The current investigation is carried out on the thin film flow of Reiner-Philippoff fluid of boundary-layer type. We have analyzed the flow of thin films of Reiner-Philippoff fluid in the changeable heat transmission and radiation over a time-dependent stretching sheet in 2D. The time-dependent governing equations of Reiner-Philippoff fluid model are simplified with the help of transformation of similarity variables. To investigate the behavior of the Reiner-Philippoff fluid with variable stretching surface for different physical effects, we considered thermophoresis and Brownian motion parameters in the flow. The Homotopy Analysis Method is implemented in the reduced model to achieve a solution of the original problem. A numerical convergence of the implemented method is also analyzed. The behavior of temperature, velocity, and concentration profiles have been investigated with the variation of skin friction, Nusselt number, and Sherwood number. A comparative graphical survey is presented for the velocity gradient, under different parameters. An analytical analysis is presented for the time-dependent parameter over thin film flow. The results we obtained are better than the previously available results. For the survey, the physical representation of the embedded parameters, like, $\beta$ depends on the stretching parameter $\zeta$ , and the Reiner-Philippoff fluid parameter $ϵ$ are discussed in detail and plotted graphically. Prandtl number $Pr$ , Brownian motion parameter $Nb$ , thermophoretic number $Nt$ , and Schmidt number $Sc$ are presented by graphs and discussed in detail.

In this research, the three-dimensional nanofluid thin-film flow of Casson fluid over an inclined steady rotating plane is examined. A thermal radiated nanofluid thin film flow is considered with suction/injection effects. With the help of similarity variables, the partial differential equations (PDEs) are converted into a system of ordinary differential equations (ODEs). The obtained ODEs are solved by the homotopy analysis method (HAM) with the association of MATHEMATICA software. The boundary-layer over an inclined steady rotating plane is plotted and explored in detail for the velocity, temperature, and concentration profiles. Also, the surface rate of heat transfer and shear stress are described in detail. The impact of numerous embedded parameters, such as the Schmidt number, Brownian motion parameter, thermophoretic parameter, and Casson parameter (Sc, Nb, Nt, γ), etc., were examined on the velocity, temperature, and concentration profiles, respectively. The essential terms of the Nusselt number and Sherwood number were also examined numerically and physically for the temperature and concentration profiles. It was observed that the radiation source improves the energy transport to enhance the flow motion. The smaller values of the Prandtl number, Pr, augmented the thermal boundary-layer and decreased the flow field. The increasing values of the rotation parameter decreased the thermal boundary layer thickness. These outputs are examined physically and numerically and are also discussed.

This work displays the structural, electronic, elastic, optical, and magnetic properties in spin-polarized configurations for cubic fluoroperovskite $AB{F}_3$ (A = Tl, B = Nb, V) compounds studied by density functional theory (DFT) by means of the Tran-Blaha-modified Becke-Johnson (TB-mBJ) approach. The ground state characteristics of these compounds, i.e., the lattice parameters $a_0$, bulk modulus (B), and its pressure derivative $\left(B\prime \right)$ are investigated. The structural properties depict that the selected compounds retain a cubic crystalline structure and have stable ground state energy. Electronic-band structures and DOS (density of states) in spin-polarized cases are studied which reports the semiconducting nature of both materials. The TDOS (total density of states) and PDOS (partial density of states) studies in both spin configurations show that the maximum contributions of states to the different bands is due to the B-site (p-states) atoms as well as F (p-states) atoms. Elastic properties including anisotropy factor (A), elastic constants, i.e., C₁₁, C₁₂, and C₄₄, Poisson’s ratio (υ), shear modulus and (G), Young’s modulus (E) are computed. In terms of elastic properties, the higher (bulk modulus) “B” and ratio of “B/G” yield that these materials exhibit a ductile character. Magnetic properties indicate that both the compounds are ferromagnetic. In addition, investigations of the optical spectra including the real (${\epsilon }_1\left(\omega \right)$) and imaginary (${\epsilon }_2\left(\omega \right)$) component of the dielectric function, refractive index $n\left(\omega \right)$, optical reflectivity $R\left(\omega \right)$, optical conductivity $\sigma \left(\omega \right)$, absorption coefficient $\alpha \left(\omega \right)$, energy loss function $L\left(\omega \right)$, and electron extinction coefficient $k\left(\omega \right)$ are carried out which shows the transparent nature of $TlV{F}_3$ and $TlNb{F}_3$. Based on the reported research work on these selected materials, their applications can be predicted in many modern electronic gadgets.

The 3D Carreau fluid flow through a porous and stretching (shrinking) sheet is examined analytically by taking into account the effects of mass transfer, thermal radiation, and Hall current. The model equations, which consist of coupled partial differential equations (PDEs), are simplified to ordinary differential equations (ODEs) through appropriate similarity relations. The analytical procedure of HAM (homotopy analysis method) is employed to solve the coupled set of ODEs. The functional dependence of the hydromagnetic 3D Carreau fluid flow on the pertinent parameters are displayed through various plots. It is found that the x-component of velocity gradient ($f^{{}^{\prime }}\left(\eta \right)$) enhances with the higher values of the Hall and shrinking parameters ($m,\varrho$), while it reduces with magnetic parameter and Weissenberg number ($M,We$). The y-component of fluid velocity ($g\left(\eta \right)$) rises with the augmenting values of m and M, while it drops with the augmenting viscous nature of the Carreau fluid associated with the varying Weissenberg number. The fluid temperature $\theta \left(\eta \right)$ enhances with the increasing values of radiation parameter ($Rd$) and Dufour number ($Du$), while it drops with the rising Prandtl number ($Pr$). The concentration field ($\varphi \left(\eta \right)$) augments with the rising Soret number ($Sr$) while drops with the augmenting Schmidt number ($Sc$). The variation of the skin friction coefficients ($C_{fx}$ and $C_{fz}$), Nusselt number ($N{u}_x$) and Sherwood number ($S{h}_x$) with changing values of these governing parameters are described through different tables. The present and previous published results agreement validates the applied analytical procedure.

We conducted a thorough investigation of Cs₂XCuF₆ (X = Sc, Y) using a first-principles approach, exploring a wide range of material properties. We began by confirming the structural and thermodynamic stability of these compounds, employing analyses such as formation energy calculations, examination of the phonon band structure, and the utilization of the Birch-Murnaghan equation of state (EOS) curve. A noteworthy finding was the tunability of the band gaps in these double perovskite materials, achieved by substituting Sc with Y, resulting in a band gap range from 2.67 to 2.62 eV. Our analysis extended to the mechanical stability of these compounds, characterized by elastic constants and revealing mechanical anisotropy and ductility. Additionally, we explored the optical properties, highlighting their broad absorption band from the infrared (IR) to visible regions, which holds significant promise for diverse optoelectronic applications. To provide a comprehensive understanding of these materials, we delved into their thermodynamic properties, encompassing thermal expansion coefficients (κ), heat capacities, entropy (S), volume, and Debye Temperature (θ _D). This investigation spanned a wide pressure range from 0 to 30 GPa and a temperature range from 0 to 1400 K, contributing to a holistic grasp of the fundamental characteristics of Cs₂XCuF₆ (X = Sc, Y).