Dodecylphosphonic acid (DPA): a highly efficient catalyst for the synthesis of 2H-indazolo[2,1-b]phthalazine-triones under solvent-free conditions

A new green protocol has been developed for the synthesis of 2H-indazolo[2,1-b]phthalazine-triones via one-pot, three-component condensation reaction of aromatic aldehydes with 1,3-dicarbonyl compounds and phthalhydrazide using reusable dodecylphosphonic acid (DPA) as heterogeneous solid acid catalyst under solvent-free conditions. This protocol provides a novel and improved method for obtaining 2H-indazolo[2,1-b]phthalazine-triones in terms of good yields with little catalyst loading.     

Resolvability in circulant graphs

A set W of the vertices of a connected graph G is called a resolving set for G if for every two distinct vertices u, v ∈ V (G) there is a vertex w ∈ W such that d(u, w) ≠ d(v, w). A resolving set of minimum cardinality is called a metric basis for G and the number of vertices in a metric basis is called the metric dimension of G, denoted by dim(G). For a vertex u of G and a subset S of V (G), the distance between u and S is the number min s∈S d(u, s). A k-partition Π = {S 1 , S 2 , . . . , S k } of V (G) is called a resolving partition if for every two distinct vertices u, v ∈ V (G) there is a set S i in Π such that d(u, Si )≠ d(v, Si ). The minimum k for which there is a resolving k-partition of V (G) is called the partition dimension of G, denoted by pd(G). The circulant graph is a graph with vertex set Zn , an additive group of integers modulo n, and two vertices labeled i and j adjacent if and only if i-j (mod n) ∈ C , where CZn has the property that C =-C and 0 ■ C. The circulant graph is denoted by Xn, Δ where Δ = |C|. In this paper, we study the metric dimension of a family of circulant graphs Xn, 3 with connection set C = {1, n/2 , n-1} and prove that dim(Xn, 3 ) is independent of choice of n by showing that dim(Xn, 3 ) ={3 for all n ≡ 0 (mod 4), 4 for all n ≡ 2 (mod 4). We also study the partition dimension of a family of circulant graphs Xn,4 with connection set C = {±1, ±2} and prove that pd(Xn, 4 ) is independent of choice of n and show that pd(X5,4 ) = 5 and pd(Xn,4 ) ={3 for all odd n ≥ 9, 4 for all even n ≥ 6 and n = 7.     

Series solutions for the stagnation flow of a second-grade fluid over a shrinking sheet

This study derives the analytic solutions of boundary layer flows bounded by a shrinking sheet. With the similarity transformations, the partial differential equations are reduced into the ordinary differential equations which are then solved by the homotopy analysis method （HAM）. Two-dimensional and axisymmetric shrinking flow cases are discussed.     

Numerical investigations of asymmetric flow of a micropolar fluid between two porous disks

Numerical solution is presented for the two- dimensional flow of a micropolar fluid between two porous coaxial disks of different permeability for a range of Reynolds number Re （-300≤ Re 〈 0） and permeability parameter A （1.0≤A ≤2.0）. The main flow is superimposed by the injection at the surfaces of the two disks. Von Karman＇s similarity transformations are used to reduce the governing equations of motion to a set of non-linear coupled ordinary differential equations （ODEs） in dimensionless form. An algorithm based on the finite difference method is employed to solve these ODEs and Richardson＇s extrapolation is used to obtain higher order accuracy. The results indicate that the parameters Re and A have a strong influence on the velocity and microrotation profiles, shear stresses at the disks and the position of the viscous/shear layer. The micropolar material constants cl, c2, c3 have profound effect on microrotation as compared to their effect on streamwise and axial velocity profiles. The results of micropolar fluids are compared with the results for Newtonian fluids.     

Hydromagnetic free convection flow with induced magnetic field effects

An exact solution is presented for the hydromagnetic natural convection boundary layer flow past an infinite vertical flat plate under the influence of a transverse magnetic field with magnetic induction effects included. The transformed ordinary differential equations are solved exactly, under physically appropriate boundary conditions. Closed-form expressions are obtained for the non-dimensional velocity (u), non-dimensional induced magnetic field component (B _x ) and wall frictional shearing stress i.e. skin friction function (τ _x ) as functions of dimensionless transverse coordinate (η), Grashof free convection number (G _r ) and the Hartmann number (M). The bulk temperature in the boundary layer (Θ) is also evaluated and shown to be purely a function of M. The Rayleigh flow distribution (R) is derived and found to be a function of both Hartmann number (M) and the buoyant diffusivity parameter (ϑ ^*). The influence of Grashof number on velocity, induced magnetic field and wall shear stress profiles is computed. The response of Rayleigh flow distribution to Grashof numbers ranging from 2 to 200 is also discussed as is the influence of Hartmann number on the bulk temperature. Rayleigh flow is demonstrated to become stable with respect to the width of the boundary layer region and intensifies with greater magnetic field i.e. larger Hartman number M, for constant buoyant diffusivity parameter ϑ ^*. The induced magnetic field (B _x ), is elevated in the vicinity of the plate surface with a rise in free convection (buoyancy) parameter G _r , but is reduced over the central zone of the boundary layer regime. Applications of the study include laminar magneto-aerodynamics, materials processing and MHD propulsion thermo-fluid dynamics.     

Effect of an Exit-Wedge Angle on Pinch-off and Mass Entrainment of Vortex Rings in Air

The effects of exit-wedge angle on evolution, formation, pinch-off, propagation and diffusive mass entrainment of vortex rings in air were studied using digital particle image velocimetry. Vortex rings were generated by passing a solenoid-valve-controlled air jet through a cylindrical nozzle. Experiments were performed over a wide range of exit-wedge angles (10° ≤ α ≤ 90°) of the cylindrical nozzle, initial Reynolds numbers (450 ≤ Re ≤ 4,580) and length-to-diameter ratios (0.9 ≤ L/D ≤ 11) of the air jet. For sharp edges (α ≤ 10°), a secondary ring may emerge at high Reynolds numbers, which tended to distort the vortex ring if ingested into it. For blunt edges (α ≥ 45°), by contrast, stable vortex rings were produced. The formation phase of a vortex ring was found to be closely related to its evolution pattern. An exit-wedge angle of 45° was found to be optimal for rapid pinch-off and faster propagation and better stability of a vortex ring. Diffusive mass entrainment was found to be between 35% and 40% in the early stages of a vortex ring propagation and it gradually increased throughout the course of vortex ring propagation. Entrainment fraction was found to be sensitive to the L/D ratio of the initial jet and decreases when the L/D ratio is increased.     

Investigation on the impact of thermal performance of fluid due to hybrid nano-structures

Journal of Thermal Analysis and Calorimetry - This article explores the role of hybrid nano-particles in enhancing the thermal performance of Sutterby fluid over a two-dimensional body of variable...     

Interaction of a Surface-Active Ionic Liquid with an Antidepressant Drug: Micellization and Spectroscopic Studies

The interaction of the antidepressant drug nortriptyline hydrochloride (NOT) with the surface-active ionic liquid (SAIL), 1-decyl-3-methylimidazolium chloride, [C₁₀mim][Cl], has been studied using multiple techniques, including conductometric titration, tensiometric, fluorometric, dynamic light scattering and UV–visible spectrophotometric measurements. There is a significant decrease in the cmc of SAIL on the addition of the drug NOT, indicating adsorption of drug molecules in the outer portion of the micelle. In the present study, the values of the packing parameter, P, lie in the range of 0–0.3, which suggests that the micelles formed are spherical in nature. More negative values of the standard Gibbs energy of adsorption, \( \Delta G_{\text{ad}}^{ \circ } \), compared to \( \Delta G_{\text{m}}^{ \circ } \) support our contention that adsorption of SAIL on the air-solution interface is relatively more favorable than its micellization in the presence of NOT. Fluorescence and DLS studies indicate that the aggregation number, N_agg, and hydrodynamic radius of SAIL increase with increase in concentration of NOT. The UV–visible spectroscopic study confirms the formation of a new complex between SAIL and NOT; this is also supported by the negative Gibbs energy of complexation.     

Ethyl (6aRS,8RS,12bRS)‐6‐oxo‐8‐phenyl‐6a,7,8,12b‐tetra­hydro‐6H‐benzo­[b]naphtho­[1,2‐d]­pyran‐6a‐carboxylate

In the title compound, C₂₆H₂₂O₄, the pyran­one ring adopts a twisted boat conformation, while the cyclo­hexane ring is close to an envelope conformation. The dihedral angle between the mean planes of the coumarin and naphthalene systems is 78.8 (1)°. The attached phenyl ring is in an equatorial position with respect to the cyclo­hexane ring.