Heat removal of in‐tube viscous flows to air with the assistance of arrays of plate fins Part I: theoretical aspects involving 3‐D, 2‐D and 1‐D models

A detailed comparative study of the heat transfer augmentation of in‐tube flows accounting for an array of equally‐spaced plate fins attached at the outer surface is undertaken. The aim of the paper is to critically examine the thermal response of this kind of finned tubes to three different mathematical models: a complete 3‐D distributed model, a reduced 2‐D distributed/lumped hybrid model and two largely simplified 1‐D lumped models. For the three models tested, the computed results consistently demonstrate that the simplest 1‐D lumped model, with embedded arithmetic spatial‐ and geometric spatial‐means of the angular external convective coefficients provide dependable algebraic estimates of the actual heat transfer provided by the 3‐D distributed model with its indispensable finite‐difference solution. Further, an arithmetic mean of the maximum and minimum heat transfer supplied by the 1‐D lumped model delivered results that match those computed with the 3‐D distributed model. The most important steps of the mathematical derivations have been highlighted. A representative group of thermal performance diagrams is explained with the intent to assist engineers engaged in the thermal design of externally finned tubes of compact heat exchangers and HVAC devices.