Heat removal of in-tube viscous flows to air with the assistance of arraysof 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 f lows accounting for an away of equally-spaced plate fins attached at the ou ter surface is undertaken. The aim of the paper is to critically examine th e thermal response of this kind of finned tubes to three different,mathemat ical models: a complete 3-D distributed model a reduced 2-D distributed/lum ped hybrid model and two largely simplified 1-D lumped models. For the thre e models tested the computed results consistently demonstrate that the simp lest 1-D lumped model, with embedded arithmetic spatial- and geometric spat ial-means of the angular external convective coefficients provide dependabl e algebraic estimates of the actual heat transfer provided by the 3-D distr ibuted 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 dis tributed model. The most important steps of the mathematical derivations ha ve been highlighted A representative group of thermal performance diagrams is explained with the intent to assist engineers engaged in the thermal des ign of externally finned tubes of compact heat exchangers and HVAC devices.