Two-dimensional heat transfer and critical radius results for natural convection about an insulated horizontal cylinder

The two-dimensional (i.e. radial and circumferential) heat transfer and fluid flow problem for a fluid-carrying, insulated horizontal cylinder which loses heat to air by natural convection was analyzed by solving the differential form of the conservation laws. The resulting conjugate problem encompassed conduction in the insulation layer and natural convection in the ambient air. A one-dimensional, radial heat flow model of the problem was also investigated in detail, and the circumferential-average natural convection heat transfer coefficients needed for its evaluation were respectively taken from the commonly used correlations of McAdams, Morgan, and Churchill and Chu. It was found that the correlation-related spread of the heat transfer results from the one-dimensional model was greater than the differences between the one- and two-dimensional results. The use of the Morgan correlation gave the most accurate set of one-dimensional heat transfer results (i.e. best agreement with the two-dimensional results). For the critical radius, the standard h₀r^* k_ins = 1 criterion led to significant errors and should no longer be used. The critical radius results from the one-dimensional model, although correlation-dependent and deviant from the two-dimensional results, can be calculated efficiently and accurately from the criterion h₀r^* k_ins = 3n (1 + n), where n is an exponent which can be determined for each specific Nusselt-Rayleigh correlation.