Effect of Nonlinear Convection on Stratified Flow of Third Grade Fluid with Revised Fourier-Fick Relations

Here thermal dependence conductivity and nonlinear convection features in third-grade liquid flow bounded by moving surface having varying thickness are formulated. Stagnation point flow is considered. Revised FourierFick relations and double stratification phenomena are utilized for modeling energy and concentration expressions.Mathematical model of considered physical problem is achieved by implementing the idea of boundary layer theory. The acquired partial differential system is transformed into ordinary ones by employing relevant variables. The homotopic scheme yield convergent solutions of governing nonlinear expressions. Graphs are constructed for distinct values of physical constraints to elaborate the heat/mass transportation mechanisms.     

MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions

This article concentrates on the steady magnetohydrodynamic(MHD) flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper(Cu), Silver(Ag), Alumina(Al2O3) and Titanium Oxide(TiO2). Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.     

Dual solutions in boundary layer flow of Maxwell fluid over a porous shrinking sheet

An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations（PDEs） are converted into a nonlinear self-similar ordinary differential equation（ODE）. For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions.     

Non-existence of Global Solutions to a System of Fractional Diffusion Equations

We present non-existence results for a system of non-linear parabolic equations with non-local diffusions posed either in \(\mathbb{R}^{N} \) or in a bounded domain. Our method of proof is based on the test function method with a judicious choice of the test function.     

Darcy–Forchheimer three-dimensional flow of carbon nanotubes with nonlinear thermal radiation

The present study elaborates three-dimensional (3D) thermally radiative flow of carbon nanotubes dispersed in water with Darcy–Forchheimer porous space. A bidirectional linear stretchable sheet is used to generate the flow. Darcy–Forchheimer relation specifies porous space. Single-wall carbon nanotubes and multi-wall carbon nanotubes are accounted. Solutions development is due to optimal homotopy analysis technique. Optimal data of sundry variables are obtained. The optimal solution interpretations of velocities and temperature are interpreted via plots. Physical quantities are also elaborated. Our results reveal that thermal field against radiation and temperature ratio parameter is enhanced.

     

Local and blowing‐up solutions for a space‐time fractional evolution system with nonlinearities of exponential growth

Local and blowing‐up solutions for the Cauchy problem for a system of space and time fractional evolution equations with time‐nonlocal nonlinearities of exponential growth are considered. The existence and uniqueness of the local mild solution is assured by the Banach fixed point principle. Then, we establish a blow‐up result by Pokhozhaev capacity method. Finally, under some suitable conditions, an estimate of the life span of blowing‐up solutions is established.     

Asymptotical stability analysis of Riemann‐Liouville q‐fractional neutral systems with mixed delays

This paper investigates the asymptotical stability of Riemann‐Liouville q‐fractional neutral systems with mixed delays (constant time delay and distributed delay). By constructing some appropriate Lyapunov‐Kravsovskii functionals, some sufficient conditions on delay‐dependent and delay‐independent asymptotical stability are obtained in terms of linear matrix inequality (LMI). Our employed method is based on the direct calculation of quantum derivatives of the Lyapunov‐Kravsovskii functionals. Finally, two examples are presented to demonstrate the availability of our obtained results.     

Nonexistence results for higher order pseudo‐parabolic equations in the Heisenberg group

Sufficient conditions are obtained for the nonexistence of solutions to the nonlinear higher order pseudo‐parabolic equation where is the Kohn‐Laplace operator on the (2N + 1)‐dimensional Heisenberg group , m≥1,p > 1. Then, this result is extended to the case of a 2 × 2‐system of the same type. Our technique of proof is based on judicious choices of the test functions in the weak formulation of the sought solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

Indeno[1,2-b]pyridin-5-one derivatives containing azo groups and their hydrazonal precursors: Synthesis,antimicrobial profile,DNA gyrase binding affinity,and molecular docking

The prevalence of germs that are resistant to many antibiotics is rising rapidly the world over. There is a large group of researchers actively looking for better medicines. Here, we designed two series of hydrazonal and indeno[1,2-b]pyridin-5-one bearing hydrazone and azo-groups to test their antimicrobial activity. Molecular structures of all derivatives were assured based on their spectral data and elemental analyses. Results of the antimicrobial activity of the tested hydrazone and azo compounds showed promising potential for several derivatives. The minimum inhibitory concentrations (MICs) of hydrazones 4a - h and 6a - g displayed good antibacterial reactivities with a range of 3.91–250 μg/mL and moderate antifungal activity with a range of 15.6–500 μg/mL. The most promising hydrazone 4f and azo- 6a compounds demonstrated MIC values against Streptococcus faecalis and Escherichia coli equal to 3.91 and 7.81 μg/mL, respectively. Moreover, azo compound 6a showed MIC value equal to 3.91 μg/mL against Enterobacter cloacae species. Additionally, derivative 4f exhibited a significant inhibitory profile against the E. coli gyrase A enzyme (IC₅₀ = 5.53 μg/mL). On the other hand, compound 6a (IC₅₀ 14.05 μg/mL) exhibited the lowest DNA gyrase inhibitory activity as compared to compounds 4f and reference standard drug novobiocin, IC₅₀ 5.53 and 1.88 μg/mL, respectively. Pharmacokinetic and pharmacodynamic profiles and molecular docking studies for the two most promising molecules 4f and 6a were computed and revealed that both compounds have good ADME profiles and high binding affinity to DNA gyrase binding site.     

Effects of heat generation/absorption on stagnation point flow of nanofluid over a surface with convective boundary conditions

Analysis has been conducted to analyze the stagnation point flow of nanofluid near a permeable stretched surface with convective boundary condition. The relevant problem formulation is presented in the presence of porous medium and internal heat generation/absorption. The effects of Brownian motion and thermophoresis occur in the transport equations. The velocity, temperature and nanoparticle concentration profiles are analyzed with respect to the involved parameters of interest namely Brownian motion parameters, thermophoresis parameter, permeability parameter, source/sink parameter, ratio of rate constants to free stream velocity and stretching velocity, Biot number and Prandtl number. A comparative study between the previous published and present results in a limiting sense is found in an excellent agreement.