Norazak Senu

Stagnation-point flow over a permeable stretching/shrinking sheet in a copper-water nanofluid

An analysis is carried out to study the heat transfer characteristics of steady two-dimensional stagnation-point flow of a copper (Cu)-water nanofluid over a permeable stretching/shrinking sheet. The stretching/shrinking velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation-point. Results for the skin friction coefficient, local Nusselt number, velocity as well as the temperature profiles are presented for different values of the governing parameters. It is found that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique. The results indicate that the inclusion of nanoparticles into the base fluid produces an increase in the skin friction coefficient and the heat transfer rate at the surface. Moreover, suction increases the surface shear stress and in consequence increases the heat transfer rate at the fluid-solid interface.MSC: 34B15, 76D10.

A Three-Stage Fifth-Order Runge-Kutta Method for Directly Solving Special Third-Order Differential Equation with Application to Thin Film Flow Problem.

In this paper, a three-stage fifth-order Runge-Kutta method for the integration of a special third-order ordinary differential equation (ODE) is constructed. The zero stability of the method is proven. The numerical study of a third-order ODE arising in thin film flow of viscous fluid in physics is discussed. The mathematical model of thin film flow has been solved using a new method and numerical comparisons are made when the same problem is reduced to a first-order system of equations which are solved using the existing Runge-Kutta methods. Numerical results have clearly shown the advantage and the efficiency of the new method.

Effect of growing graphene flakes on branched carbon nanofibers based on carbon fiber on mechanical and thermal properties of polypropylene

A one-step process, the chemical vapor deposition method, has been used to fabricate graphene flakes (G) on branched carbon nanofibers (CNF) grown on carbon fibers (CF). In this contribution, the G–CNF–CF fibers have been used as reinforcing fillers in a polypropylene (PP) matrix in order to improve the mechanical and thermal properties of the PP. A bimetallic catalyst (Ni/Cu) was deposited on a CF surface to synthesize branched CNF using C2H2/H2 precursors at 600 °C followed by growing G flakes at 1050 °C. The morphology and chemical structure of the G–CNF–CF fibers were characterized by means of electron microscopy, transmission electron microscopy, and Raman spectroscopy. The mechanical and thermal behaviors of the synthesized G–CNF–CF/PP composite were characterized by means of tensile tests and thermal gravimetric analysis. Mechanical measurements revealed that the tensile stress and Youngs modulus of the G–CNF–CF/PP composites were higher than the neat PP with the contribution of 76%, 73%, respectively. Also, the thermal stability of the resultant composite increased about 100 °C. The measured reinforcement properties of the fibers were fitted with a mathematical model obtaining good agreement between the experimental results and analytical solutions.

A New fractional derivative for differential equation of fractional order under interval uncertainty

In this article, we develop a new definition of fractional derivative under interval uncertainty. This fractional derivative, which is called conformable fractional derivative, inherits some interesting properties from the integer differentiability which is more convenient to work with the mathematical models of the real-world phenomena. The interest for this new approach was born from the notion that makes a dependency just on the basic limit definition of the derivative. We will introduce and prove the main features of this well-behaved simple fractional derivative under interval arithmetic uncertainty. The actualization and usefulness of this approach are validated by solving two practical models.

Zero-dissipative phase-fitted hybrid methods for solving oscillatory second order ordinary differential equations

In this paper, zero-dissipative phase-fitted two-step hybrid methods are developed for the integration of second-order periodic initial value problems. The phase-fitted hybrid methods are constructed using similar approaches introduced by Papadopoulos et al. [1]. This new methods are based on the existing explicit hybrid methods of order four and six. Numerical illustrations indicate that the new methods are much more efficient than the existing methods.

Feedback Control of the Marangoni–Bénard Instability in a Fluid Layer with a Free-Slip Bottom

Feedback control was applied to the steady Marangoni–Benard convection in a horizontal layer of fluid with a free-slip bottom heated from below and cooled from above. The critical values of the Marangoni numbers for the onset of steady convection are calculated and the latter is found to be critically dependent on the Crispation and Bond numbers. It is shown that the onset of instability can be delayed and the critical Marangoni number can be increased through the use of feedback control.

A new variable step size block backward differentiation formula for solving stiff initial value problems

A new block backward differentiation formula of order 4 with variable step size is formulated. By varying a parameter in the formula, different sets of formulae with A-stability property can be generated. At the cost of an additional function evaluation, the accuracy of the method is seen to outperform some existing backward differentiation formula algorithms. The strategy involved in controlling the step size ratio is also described. The problems tested with the method show its efficiency in solving stiff initial value problems.

A Zero-Dissipative Runge-Kutta-Nyström Method with Minimal Phase-Lag

A three-stage third-order explicit Runge-Kutta-Nystrom method is developed to integrate second-order differential equations of the form where the solution is oscillatory. Presented are formula which has zero-dissipation, maximum order of dispersion (or minimal phase-lag) and at the same time with ’small’ principal local truncation error terms . The interval of periodicity is investigated and calculated. Numerical comparisons with current methods in the literature show its clear advantage in term of accuracy.

Prediction of silver nanoparticles' diameter in montmorillonite/chitosan bionanocomposites by using artificial neural networks

Artificial neural networks (ANNs) are computational tools that have found comprehensive utilization in solving many complex real world problems. Major benefits in using ANNs are their remarkable information-processing characteristics pertinent mainly to high parallelism, nonlinearity, fault and noise tolerance, and learning and generalization capabilities. An ANN approach is used to model the size of silver nanoparticles (Ag-NPs) in montmorillonite/chitosan bionanocomposites layers as a function of the silver nitrate concentration, reaction of temperature, chitosan percentage, and d-spacing of clay layers. The best ANN model is found and this final model is capable of predicting the size of nanosilver for a wide range of conditions with a mean absolute error of less than 0.004 and a regression error of about 1. Results obtained showed good ability predictive of neural network model for the prediction of the size of Ag-NPs in chemical reduction methods.

A Legendre Approximation for Solving a Fuzzy Fractional Drug Transduction Model into the Bloodstream

While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics-pharmacodynamic (PKPD) literature. In this research, we are confined with the application of Legendre operational matrix for solving fuzzy fractional differential equation arising in the drug delivery model into the bloodstream. The results illustrates the effectiveness of the method which can be in high agreement with the exact solution.