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Longitudinal surface curvature effects on boundary layer of a micropolar fluid

Einfluß der longitudinalen Oberflächenkrümmung auf die Grenzschicht einer mikropolaren Flüssigkeit

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Summary

The effect of longitudinal surface curvature on steady two-dimensional incompressible laminar boundary layer of a micropolar fluid has been considered. Van Dyke's first oder perturbation analysis is applied to the full equations of motion derived in curvilinear coordinate system which facilitates to carry out boundary layer approximation for flow past a curved surface. This results into two systems of partial differential equations which are called the zeroth order and the first order boundary layer equations. The zeroth order equations are the usual boundary layer equations for a micropolar fluid. The first order equations take into account the longitudinal surface curvature effect explicitly. Similar solution of the governing equations exists if (i) the inviscid flow velocity on the surface varies linearly along the surface and (ii) the longitudinal surface curvature is constant. Numerical results are presented illustrating the dependence of the important flow quantities of both zeroth order and first order boundary layers on the micropolar fluid parameters. The results have been compared with the corresponding results for a Newtonian fluid. It has been found that the skin friction decreases and the wall couple stress increases for convex side of the surface and vice versa for the concave side.

Zusammenfassung

Der Einfluß einer longitudinalen Oberflächenkrümmung auf die stationäre, zweidimensionale, inkompressible, laminare Grenzschicht einer mikropolaren Flüssigkeit wird untersucht. Van Dyke's Strömungsanalyse erster Ordnung wird angewendet auf die Bewegungsgleichungen in krummlinigen Koordinaten, die einfach die Grenzschichtnäherung für die Strömung hinter einer gekrümmten Oberfläche aufzeigen. Dies führt zu zwei Systemen partieller Differentialgleichungen, die die Grenzschichtgleichungen nullter und erster Ordnung genannt werden. Die Gleichungen nullter Ordnung sind die üblichen Grenzschichtgleichungen für eine mikropolare Flüssigkeit. Die Gleichungen erster Ordnung berücksichtigen den Einfluß der longitudinalen Oberflächenkrümmung explizit. Ähnliche Lösungen der Grundgleichungen existieren wenn: (i) sich die reibungsfreie Strömungsgeschwindigkeit an der Oberfläche linear entlang der Oberfläche ändert und (ii) die longitudinale Oberflächenkrümmung konstant ist. Numerische Ergebnisse werden angegeben, um die Abhängigkeit der wichtigsten Strömungsgrößen der Grenzschicht nullter und erster Ordnung von den Parametern der mikropolaren Flüssigkeit aufzuzeigen. Die Ergebnisse werden verglichen mit den entsprechenden Ergebnissen für eine Newtonsche Flüssigkeit. Es wurde festgestellt, daß für eine konvexe Fläche die Wandreibung abnimmt und die gekoppelten Spannungen an der Wand zunehmen; das Umgekehrte gilt für eine konkave Fläche.

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Authors and Affiliations

  1. Department of Aeronautical Engineering, Indian Institute of Technology, Bombay, India

    S. K. Ojha

  2. Department of Mathematics, Indian Institute of Technology, Powai, 400 076, Bombay, India

    M. N. Mathur & A. K. Banerjee

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  1. S. K. Ojha
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  2. M. N. Mathur
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  3. A. K. Banerjee
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Ojha, S.K., Mathur, M.N. & Banerjee, A.K. Longitudinal surface curvature effects on boundary layer of a micropolar fluid. Acta Mechanica 34, 215–231 (1979). https://doi.org/10.1007/BF01227986

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  • DOI: https://doi.org/10.1007/BF01227986

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