Application of Logarithmic Mean Area in Thermal Analysis of Hollow Spherical Shells: Review

The accurate estimation of surface area is essential in modeling heat transfer through hollow spherical structures, especially in thermal insulation, reactor vessels, and spherical containment systems. This study presents the derivation and application of the logarithmic mean area (LMA) for a hollow sphere, which provides a more precise representation of the effective heat transfer area compared to arithmetic or geometric means. By incorporating the LMA in conduction heat transfer equations, the thermal resistance of spherical shells can be evaluated with improved accuracy. Case studies illustrate the benefit of using LMA in comparison to traditional methods. This formulation enhances thermal design efficiency for engineering systems involving concentric spherical configurations.