An exact solution for unsteady free convection flow of chemically reacting Al2O3−SiO2/water hybrid nanofluid

An unsteady natural convective boundary layer fluid flow of thick incompressible [Formula: see text] water hybrid nanofluid is discussed over an oscillating permeable stretching surface. The radiative and chemically reactive hybrid nanofluid flow is induced in rotating coordinates. Essential thermophysical properties of hybrid nanofluid are utilized. The boundary layer equations governing the present phenomena are converted into nondimensional form using appropriate dimension free transformations. The non dimensionalized partial differential equations are then solved analytically by Laplace transform technique and the exact solutions are attained. The performance of all the involving parameters are surveyed and the set of mathematical outputs for temperature, velocity and concentration are graphically depicted. The expressions for skin friction, Nusselt number and Sherwood number have been derived and the numerical results are displayed through tables and graphs. Growth of heat transfer rate is observed by rising radiation parameter and frequency of oscillation. Important aspects of the present study in the physical ground are examined.

Particle properties outside of the static limit in cosmology

It is shown that in the rest frame of the observer in expanding Universe states of particles with negative energy exist.The properties of such states are studied. The comparison with the case of negative energies of particles in black holes and rotating coordinates out of the static limit is made.