Steady and unsteady forced convection past an inclined elliptic cylinder
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 \(40\leq Re\leq 70\).
scientific article; zbMATH DE number 1143222