Conduction shape factors are newly defined for rectangular plate fins with in-line tubes. They are calculated numerically for various geometric and fin parameters. And approximate analytical expressions for them are found. Fin conduction shape factors are the heat transfer conductances from tube to air and from a tube to another one. They are thus one of the most important parameters when estimating the heat exchanger performance. In this reasons, they are numerically solved using an FEM code for 625 cases of two-tube and four-tube plate fins and for 3125 cases of two-tube plate fin with slit. The numerical solutions show that the fin tip length has no effect on the conduction shape factors between tubes and that the conduction shape factors between non-neighboring tubes are small enough to be neglected. In addition, the conduction shape factors between neighboring tubes are dependent only on the relative geometry between the two tubes. The convective heat transfer rate from a symmetric two-tube fin to air is independent of the slit length when the temperature of a tube is high and the other one is of the same temperature as the air. Using the above results, regression of the conduction shape factors between neighboring tubes is made as a function of fin parameter, dimensionless fin width and tube-to-tube distance by nonlinear multiple regression analysis. Also the convective heat transfer rate from a fin to air is approximately calculated from the analytic solution of the radial fin. All the conduction shape factors under consideration are expressed in terms of these two factors, with an additional correction factor. The obtained expressions facilitate to analyze the performance of a heat exchanger including the conduction through fin between tubes.
