Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H2O nanofluid on a flat surface in a porous medium: A stability analysis

The nanofluid and porous medium together are able to fulfill the requirement of high cooling rate in many engineering problems. So, here the impact of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium is examined. Moreover, the thermal radiation and viscous dissipation effects are considered. The problem governing partial differential equations are converted into self-similar coupled ordinary differential equations and those are numerically solved by the shooting method. The computed results can reveal many vital findings of practical importance. Firstly, dual solutions exist for decelerating unsteady flow and for accelerating unsteady and steady flows, the solution is unique. The presence of nanoparticles affects the existence of dual solution in decelerating unsteady flow only when the medium of the flow is a porous medium. But different shapes of nanoparticles are not disturbing the dual solution existence range, though it has a considerable impact on thermal conductivity of the mixture. Different shapes of nanoparticles act differently to enhance the heat transfer characteristics of the base fluid, i.e., the water here. On the other hand, the existence range of dual solutions becomes wider for a larger permeability parameter related to the porous medium. Regarding the cooling rate of the heated surface, it rises with the permeability parameter, shape factor (related to various shapes of Cu-nanoparticles), and radiation parameter. The surface drag force becomes stronger with the permeability parameter. Also, with growing values of nanoparticle volume fraction, the boundary layer thickness (BLT) increases and the thermal BLT becomes thicker with larger values of shape factor. For decelerating unsteady flow, the nanofluid velocity rises with permeability parameter in the case of upper branch solution and an opposite trend for the lower branch is witnessed. The thermal BLT is thicker with radiation parameter. Due to the existence of dual solutions, a linear stability analysis is made and it is concluded that the upper branch and unique solutions are stable solutions.     

A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis

A nonlocal Boussinesq equation is deduced from the local one by using consistent correlated bang method. To study various exact solutions of the nonlocal Boussinesq equation, it is converted into two local equations which contain the local Boussinesq equation. From the N-soliton solutions of the local Boussinesq equation, the N-soliton solutions of the nonlocal Boussinesq equation are obtained, among which the (N=2,3,4)-soliton solutions are analyzed with graphs. Some periodic and traveling solutions of the nonlocal Boussinesq equation are derived directly from the known solutions of the local Boussinesq equation. Symmetry reduction solutions of the nonlocal Boussinesq equation are also obtained by using the classical Lie symmetry method.     

Studies on the growth and characterization of tris (glycine) calcium(ΙΙ) dichloride—a nonlinear optical crystal

A systematic characterization of a novel nonlinear optical material tris (glycine) calcium(ΙΙ) dichloride (TGCC) is performed. The solubility and metastable zone width of TGCC were studied. TGCC single crystal of dimensions 34×23×5 mm³ was grown by the slow evaporation technique. Single crystal X-ray diffraction studies reveal that the crystal belongs to orthorhombic system. Energy dispersive X-ray analysis confirms the presence of elements in the crystal. Structural perfection of the as-grown single crystal was studied through multicrystal X-ray diffraction analysis. The thermal characteristics of TGCC were analyzed by thermogravimetric and differential thermal analysis and differential scanning calorimetry. The transmittance of TGCC crystal has been used to calculate the optical band gap of the crystal. Chemical etching studies of TGCC crystal was carried out. The dielectric and mechanical behavior of the crystals were analyzed. The second harmonic conversion property of TGCC was identified by the Kurtz and Perry powder technique and was observed to be higher than that of KDP.     

Growth, optical and thermal studies on organic nonlinear optical crystal: 2-Furoic acid

2-Furoic acid (2FA), an organic third order nonlinear optical single crystal, has been synthesized and grown successfully by slow solvent evaporation technique. The space group and lattice parameters of the grown crystals were obtained by single crystal X-ray diffraction analysis. The presence of the functional groups was confirmed by Fourier Transform Infrared (FTIR) spectroscopy. Optical absorption studies reveal low absorption in the UV and visible regions and the UV cut-off wavelength is found to be at 240 nm. The thermal stability of the material examined by TGA analysis, reveals that the material is thermally stable up to 130 °C. The third order nonlinear optical parameters (nonlinear refractive index, nonlinear absorption coefficient and real and imaginary parts of the third order nonlinear optical susceptibility) were derived by Z-scan technique. This reveals that the crystal has a negative refractive index, which indicates the defocusing nature of the material.     

Growth, optical, mechanical and dielectric studies on NLO active pure and metal ion doped single crystals of bis-thiourea zinc chloride

Good quality single crystals of pure and metal ion (Ni²⁺) doped bis-thiourea zinc chloride (BTZC) possessing excellent nonlinear optical properties have been grown from aqueous solution by the slow solvent evaporation technique. The lattice parameters of the grown crystals are determined by single crystal X-ray analysis. The well defined sharp peaks in the powder X-ray diffraction pattern reveals the crystalline perfection and the EDAX spectrum confirms the presence of dopant in the lattice of the parent crystal. The DRS UV-visible spectral study reveals improved transparency for the doped crystal, ascertaining the inclusion of metal ion in the lattice. The optical band gap of the pure and doped crystals was calculated to be 4.8 and 5.2 eV respectively from the UV transmission spectrum. The vickers hardness test brings forth higher hardness value for Ni²⁺doped BTZC as compared to pure BTZC crystal. The dielectric measurement exhibits very low dielectric constant and dielectric loss at higher frequencies for both the pure and Ni²⁺doped BTZC. The existence of second harmonic generation signals in the crystal also has been confirmed by performing the Kurtz powder test.     

An Exner-based coupled model for two-dimensional transient flow over erodible bed

Transient flow over erodible bed is solved in this work assuming that the dynamics of the bed load problem is described by two mathematical models: the hydrodynamic model, assumed to be well formulated by means of the depth averaged shallow water equations, and the Exner equation. The Exner equation is written assuming that bed load transport is governed by a power law of the flow velocity and by a flow/sediment interaction parameter variable in time and space. The complete system is formed by four coupled partial differential equations and a genuinely Roe-type first order scheme has been used to solve it on triangular unstructured meshes. Exact solutions have been derived for the particular case of initial value Riemann problems with variable bed level and depending on particular forms of the solid discharge formula. The model, supplied with the corresponding solid transport formulae, is tested by comparing with the exact solutions. The model is validated against laboratory experimental data of different unsteady problems over erodible bed.     

A Revisit on the Derivation of the Particular Solution for the Differential Operator ∆2 ± λ2

In this paper, we applied the polyharmonic splines as the basis functions to derive particular solutions for the differential operator ∆² ± λ². Similar to the derivation of fundamental solutions, it is non-trivial to derive particular solutions for higher order differential operators. In this paper, we provide a simple algebraic factorization approach to derive particular solutions for these types of differential operators in 2D and 3D. The main focus of this paper is its simplicity in the sense that minimal mathematical background is required for numerically solving higher order partial differential equations such as thin plate vibration. Three numerical examples in both 2D and 3D are given to validate particular solutions we derived.     

垂直上升管内非牛顿流体流动沸腾的壁温工况和临界热负荷

本文研究了一种非牛顿流体-高聚物水溶液在垂直上升管内强制流动沸腾过程中的壁温沿管长变化及临界热负荷的特点，并考察了高聚物种类、浓度、质量流速等对临界热负荷和壁温工况的影响。