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Crane L.J.,Institute for Numerical Computation and Analysis | Mcveigh A.G.,Institute for Numerical Computation and Analysis
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik | Year: 2015

This work gives a mathematical account of the propagation of disturbances produced by a sudden draught of air impinging on a cylindrical fibre produced by the melt-spinning process. Accounting for varying tension and aerodynamic drag, the non-dimensional wave-type equation of motion is derived in dimensionless form; the solution of which is sought using the Riemann method of characteristics. Using this procedure, the solutions along the leading forward and reflected characteristics are obtained in closed-form and enable numerical solutions to be obtained via a finite difference routine along the entire computational domain. The analysis shows how such disturbances may be prevented from penetrating beyond the material crystallisation point (where it is extremely susceptible to disturbances) and discusses the application of these findings by optimising the location of a protective shroud. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Source


Crane L.J.,Institute for Numerical Computation and Analysis | McVeigh A.G.,Institute for Numerical Computation and Analysis
Acta Mechanica | Year: 2013

This work investigates the boundary layer development and resulting net frictional drag along a general blunt-nosed body of revolution in uniform slip flow. The curvilinear boundary layer equations are subjected to a Navier slip condition near the surface. For motion near the nose, a similarity-type solution is obtained as a double series, comprising a small velocity slip parameter, from which the non-dimensional drag coefficient is obtained. In addition, the displacement effect of the boundary layer on the outer inviscid flow is determined and interpreted by means of a dimensionless parameter. The general analysis is then applied to the special case of the Rankine half-body. Considering laminar flow along the nose and downstream regions, results are presented for prescribed slip parameters and Reynolds numbers with particular emphasis on the influence of slip on the flow. © 2012 Springer-Verlag Wien. Source


Crane L.J.,Institute for Numerical Computation and Analysis | McVeigh A.G.,Institute for Numerical Computation and Analysis
Archive of Applied Mechanics | Year: 2014

The axisymmetric laminar boundary layer flow along the entire length of a semi-infinite stationary cylinder under an accelerated free-stream is investigated. Considering flow at reduced dimensions, the boundary layer equations are developed with the conventional no-slip boundary condition for tangential velocity and temperature replaced by a linear slip-jump boundary condition. Asymptotic series solutions are obtained for the heat transfer coefficient in terms of the Nusselt number. These solutions correspond to prescribed values of the momentum and temperature slip coefficients and the index of acceleration. Heat transfer at both small and large axial distances is determined in the form of series solutions; whereas at intermediate distances, exact and interpolated numerical solutions are obtained. Using these results, the heat transfer along the entire cylinder wall is evaluated in terms of the parameters of acceleration and slip. © 2014 Springer-Verlag Berlin Heidelberg. Source


Crane L.,Institute for Numerical Computation and Analysis | Mcveigh A.,Institute for Numerical Computation and Analysis
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik | Year: 2011

This paper deals with the net frictional drag on a Rankine half-body in uniform axisymmetric flow. Asymptotic series solutions for the non-dimensional drag coefficient are developed for flow close to the forward stagnation point and downstream, while for the intermediate region, the solution is obtained by employing interpolating polynomials. Consideration is given to flows having Reynolds number of 100 and 1000. The results are compared to those for a slender uniform cylinder obtained by Seban and Bond [1], Glauert and Lighthill [2], and Curle [3]. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Source


Crane L.J.,Institute for Numerical Computation and Analysis | McVeigh A.G.,Institute for Numerical Computation and Analysis
Zeitschrift fur Angewandte Mathematik und Physik | Year: 2010

The purpose of this paper is to determine the heat transfer from a semi-infinite microcylinder under uniform axial flow in the slip regime. Following the treatments of Glauert and Lighthill (Proc Royal Soc 230A:188-203, 1955), and Crane (Ingenieur-Archiv 43:203-214, 1974), an asymptotic series solution is developed to account for the heat flux in terms of the Nusselt number for large axial distances along a cylinder maintained at constant temperature. © 2010 Springer Basel AG. Source

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