Steady and unsteady forced convection past an inclined elliptic cylinder
type: Item
instance of: scholarly article
title: Steady and unsteady forced convection past an inclined elliptic cylinder
zbMATH Open document ID: 0913.76084
DOI: 10.1007/BF01178404
author: S. J. D. D'Alessio
published in: Acta Mechanica
publication date: 1999-06-07T00:00:00Z
review text: This paper deals with two-dimensional forced convective heat transfer from an inclined elliptic cylinder. Both the steady and unsteady cases are considered at moderate Reynolds numbers. The governing continuity, Navier-Stokes and energy equations are written in polar coordinates \((\xi,\theta)\) related to the Cartesian coordinates through the conformal transformation \(x+ iy= \text{cosh}[(\xi+ \xi_0)+ i\theta]\), where \(\text{tanh }\xi_0= r\) with \(r\) being the ratio of the minor to the major axis of the ellipse. The transformed equations are then solved numerically by a finite difference method for Reynolds numbers \(Re\) in the range \(40\leq Re\leq 70\), inclination angle \(0^\circ\leq\alpha\leq 90^\circ\), the Prandtl number \(Pr= 1\), and \(r= 0.1\) and \(0.2\). The numerical results show that for low values of \(Re\) the unsteady problem converges to the steady-state case. However, as \(Re\) increases, steady and unsteady problems generate essentially different isotherms. It is believed that this is due to the vortex shedding that takes place as \(Re\) increases. Further, the author shows that the averaged Nusselt number \(\overline{Nu}\) takes a maximum value for the horizontal cylinder \((\alpha= 0^\circ)\) and decreases with inclination to a minimum value at \(\alpha= 90^\circ\). It is also demonstrated that \(\overline{Nu}\) increases almost uniformly with \(Re\) in the range \(40\leq Re\leq 70\).
reviewed by: Ioan Pop
Mathematics Subject Classification ID: 76R05
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 1143222
zbMATH Keywords: energy equation
zbMATH Keywords: polar coordinates
zbMATH Keywords: conformal transformation
zbMATH Keywords: inclination angle
zbMATH Keywords: vortex shedding
zbMATH Keywords: averaged Nusselt number
MaRDI profile type: Publication
cites work: Steady laminar forced convection from an elliptic cylinder
cites work: Time-dependent viscous flow past an impulsively started rotating and translating circular cylinder
cites work: Compact \(h^ 4\) finite-difference approximations to operators of Navier- Stokes type
full work available at URL: https://doi.org/10.1007/bf01178404
OpenAlex ID: W2318985137
description: scientific article; zbMATH DE number 1143222