AbstractTemperature and thermal stress distributions for a first wall with non-circular coolant channels are calculated without using an empirical heat transfer coefficient. The energy coolant and heat conduction equation are solved simultaneously. The flow is assumed to be laminar; an approximate extension is made to the turbulent flow. The results indicate that the circumferential non-uniformity of the heat transfer coefficient causes thermal stresses that are higher than those predicted by an empirically determined average heat transfer coefficient. The effects of wall thickness and the shape of the coolant channel are discussed.