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.     

Structural,dielectric and electrical properties of zinc doped nickel nanoferrites prepared by simplified sol–gel method

Zinc doped nickel ferrite nanoparticles having the general formula Ni_1−xZn_xFe₂O₄ (x = 0.1, 0.2, 0.3, 0.4, 0.5) were prepared with simplified sol–gel method. The structural and dielectric properties of these samples sintered at 750 ± 5 °C were studied. X-ray diffraction patterns confirm the single phase spinel structure for prepared samples. The scanning electron microscope images indicated that the particle size of the samples lies in the nanometer regime. The dielectric constant (ε_r) and dielectric loss tangent (tan δ) of nanocrystalline nickel ferrites were investigated as a function of frequency and Zn concentration. The dependence of ε_r and tan δ on the frequency of the alternating applied electric field is in accordance with the Maxwell–Wagner model. The prepared samples have a lowest dielectric constant compared to the already reported samples of the same composition to the best of our knowledge. The effect of Zn doping on the dielectric properties of nickel ferrites is explained on the basis of cations distribution in the crystal structure.     

Synthesis, characterization and fluorescent property evaluation of 1,3,5-triaryl-2-pyrazolines

A series of 1,3,5-triaryl-2-pyrazolines was synthesized by dissolving the corresponding 4-alkoxychalcones in glacial acetic acid containing a few drops of concentrated hydrochloric acid. This step was followed by the addition of (3,4-dimethylphenyl) hydrazaine hydrochloride. Finally the target compounds were precipitated by pouring the reaction mixture onto crushed ice. The structures of the synthesized compounds were established by physicochemical and spectroscopic methods. The 1,3,5-triaryl-2-pyrazolines bearing homologous alkoxy groups were found to possess fluorescence properties in the blue region of the visible spectrum when irradiated with ultraviolet radiation. The fluorescent behavior of these compounds was studied by UV-Vis and emission spectroscopy, performed at room temperature.     

Linearizability criteria for systems of two second-order differential equations by complex methods

Lie??s linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing transformations but also the solutions of the nonlinear equations. Here, complex methods for a scalar ordinary differential equation are used for linearizing systems of two second-order ordinary and partial differential equations, which can use the power of the geometric method for writing the solutions. Illustrative examples of mechanical systems including the Lane?CEmden type equations which have roots in the study of stellar structures are presented and discussed.     

Perturbation analysis of a modified second grade fluid over a porous plate

A modified second grade non-Newtonian fluid model is considered. The model is a combination of power-law and second grade fluids in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The flow of this fluid is considered over a porous plate. Equations of motion in dimensionless form are derived. When the power-law effects are small compared to second grade effects, a regular perturbation problem arises which is solved. The validity criterion for the solution is derived. When second grade effects are small compared to power-law effects, or when both effects are small, the problem becomes a boundary layer problem for which the solutions are also obtained. Perturbation solutions are contrasted with the numerical solutions. For the regular perturbation problem of small power-law effects, an excellent match is observed between the solutions if the validity criterion is met. For the boundary layer solution of vanishing second grade effects however, the agreement with the numerical data is not good. When both effects are considered small, the boundary layer solution leads to the same solution given in the case of a regular perturbation problem.     

Homotopy Solution for the Channel Flow of a Third Grade Fluid

The solution for the flow of a third grade fluid bounded by two parallel porous plates is given using homotopy analysis method (HAM). A comparison is made with the exact numerical solution for the various values of the physical parameters. It is found that a proper choice of the auxiliary parameter occurring in HAM solution gives very close results.     

Fission-fragment energy correlation measurements for (nth, f) of 232U and 233U

Fission-fragment mass and kinetic energy distributions and their correlations have been measured for ²³²U and ²³³U. The results on these uranium isotopes and ²³⁵U are compared. The mass peak/valley ratio of 785 ± 68 for ²³²U is the highest of the three isotopes. The 〈E_K〉(μ_H) distributions show significant differences. The dip ΔE_K at symmetry is $\text{16.2 ± 1.0}\text{MeV}\text{(}{}^{232}\text{U}\text{)}$, $\text{17.0 ± 1.0}\text{MeV}\text{(}{}^{233}\text{U}\text{)}\text{and}\text{20.6 ± 1.1}\text{MeV}\text{(}{}^{235}\text{U}\text{)}$. In the yields for high-kinetic-energy-selected events, the mass 134 dominates for ²³³U and ²³⁵U, but for ²³²U it is μ_H≈144, which dominates. This complete reversal of profiles can be understood in terms of fragment shells.     

Vibrational analysis of the products from thermal decomposition of OCS and CO2

The thermal decomposition of CO₂ and OCS has been studied using a shock tube and cw CO probe laser. The energies of activation are in good agreement with the values of other workers. It has been shown that the CO formed from OCS has an initial non-thermal vibrational distribution with a large excess in ν = 0.     

Fission-fragment energy correlation measurements for 252Cf(sf) and structures in far-out asymmetric fission

Fragment-mass and kinetic-energy distribution measurements for ²⁵²Cf(sf) have been extended to the far-out asymmetric low-yield fission region of M_H = 190 compared with the existing data that go up to M_H ≈ 168. The mass yield Y(m) shows a shoulder for M_H ≈ 163 and an important enhancement for M_H ? 176. The 〈E_K〉(m), σ_EK(m) and, to a lesser extent, Y(m) distributions show strong and correlated amplitude fluctuations for M_H ? 170. These data indicate strong and rapid changes in deformation of the nascent fragments and the coexistence of more than one deformed-shell stabilized scission configuration for the same mass splits. These structures and those present in the relatively high-yield regions are discussed in terms of the static macro-microscopic potential-energy calculations.