The laminar boundary layer of a viscous incompressible fluid subject to a two-dimensional wall curvature is evaluated. It is well known that a curved surface induces streamwise pressure gradient as well as wall curvature driven pressure gradient. Under certain assumptions, a family of similarity solutions can be obtained under the influence of flow acceleration/deceleration, which is known as the Falkner-Skan similarity solutions. In this study, the effect of the wall normal pressure gradient is taken into consideration, and the
freestream flow parameters are adjusted for flow over a curved surface. Present results are obtained by numerical solution of a generalized Falkner-Skan equation governing similar solutions for flows over curved surfaces. The Falkner-Skan equations are solved by an RK4 shooting algorithm. Additionally, the transport of a passive scalar is incorporated in the present analysis at different Prandtl numbers. The objective of this paper is to use the curvilinear or axisymmetric boundary layer and energy equations to assess the effect of
Favorable, Adverse and Zero pressure gradient on the laminar momentum and thermal boundary layer development.
Major conclusions are summarized as follows: (i) as the pressure gradient β increases from negative values (APG) towards positive (FPG) values, the displacement (Δ∗) and momentum (θ∗) thickness tend to decrease no matter the curvature type, and, (ii) the normalized wall shear stress (i.e., f′′) exhibits a linear decreasing behavior as the wall curvature switches from concave (negative) to convex (positive) at a constant pressure gradient.
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Normal mode analysis of 3D incompressible viscous fluid flow models
In this paper, we study the normal mode solutions of 3D incompressible
viscous fluid flow models. The obtained theoretical results are then applied
to analyze several time-stepping schemes for the numerical solutions of the
3D incompressible fluid flow models.
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- NSF-PAR ID:
- 10092053
- Date Published:
- Journal Name:
- Applicable analysis
- ISSN:
- 0003-6811
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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