfer rates in simple bodies (infinite plate, infinite cylinder and sphere) have been traditionally explained in courses on heat transfer by way of the popular Heisler/Gröber charts, which are applicable to dimensionless times, τ, greater than 0.2. This imposing restriction comes from the ‘one-term series solutions' used in their construction. The central goal of this educational paper is to predict mean, surface and centre temperatures, as well as heat transfer rates of simple bodies, by implementing a 1-D composite lumped analysis. This effortless analysis brings about a handful of algebraic equations that can be easily evaluated with a pocket-size calculator. Even more important, the same algebraic equations can be extended into the sensible subregions described by dimensionless times less than 0.2; these subregions are ignored by the Heisler/Gröber charts.