The Critical Thickness of Insulation

Abstract

The theory of critical thickness of insulation for cylindrical and spherical geometries is discussed in a comprehensive and methodical manner. The article begins with the introduction of the classical analysis, which assumes surface convection with a constant heat transfer coefficient, h. Next, various modifications of the basic theory are discussed in detail. These modification allow for: The variation of h with outside radius, ro (constant-property forced convection) The variation of h with ro, with temperature-dependent fluid properties (variable-property forced convection) Circumferential variation of h with forced convection The variation of with outside radius and the temperature difference between the outside surface and the surroundings (natural convection) Surface radiation Combined radiation and natural convection Combined radiation, natural convection, and surface heat release due to change of phase of the surrounding fluid Effects of radiation, inclination, and insulation opacity The last three sections of the article consider the optimum configurations for a circular pipe covered with insulations of equilateral polygonal, rectangular, and eccentric circular shapes. For polygonal and rectangular geometries, the two-dimensional conduction analysis reveals that the conduction for the critical configuration is the same whether the outside surface boundary condition is that of convection or constant temperature. This permits the use of conduction shape factors to determine the optimum configuration for polygonal and rectangular insulations. The analysis leads to the concept of critical perimeter, which is more general than the concept of critical radius. The optimum sizing of eccentric circular insulation, however, requires a complete two-dimensional analysis. A total of 12 examples have been included to illustrate the various theoretical models described in the article. The detail and the number of examples makes the article pedagogicatly as well as practically appealing.