Average and extremal properties of heat transfer and shear stress on a wall surface in Rayleigh–Bénard convection

In this study surface-averaged and extremal properties of heat transfer and shear stress on the upper wall surface of Rayleigh–Bénard convection are numerically examined. The Prandtl number was raised up to 10³, and the Rayleigh number was changed between 10⁴ and 10⁷. As a result, average Nusselt number Nu and shear rate τ/Pr depends on Pr, Ra, and the entire numerical results are distributed between two correlation equations corresponding to small and large Pr. The small and large Pr equations are closely related to steady and unsteady flow regimes, respectively. Nevertheless, a single relation τ/Pr ~ Nu ^3.0 exists to explain the entire results. Similarly the change of local maximal properties Nu _max and τ _max/Pr depends on Pr, Ra, and these values are also distributed between two correlation equations corresponding to small and large Pr cases. Despite such complicated dependence we can obtain a correlation equation as a form of τ _max/Pr ~ Nu _max^2.6, which has not been obtained theoretically.     

Entropy Solutions in <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">∞</Emphasis></Superscript> for the Euler Equations in Nonlinear Elastodynamics and Related Equations

A compactness framework is established for approximate solutions to the Euler equations in one-dimensional nonlinear elastodynamics by identifying new properties of the Lax entropies, especially the higher order terms in the Lax entropy expansions, and by developing ways to employ these new properties in the method of compensated compactness. Then this framework is applied to establish the existence, compactness, and decay of entropy solutions in L for the Euler equations in nonlinear elastodynamics with a more general stress-strain relation than those for the previous existence results. This compactness framework is further applied to solving the Euler equations of conservation laws of mass, momentum, and energy for a class of thermoelastic media, and the equations of motion of viscoelastic media with memory.     

MHD flow and heat transfer of a power-law non-Newtonian nanofluid (Cu–H<Subscript>2</Subscript>O) over a vertical stretching sheet

A steady-state mixed convection boundary layer flow of an electrically conducting nanofluid (Cu–H₂O) obeying a power-law model in the presence of an alternating magnetic field due to a stretching vertical heated sheet is investigated numerically through the use of Wolfram Mathematica. The surface stretching velocity and the surface temperature are assumed to vary as linear functions of the distance from the origin. A similarity solution is presented, which depends on the nanoparticle volume fraction, power-law parameter, magnetic field parameter, buoyancy convection parameter, and modified Prandtl number.     

Young’s modulus defect for the solid solution of hydrogen in palladium (PdH<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>)

We use the internal friction method in the free vibration mode to study the temperature dependence of the spectra of dissipative losses and shear modulus in the Pd polycrystalline system, the PdH _x penetration solid solution, and in the dehydrogenized Pd system. Studying the spectra and shear moduli, we discovered that the hydrogen desorption from the α- and β-phases of the PdH _x system occurs completely after the first cycle of heating of this system. The temperature dependences of the shear modulus of the original and dehydrogenized systems coincide. The existence of dissipative processes in the solid solution is related to the mobility of hydrogen atoms in the face-centered cubic lattice of the Pd structure and provokes the appearance of peaks of losses on the modulus defect spectrum in the temperature region. We consider the possibility of describing the modulus defect in the framework of phenomenological models of elasticity. Dissolution of hydrogen atoms in a metal structure results in changes in the physical-mechanical characteristics of the obtained solid solutions compared with the original dehydrogenized metals.