Problems with Closed Streamlines or Stream Surfaces

Problems with Closed Streamlines (or Stream Surfaces) 

To do this, we must anticipate one result from the general discussion of Section L on high-Peclet-number heat transfer in regions of closed-streamlines The dimensionless temperature gradient in such regions is determined primarily by its size. For example, in a closed-streamline region of 0(1) in extent, dimensionless, steady-state temperature gradients will also be 0(1). 

Suppose we consider a hypothetical situation in which a region of closed-streamline flow, with a linear dimension of 0(1) relative to the body, is generated downstream of some point A on the body surface. Upstream of A, the streamlines adjacent to the body surface are all open and the boundary-layer scaling is still relevant so that dO/dq 0(Pe1/3). 

SPHERE IN GENERALIZED SHEAR FLOWS AT LOW REYNOLDS NUMBER 

It is perhaps timely to stop and reflect upon the nature of the thermal boundary-layer analysis to determine whether other generalizations of the basic result (9-230) may be possible. In particular, heat transfer from solid bodies occurs frequently when the fluid motion seen by the body cannot be approximated as a uniform streaming flow, and the reader may ask whether the correlation (9-230) can be applied in these cases with a proper choice for the characteristic velocity that appears in Pe. It is especially interesting, in this regard, to compare the present analysis with the corresponding low-Peclet-number problem that appeared earlier in this chapter. 

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