Optimum interior area thermal resistance model to analyze the heat transfer characteristics of an insulated pipe with arbitrary shape

The heat transfer characteristics for an insulated regular polygonal (or circular) pipe are investigated by using a wedge thermal resistance model as well as the interior area thermal resistance model R-th = t/K-s/[(1 - alpha)A(2) + alphaA(3)] with a surface area weighting factor alpha. The errors of the results generated by an interior area model can be obtained by comparing with the exact results generated by a wedge model. Accurate heat transfer rates can be obtained without error at the optimum alpha(opt) with the related t/R-2. The relation between alpha(opt) and t/R-2 is alpha(opt) = 1/ln(1 + t/R-2) - 1/(t/R-2). The value of alpha(opt) is greater than zero and less than 0.5 and is independent of pipe size R-2/R-cr but strongly dependent on the insulation thickness t/R-2. The interior area model using the optimum value alpha(opt) with the related t/R-2 should also be applied to an insulated pipe with arbitrary shape within a very small amount of error for the results of heat transfer rates. The parameter R-2 conservatively corresponds to the outside radius of the maximum inside tangent circular pipe within the arbitrary shaped pipes. The approximate dimensionless critical thickness t(cr)/R-2 and neutral thickness t(e)/R-2 of an insulated pipe with arbitrary shape are also obtained. The accuracies of the value of t(cr)/R-2 as well as t(e)/R-2 are strongly dependent on the shape of the insulated small pipe. The closer the shape of an insulated pipe is to a regular polygonal or circular pipe, the more reliable will the values Of t(cr)/R-2 as well as t(e)/R-2 be. (C) 2003 Elsevier Ltd. All rights reserved.