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ISSN Online: 2379-1748

7th Thermal and Fluids Engineering Conference (TFEC)
SJR: 0.152 SNIP: 0.14 CiteScore™:: 0.5

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Clarivate CPCI (Proceedings) Scopus
May, 15-18, 2022 , Las Vegas, NV, USA


Get access (open in a dialog) pages 1493-1508
DOI: 10.1615/TFEC2022.cmd.040936


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 wallcurvature 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 in similarity 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 (namely, FPG, APG and ZPG) 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 boundary layer (δ), displacement (Δ*) and momentum (θ*) thickness tend to decrease no matter the curvature type (concave or convex), (ii) the normalized wall shear stress (i.e., fII ) exhibits a linear decreasing behavior as the wall curvature switches from concave (negative) to convex (positive) at a constant pressure gradient, (iii) the wall curvature impact on the velocity field is weak at very strong APG, (iv) the previously described effects of wall curvature on momentum boundary layer parameters have also been detected on thermal parameters, such as thermal boundary layer thickness and normalized wall heat flux, (v) partial conclusion (iv) may lead us to infer that the Reynolds analogy (similarity between the velocity and thermal field) was fulfilled under the influence of surface curvature, at least from qualitative point of view.