Streamlining the teaching of unsteady heat conduction in regular solid bodies with heat convection to neighboring fluids

Abstract

In the analysis of unidirectional, unsteady heat conduction for simple solid bodies (large slab, long cylinder and sphere), the modern tendency adopted by authors of heat transfer textbooks is to calculate the temperatures and total heat transfer with “one-term” series accounting for the proper eigenquantities, which are expressed in terms of the Biot number. The supporting information is available in tables for a large slab, a long cylinder and a sphere. To avoid linear and quadratic interpolation for the Biot numbers listed in the tables, the goal of the present study is to use regression analysis in order to develop compact correlation equations for the first eigenvalues, the first eigencontants and the first constants (for the total heat transfer) varying with the Biot number for large slabs, long cylinders and spheres, all in the ample range 0 < Bi ≤ 100. This direct approach will speed up the step-by-step calculations of a multitude of unsteady heat conduction problems for engineering students.

Keywords

One-dimensional unsteady heat conduction simple solid bodies convective heat exchange local and mean temperatures total heat transfer

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