The Third International Symposium on Advances in Computational Heat Transfer, CHT-04, took place on 19–24 April 2004 on the Hurtigruten Coastal Steamer MS Midnatsol during its voyage down the Norwegian coast between Kirkenes and Bergen, Norway. The symposium was sponsored by the International Centre for Heat and Mass Transfer and the CFD Research Laboratory of The University of NSW. The weather was, of course, cold—Kirkenes is at 70◦N latitude—but was generally ne and the venue provided opportunities for both professional interaction and tourism among the 114 delegates from 31 countries. The theme of ‘computational heat transfer’ at the conference was directed as much at industrial problems—in many cases at very complex industrial ows and processes, often involving phase change—as pure or applied research problems. Of the 104 papers presented at the meeting, we considered some of outstanding value for a wider public while typical for the symposium. Of these presentations, we have invited the authors to write a paper based on their presentation and to submit it to this special issue. These papers have been reviewed in line with the usual IJNMF practice. We hope that this resulting compendium provides a valuable overview for our readers of the application of computational methods for convective heat transfer to a range of research and industrial problems.