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.