Do general viscoelastic stresses for the flow of an upper convected Maxwell fluid satisfy the momentum equation?

    Authors

    R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    Meccanica

    Keywords

    Stress singularities; Stagnation point flow; Upper convected Maxwell; fluid; Method of characteristics; DILUTE POLYMER-SOLUTIONS; Mechanics

    Abstract

    Given a general velocity field consistent with the stagnation point flow, can the viscoelastic stresses arising in the flow of an upper convected Maxwell fluid found by solving the constitutive equation also satisfy the momentum equation? Consideration is given to the study of the stress tensor arising in the steady flow of an upper convected Maxwell (UCM) fluid with a velocity field consistent with the stagnation point flow. By the method of characteristics, exact solutions to the partial differential equations arising in the approximating model of the viscoelastic stresses in the flow of an upper convected Maxwell (UCM) fluid are obtained for the three components of the stress tensor, for reasonably general velocity fields. We are able to account for the effects of variable boundary data at the inflow by considering the viscoelastic stresses over two spatial variables. Furthermore, we assume a relatively general velocity field. As a special case, some results present in the recent literature are obtained; it is known that these special case solutions do not satisfy the momentum equation. In the general case we consider, we find that the general solution will not satisfy the momentum equation except in a limited restricted case. We discuss how this shortcoming might be rectified by use of a more general velocity field.

    Journal Title

    Meccanica

    Volume

    47

    Issue/Number

    8

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    1977

    Last Page

    1985

    WOS Identifier

    WOS:000310322800013

    ISSN

    0025-6455

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