Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theoretical Investigation of Creeping Viscoelastic Flow Transition
  Around a Rotating Curved Pipe   The study of creeping motion of viscoelastic fluid around a rotating rigid
torus is investigated. The analysis of the problem is performed using a
second-order viscoelastic model. The study is carried out in terms of the
bipolar toroidal system of coordinates where the toroid is rotating about its
axis of symmetry (z-axis). The problem is solved within the frame of slow flow
approximation. Therefore, all variables in the governing equations are expanded
in a power series of angular velocity. A set of successive partial differential
equations is obtained. The equations of motion governing the first and
second-order are formulated and solved for the first-order only in this paper.
However, the solution of the second-order equations will be the subject of a
part two of this series of papers. Analytically, Laplace's equation is solved
via the usual method of separation of variables. This method shows that, the
solution is given in a form of infinite sums over Legendre functions of the
first and second kinds. From the obtained solution it is found that, the
leading term, W(1), of the velocity represents the Newtonian flow. The
second-order term shows that, the only non vanishing term is the stream
function, which describes a secondary flow. The distribution of the surface
traction at the toroid surface is calculated and discussed. Considering
hydrodynamically conditions, the effects of toroidal geometrical parameters on
the flow field are investigated in detail.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: math
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph