On Maximum Signless Laplacian Estrada Indices of Graphs with Given Parameters

Signless Laplacian Estrada index of a graph $G$, defined as $SLEE(G)=\sum^{n}_{i=1}e^{q_i}$, where $q_1, q_2, \cdots, q_n$ are the eigenvalues of the matrix $\mathbf{Q}(G)=\mathbf{D}(G)+\mathbf{A}(G)$. We determine the unique graphs with maximum signless Laplacian Estrada indices among the set of graphs with given number of cut edges, pendent vertices, (vertex) connectivity and edge connectivity.Comment: 14 pages, 3 figure

Chemical reaction and heat transfer on boundary layer Maxwell Ferro-fluid flow under magnetic dipole with Soret and suction effects

AbstractIn this article, the influence of chemical reaction and heat transfer analysis of Maxwell saturated Ferro-fluid flow over a stretching sheet under the influence of magnetic dipole with Soret and suction effects are investigated. The sheet is assumed to be permeable in a semi-infinite domain. Firstly, partial differential equations of mass, momentum and concentration for the governing flow problem are modelled and converted into a system of differential equations by utilizing similarity approach. Then the solution of resulting non-linear differential equations is solved by efficient Runge-Kutta technique based on shooting algorithm with the help of MATLAB. Effect of all appropriate parameters like ferromagnetic interaction parameter, chemical reaction parameter, Maxwell parameter, Soret number, suction parameter, Maxwell parameter, Schmidt number, and suction parameter on velocity, temperature and concentration field are confirmed through graphs and table. From the present conclusions, it is examined that by increasing the Maxwell parameter there is a decrease in the fluid velocity and boundary layer thickness. On the other hand, the uprising behaviour is prominent for both temperature and concentration profiles. Also predicted that there is an enhancement in skin friction coefficient and rate of heat transfer by enlarging suction parameter, but opposite trend is noted for Sherwood number. Also noted that the values of Prandtl are taken ranges from 0.72 to 10. The Nusselt number increases from 1.09 to 4.80

The Effects of Variable Viscosity on the Peristaltic Flow of Non-Newtonian Fluid through a Porous Medium in an Inclined Channel with Slip Boundary Conditions

The present paper investigates the peristaltic motion of an incompressible non-Newtonian fluid with variable viscosity through a porous medium in an inclined symmetric channel under the effect of the slip condition. A long wavelength approximation is used in mathematical modeling. The system of the governing nonlinear partial differential equation has been solved by using the regular perturbation method and the analytical solutions for velocity and pressure rise have been obtained in the form of stream function. In the obtained solution expressions, the long wavelength and low Reynolds number assumptions are utilized. The salient features of pumping and trapping phenomena are discussed explicitly. The flow is investigated in a wave frame of reference moving with velocity of the wave. The features of the flow characteristics are analyzed by plotting the graphs of various values of the physical parameters in detail

Peristaltic Transport of a Jeffrey Fluid with Variable Viscosity through a Porous Medium in an Asymmetric Channel

The peristaltic flow of a Jeffrey fluid with variable viscosity through a porous medium in an asymmetric channel is investigated. The channel asymmetric is produced by choosing the peristaltic wave train on the wall of different amplitude and phase. The governing nonlinear partial differential equations for the Jeffrey fluid model are derived in Cartesian coordinates system. Analytic solutions for stream function, velocity, pressure gradient, and pressure rise are first developed by regular perturbation method, and then the role of pertinent parameters is illustrated graphically

Convection of heat and thermodynamic irreversibilities in two-phase, turbulent nanofluid flows in solar heaters by corrugated absorber plates

The effects of simultaneous implementation of corrugated walls and nanoparticles upon the performance of solar heaters are investigated. Triangular and sinusoidal wall profiles along with varying concentration of nanoparticles are analyzed. The multi-phase mixture and the SST κ-ω models are used to simulate turbulent nanofluid flows inside the corrugated channels. The staggered computational grid is employed for storing the velocity and pressure terms at cell faces and cell center, respectively. The governing equations are first discretized by employing a second-order upwind differencing technique and are then solved by means of pressure-based finite volume approach. The convergence criterion is also presented for the validation of obtained results. The effects of wall profiles and nanoparticle concentration on the pertinent parameters including Nusselt number, pressure drop, performance evaluation criterion (PEC), and thermal and frictional irreversibilities are studied. This reveals that, in general, the triangular duct features superior heat transfer and inferior hydraulic characteristics in comparison with the sinusoidal duct. It is demonstrated that as long as the base fluid (water) is used the highest value of PEC corresponds to the straight duct. Yet, by introducing nanofluids the PEC values of the corrugated ducts exceed those of the straight duct. The analysis further shows that on the basis of the performance evaluation criterion, the sinusoidal duct appears to be a better choice in comparison with the triangular duct. However, the situation is reversed when thermodynamic irreversibilities are considered. It is argued that vortex formation in the two investigated wavy walls and shear layer developed in the triangular case are the essential physical reasons for the observed thermal, hydraulic and entropic behaviors

CuO–Water Nanofluid Magnetohydrodynamic Natural Convection inside a Sinusoidal Annulus in Presence of Melting Heat Transfer

Impact of nanofluid natural convection due to magnetic field in existence of melting heat transfer is simulated using CVFEM in this research. KKL model is taken into account to obtain properties of CuO–H2O nanofluid. Roles of melting parameter (δ), CuO–H2O volume fraction (ϕ), Hartmann number (Ha), and Rayleigh (Ra) number are depicted in outputs. Results depict that temperature gradient improves with rise of Rayleigh number and melting parameter. Nusselt number detracts with rise of Ha. At the end, a comparison as a limiting case of the considered problem with the existing studies is made and found in good agreement

Dietary Calcium Intake, Vitamin D Status, and Bone Health in Postmenopausal Women in Rural Pakistan

The high prevalence of osteoporosis in Pakistan is of public-health concern. However, there is a paucity of information regarding nutrition and bone density in rural communities. The purpose of this study was to evaluate the dietary and lifestyle factors that impact bone health in Nahaqi. Data were collected from 140 postmenopausal women using an interviewer-administered 24-hour dietary recall questionnaire. Bone mineral density was estimated using the quantitative ultrasound index (QUI). Serum 25(OH)D was measured in fasting blood samples. The QUI scores revealed that 42% and 29% of the women had T-scores, indicative of osteopaenia and osteoporosis respectively. The mean calcium intake was 346 mg/d, which is less than 50% of the recommended daily intake. The QUI correlated with 25(OH)D after controlling for age (p=0.021, r=0.41, r2=0.168). Vitamin D deficiency and low intake of dietary calcium are two key factors contributing to poor bone health in this population

Exact Solution for Peristaltic Flow of Jeffrey Fluid Model in a Three Dimensional Rectangular Duct having Slip at the Walls

In the present article, we tried to develop the exact solutions for the peristaltic flow of Jeffrey fluid model in a cross section of three dimensional rectangular channel having slip at the peristaltic boundaries. Equation of motion and boundary conditions are made dimensionless by introducing some suitable nondimensional parameters. The flow is considered under the approximations of low Reynolds number and long wavelength. Exact solution of the obtained linear boundary value problem is evaluated. However, the expression for pressure rise is calculated numerically with the help of numerical integration. All pertinent parameters are discussed through graphs of pressure rise, pressure gradient, velocity and stream functions. It is found that presence of slip at the walls reduces the flow velocity but increases the peristaltic pumping characteristics