Natural Convection Heat Transfer from an Inclined Cylinder

TL;DR

This paper develops a physics_based, first_principles model for natural convection heat transfer from an external inclined cylinder, unifying conduction and buoyancy driven convection via an ell_p_norm framework and a Pr dependent self_obstruction factor. The theory introduces geometry dependent characteristic lengths and multiple scale free surface conductances, then blends them to predict the average Nusselt number across flow regimes. Validation against 93 inclined_cylinder measurements from nine datasets shows RMSRE between 1.6% and 4.7% for inclined cylinders, with notable improvements over prior level_cylinder and vertical_cylinder correlations (e.g., ~11% RMSRE for level cylinders). The work demonstrates robust performance across wide Ra ranges, clarifies the role of inclination via scaled Ra components, and discusses extensions to short, non_circular, rough, and small_Ra configurations, highlighting practical implications for design and analysis of convective heat_transfer around cylindrical bodies.

Abstract

This investigation derives a novel formula predicting the natural convective heat transfer from an inclined cylinder given its length, diameter, inclination angle, Rayleigh number, and the fluid's Prandtl number and thermal conductivity. The present formula was tested with 93 inclined cylinder measurements having length-to-diameter ratios between 1.48 and 104 in nine data-sets from three peer-reviewed studies, yielding (data-set) root-mean-squared relative error values between 1.6% and 4.7%.