Reliable one dimensional 46-CPWTR model applied to two dimensional heat transfer problem of insulated triangular duct

In this study, the heat transfer characteristics of an insulated long triangular duct are analyzed by using the one dimensional plane wedge thermal resistance (PWTR) and plate thermal resistance (PTR) models. It is found that the errors produced by the PWTR model are all positive, but the errors produced by the PTR model are all negative. Thus, the combined plate wedge thermal resistance (CPWTR) model generated by paralleling PWTR and PTR models with the proportion factors of α = 0.4 vs. β = 0.6 (46-CPWTR model) is capable of neutralizing the positive and negative errors and returning very accurate results in comparison with the two dimensional numerical solutions analyzed by CFD software. The errors generated by the one dimensional 46-CPWTR model are within 1% for practical insulation thickness (t/R₂ < 0.5). In the rare situations of thicker insulation (0.5 ≦ t/R₂ ≦ 2), most of the errors returned by the one dimensional 55-CPWTR model are within 2%. Thus, engineers can obtain very reliable heat transfer results by applying the one dimensional 46-CPWTR or 55-CPWTR models to an insulated triangular duct. Meanwhile, the PTR model can still be used to estimate the highest surface temperature for a hot fluid duct or the lowest surface temperature for a cool fluid duct.