On Solutions of Some Non-Linear Differential Equations Arising in Newtonian and Non-Newtonian Fluids

Some steady as well as unsteady solutions of the equations of motion for an incompressible Newtonian and non-Newtonian (second-grade) fluids are obtained by applying different methods including the Lie symmetry group method. The flows considered are axially symmetric with the swirling motion, and the governing equations for second-grade fluid flow have been modeled. Expressions for streamlines, velocity and vorticity components are constructed explicitly in each case. Exact analytical solutions in second-grade fluid are obtained and compared with the corresponding viscous solutions.     

Resonance behaviour of viscoelastic fluid in Poiseuille flow in the presence of a transversal magnetic field

The oscillatory flow of a viscoelastic fluid in a circular pipe under the influence of a transversal magnetic field is studied. Exact solutions for the axial velocity and flow rate are presented. The velocity enhancement and the resonance behaviour are analysed both numerically and asymptotically in the case of small pipe radii. Approximations for the resonance frequencies and the achievable velocity enhancements are derived. Copyright © 2005 John Wiley & Sons, Ltd.     

Lie group analysis of viscoelastic MHD aligned flow and heat transfer

Exact solutions for an incompressible, viscoelastic, electrically conducting MHD aligned fluid are obtained for velocity components and temperature profiles. Lie Group method is applied to obtain the solution and the symmetries used are of translational type.The English text was polished by Keren Wang and Yunming Chen.     

Structural and Electronic (Absorption and Fluorescence) Properties of a Stable Triplet Diphenylcarbene: A DFT Study

A triplet diphenylcarbene, bis[3-bromo-5-(trifluoromethyl)[1,1'-biphenyl]-4-yl]methylidene (B3B), with exceptional stability was discovered by chemists from Japan's Mie University. To investigate its different quantum chemical features, a theoretical analysis was predicated on Density Functional Theory (DFT) and Time Dependent-DFT (TD-DFT) based technique. According to the findings, the singlet–triplet energy gap (ES-T), as well as HOMO–LUMO energy bandgap (E_H-L), was found to be diminished when nucleophilicity (N) rose. We looked at the geometrical dimensions, molecular orbitals (MOs), electronic spectra, electrostatic potential, molecular surfaces, reactivity characteristics, and thermodynamics features of the title carbene (B3B). Its electronic spectra in different solvents were calculated using TD-DFT and Polarizable Continuum Model (PCM) framework. The estimated absorption maxima of B3B were seen between 327 and 340 nm, relying on the solvents, and were attributed to the S⁰?→?S¹ transition. Estimated fluorescence spectral peaks were found around 389 and 407 nm with the S¹ and S⁰ transitions being identified. Its fluorescence/absorption intensities revealed a blue shift change when the solvent polarity was increased. The least exciting state has been discovered to be the π?→?π^* charge-transfer (CT) phase. According to the Natural Bonding Orbital (NBO) exploration, ICT offers a significant role in chemical system destabilization. Furthermore, several hybrid features were used to determine the NLO (nonlinear optical) features (polarizability, first-order hyperpolarizability, and dipole moment). The calculated values suggest that B3B is a promising candidate for further research into nonlinear optical properties.

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