Stagnation Flow and Heat Transfer From a Finite Disk Situated Perpendicular to a Uniform Stream

The stagnation flow and heat transfer from the blunt surface of a finite circular disk subjected to a uniform stream of an incompressible fluid is revisited in this paper. A laminar boundary layer analyses were carried out employing the method developed by Frössling. The involved auxiliary functions were calculated for several Prandtl numbers. It was found that the exact knowledge of the velocity at the outer edge of the boundary layer was essential to achieve an accurate velocity solution. In addition to the analytical work, computational fluid dynamics (CFD) simulations and a detailed experimental study were conducted including heat transfer measurements in a wind tunnel and a large water towing tank. The analytical treatment enabled a clear discussion of the effect of the Prandtl number on convective heat transfer from a blunt disk. A primary effect and a secondary effect were distinguished based on the analytical treatment. The boundary layer theory offered a rather efficient calculation method, and its results were in an excellent agreement with experimental data.

Stagnation Flow and Heat Transfer From a Finite Disk Situated Perpendicular to a Uniform Stream

The stagnation flow and heat transfer from the blunt surface of a finite circular disk subjected to a uniform stream of an incompressible fluid is revisited in this paper. A laminar boundary layer analyses was carried out employing the method developed by Frössling. The involved auxiliary functions were calculated for several Prandtl numbers. It was found that the exact knowledge of the velocity at the outer edge of the boundary layer was essential to achieve an accurate velocity solution. In addition to the analytical work, computational fluid dynamics (CFD) simulations and an experimental study were carried out. The analytical treatment enabled a clear discussion of the effect of the Prandtl number on convective heat transfer from a blunt disk. A primary and a secondary effect were distinguished based on the rigorous analytical treatment. The boundary layer theory offered a rather efficient calculation method, and its results were in an excellent agreement with available literature data.

A higher-order slender-body theory for axisymmetric flow past a particle at moderate Reynolds number

Slender-body theory is utilized to derive an asymptotic approximation to the hydrodynamic drag on an axisymmetric particle that is held fixed in an otherwise uniform stream of an incompressible Newtonian fluid at moderate Reynolds number. The Reynolds number, $Re$ , is based on the length of the particle. The axis of rotational symmetry of the particle is collinear with the uniform stream. The drag is expressed as a series in powers of $1/\text{ln}(1/\unicode[STIX]{x1D716})$ , where $\unicode[STIX]{x1D716}$ is the small ratio of the characteristic width to length of the particle; the series is asymptotic for $Re\ll O(1/\unicode[STIX]{x1D716})$ . The drag is calculated through terms of $O[1/\text{ln}^{3}(1/\unicode[STIX]{x1D716})]$ , thereby extending the work of Khayat & Cox (J. Fluid Mech., vol. 209, 1989, pp. 435–462) who determined the drag through $O[1/\text{ln}^{2}(1/\unicode[STIX]{x1D716})]$ . The calculation of the $O[1/\text{ln}^{3}(1/\unicode[STIX]{x1D716})]$ term is accomplished via the generalized reciprocal theorem (Lovalenti & Brady, J. Fluid Mech., vol. 256, 1993, pp. 561–605). The first dependence of the inertial contribution to the drag on the cross-sectional profile of the particle is at $O[1/\text{ln}^{3}(1/\unicode[STIX]{x1D716})]$ . Notably, the drag is insensitive to the direction of travel at this order. The asymptotic results are compared to a numerical solution of the Navier–Stokes equations for the case of a prolate spheroid. Good agreement between the two is observed at moderately small values of $\unicode[STIX]{x1D716}$ , which is surprising given the logarithmic error associated with the asymptotic expansion.