Many different forms of the de Sitter metric in different coordinate systems are used in the general relativity literature. Two of them are the most common, the static form and the cosmological (exponentially expanding) form. The staticity and non-stationarity of these two different forms are traced back to the noncomoving and comoving nature of the corresponding coordinate systems. In this paper using the quasi-Maxwell form of the Einstein field equations and a definition of static spacetimes based upon them, we look at these two different forms of the same solution from a new perspective which classifies them as a special case in a general one-parameter family of solutions. fluid's velocity in defining a preferred (comoving) coordinate system in de Sitter-type spacetimes.

Unlike the Lorentz transformation which replaces the Galilean transformation among inertial frames at high relative velocities, there seems to be no such a consensus in the case of coordinate transformation between inertial frames and uniformly rotating ones. There have been some attempts to generalize the Galilean rotational transformation to high rotational velocities. Here we introduce a modified version of one of these transformations proposed by Philip Franklin in 1922. The modified version is shown to resolve some of the drawbacks of the Franklin transformation, specially with respect to the corresponding spacetime metric in the rotating frame. This new transformation introduces non-inertial eccentric observers on a uniformly rotating disk and the corresponding metric in the rotating frame is shown to be consistent with the one obtained through Galilean rotational transformation for points close to the rotation axis. Employing the threading formulation of spacetime decomposition, spatial distances and time intervals in the spacetime metric of a rotating observer's frame are also discussed.

Employing a relativistic rotational transformation to study and analyze rotational phenomena, instead of the rotational transformations based on consecutive Lorentz transformations and Fermi coordinates, leads to different predictions. In this article, after a comparative study between the Fermi metric of a uniformly rotating eccentric observer and the spacetime metric in the same observer's frame obtained through the modified Franklin transformation, we consider rotational phenomena including the transverse Doppler effect and the Sagnac effect in both formalisms and compare their predictions. We also discuss length measurements in the two formalisms.

In a recent paper EPJC 79:187 the general relativistic framework of the Sagnac effect was investigated. We have some comments on this paper. We show that their conclusion about the apparent variation of the speed of light does not hold in stationary spacetimes. Also, We show that their definition of gravitational Coriolis potential and gravitational Coriolis time dilation are inconsistent with what is stated in standard references. * Electronic address: ramezani@gonabad.ac.ir

The electrically conducting magnetic nanofluid of Fe3O4-water was made to flow in a heat exchanger. Afterwards, the ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD) effects of the nanofluid on the enhancement of the overall heat transfer coefficient of the heat exchanger were studies at different nanofluid concentrations, inlet temperatures, and different constant magnetic field intensities. The study dealt with both laminar and turbulent nanofluid flows. The electrical conductivity of the magnetic nanofluid was determined by a Jenway 4510 conductivity meter. By using the experimental data, a Sprint CFD code identified the hydrodynamic and thermal behavior of the nanofluid flow in the presence of constant magnetic fields of intensities of 0, 0.05, 0.1 and 1 Tesla. The results showed that an increase in the concentration of Fe3O4-water nanofluid enhanced its electrical conductivity so considerably that the nanofluid, at the volume fraction of 1%, was observed to be 12.5 times more electrically conductive than distilled water. Also, it was shown that increase in magnetic field intensity had an enhancing effect on the overall heat transfer coefficient, and the effect was stronger at higher magnetic nanofluid concentrations. Furthermore, due to generation of chainlike structures by the FHD effect of the Fe3O4 magnetic nanoparticles, the nanoparticles increased the effective thermal conductivity of the nanofluid and, consequently, the overall heat transfer coefficient in both the laminar and turbulent regimes. Finally, unlike the turbulent flow, the laminar regime allowed for the MHD effect having only a negligible effect on the enhancement of the overall heat transfer coefficient. This was due to velocities in the laminar regime being small.