Abstract
Formal use of constitutive equations such as that ofOldroyd in the mathematical model of a flow leads, in general, to a higher order differential equation than is obtained for a purely viscous fluid, and so we expect to need more boundary conditions in order to specify the problem completely. (These extra boundary conditions may be thought of as arising from the need to specify what the fluid “remembers” of the flow outside the region of interest.) In flows which are uniform spatially, or uniform with time for a material element, the uniformity will provide the extra information and so no extra conditions are needed. Similarly for confined flows, where no new fluid enters the region of interest, no information about flow outside this region is needed.
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