The temperature profile in a circular tube of infinite extent through which a fluid is moving under conditions of small Péclet numbersεis determined by means of an asymptotic analysis inε. The walls of the tube are heated forx>0 and are insulated whenx<0. It is shown that the heated region extends anO(ε−1) distance — relative to the radius of the tube — upstream of the pointx=0, and that convective effects remain important even whenε→0. These results apply to a wider class of problems in which the Péclet nu
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