The Correlation of Heat Transfer Coefficients for the Laminar Natural Convection in a Circular Finned-Tube Heat Exchanger

This study proposes an empirical correlation for laminar natural convection applicable to external circular finned-tube heat exchangers with wide range of configuration parameters. The transient temperature response of the heat exchangers was used to obtain the heat transfer coefficient, and the experimental data with their characteristic lengths are discussed. The data lie in the range from 1 to 1000 for Rayleigh numbers based on the fin spacing: the ratio of fin height to tube diameter ranges from 0.1 to 0.9, and the ratio of fin pitch to height ranges from 0.13 to 2.6. Sixteen sets of finned-tube electroplated with nickel–chrome were tested. The convective heat transfer coefficients on the heat exchangers were measured by elimination of the thermal radiation effect from the heat exchanger surfaces. The Nusselt number was correlated with a newly suggested composite curve formula, which converges to the quarter power of the Rayleigh number for a single cylinder case. The proposed characteristic length for the Rayleigh number is the fin pitch while that for the Nusselt number is mean flow length, defined as half the perimeter of the mean radial position inside the flow region bounded by the tube surface and two adjacent fins. The flow is regarded as laminar, which covers heat exchangers from a single horizontal cylinder to infinite parallel disks. Consequently, the result of curve fitting for the experimental data shows the reasonable physical interpretation as well as the good quantitative agreement with the correction factors.