AXIAL CONDUCTION AND THE GRAETZ PROBLEM FOR A BINGHAM PLASTIC IN LAMINAR TUBE FLOW

The problem of heat transfer for a Bingham plastic in laminar tube flow is studied with axial conduction both excluded and included. It is demonstrated that the assumption of ignoring axial conduction for Peclet numbers greater than 100 is erroneous, especially near the start of the heated zone of the pipe. A new technique, based on the Sturm-Liouville theory, is introduced to solve these problems. In contrast to other techniques previously published, it requires only simple eigenvalues and eigenfunctions and is easily generalized to include the effects of axial conduction-a difficult proposition for semi-analytic methods.