In this paper, we investigate the flow instability of a horizontal fluid layer under an inclined temperature gradient. The fluid layer is supposed to be of infinite extension, and the differentially heated lateral walls are very far away from the central region which is the subject of research. The layer is also inside two rigid, horizontal and parallel walls which are perpendicular to gravity and subjected to a vertical adverse temperature gradient. Calculations are done for Prandtl numbers Pr in the range from 0.026 to 1, which include materials from liquid metals to gases. By improving the Galerkin numerical method, new results and important extensions and corrections to the work of Nield [Int. J. Heat Fluid Flow 15, 157 (1994)] are obtained. It is found that inside the range 0.2 < Pr < 0.45, a new oblique oscillatory mode starts to appear and that it can be the first unstable one in a particular range of the horizontal Rayleigh number R_H for all Prandtl numbers until Pr = 1. To the left, this mode separates from an oscillatory longitudinal even mode already found by Nield [Int. J. Heat Fluid Flow 15, 157 (1994)]. A new codimension two point is found when the Prandtl number is increased to Pr = 0.4886, where the curves of the oblique oscillatory mode and the even stationary longitudinal mode touch each other for the first time. Another new codimension two point starts to appear in the range 0.5 < Pr < 1.0 which corresponds to the crossing between the curves of the oblique oscillatory mode and the odd stationary longitudinal mode. As a consequence, another interesting result is that, to the right of this point, the odd stationary longitudinal mode is the first unstable one in a range of R_H. The qualitative form of the curves of criticality changes notably between Pr = 0.026 and Pr = 1.0. Therefore, here we present a detailed description of this change by means of calculations for different Prandtl numbers inside that range.

Choosing a suitable prosthesis to restore the functionality of the hip joint is a complex problem. The stem geometries, materials, and type of hip damage are critical factors for avoiding potential issues (aseptic loosening, fracture, and natural wear and tear). Comparing the available stems to select the best option is not straightforward because of the various loads and boundary conditions used in the tests, making the process difficult to compare the advantages and disadvantages among them. This work proposes stem assessment using a standardized base (generated from a literature review and ISO standards) to compare the stem geometries and present a new hybrid design to improve performance using the best qualities of the implants reported in the literature review. Sixteen hip prostheses were evaluated with the finite element method (FEM) using the same boundary and loading conditions through multi-objective analysis (von Mises stress and strain). Consequently, a hybrid geometry proposal was obtained by assessing specific points through the stem length (medial and lateral region) to define the cross-section (trapezoidal) and the new profile. The new hybrid implant proposal presented a stress reduction of 9.6% when compared to the reference implant P2-T (the implant with the best behavior) in the most critical activity (activity 4) using a titanium alloy. A similar stress reduction of 9.98% was obtained using ASTM F2996-13 and ISO 7206–4:2010(E) standards.

Rayleigh and Marangoni convection and rheology are linked in the thermal convection of viscoelastic fluids to some recent technological applications. Such technology developments as the ones presented here undoubtedly shall be based on interdisciplinary projects involving not only rheology or fluid mechanics but several other disciplines. Three practical applications which use Rayleigh or Marangoni convection in their working principle are presented along with some technical details. This contribution focus mainly on the physical mechanism and the involved hydrodynamics of some lab and industrial applications. Finally, a short discussion on the role play by the convective mechanisms is given in order to provide integration of the exposed ideas.