Fatima Riaz

Off-Centered Stagnation Point Flow of a Couple Stress Fluid towards a Rotating Disk

An investigation has been made to study the off-centered stagnation flow of a couple stress fluid over a rotating disk. The model developed for the governing problem in the form of partial differential equations has been converted to ordinary differential equations with the use of suitable similarity transformation. The analytical approximation has been made with the most promising analytical approach, homotopy analysis method (HAM). The convergence region of the obtained solution is determined and plotted. The effects of couple stress and nondimensional parameters have been observed on the flows of couple stress fluid. Also comparison has been made with the Newtonian fluid as the special case of considered problem.

Heat Transfer Analysis for Couple Stress Fluid over a Nonlinearly Stretching Sheet

Abstract An investigation has presented to analyze the heat transfer in a boundary layer flow of an incompressible couple stress fluid over a nonlinear stretching sheet. The heat transfer problem have been analyzed for the two heating processes, 1) PST (prescribed surface temperature case) and 2) PHF (prescribed heat flux case). The governing partial differential equations for flow and heat transfer are transformed to ordinary differential equations. The numerical solutions have been obtained by using fourth order Runge-Kutta method coupled with shooting method. The effects of dimensionless surface temperature, couple stress parameter beta, Prandtl number Pr, Eckert number Ec, nonlinear stretching sheet parameter n and lambda1; lambda2 have been observed by graphical illsurations.

Effects of Slip Factors and Couple Stresses for Stagnation Point Flow over a Moving Plate

An investigation is presented for the two-dimensional and axisymmetric stagnation flows of a couple stress fluids intrude on a moving plate under partial slip conditions. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The important physical parameters of skin friction coefficients of the fluid are also obtained. The homotopy analysis method (HAM) is employed to obtain the analytical solution of the problem. Also, the convergence of the solutions is established by plotting graphs of convergence control parameter. The impacts of couple stresses and slip conditions on the flow and temperature of the fluid have been observed. The numerical comparison for the considered fluid is compared with previous solutions as special case.

Dynamic Analysis of Rotating Pendulum by Hamiltonian Approach

A conservative system always admits Hamiltonian invariant, which is kept unchanged during oscillation. This property is used to obtain the approximate frequency-amplitude relationship of the governing equation with sinusoidal nonlinearity. Here, we applied Hamiltonian approach to obtain natural frequency of the nonlinear rotating pendulum. The problem has been solved without series approximation and other restrictive assumptions. Numerical simulations are then conducted to prove the efficiency of the suggested technique.

Numerical Simulations for Solving Fuzzy Fractional Differential Equations by Max-Min Improved Euler Methods

Abstract In this paper, an extension is introduced into Max-Min Improved Euler methods for solving initial value problems of fuzzy fractional differential equations (FFDEs). Two modified fractional Euler type methods have been proposed and investigated to obtain numerical solutions of linear and nonlinear FFDEs. The proposed algorithms are tested on various illustrative examples. Exact values are also simulated to compare and discuss the closeness and accuracy of approximations so obtained. Comparatively, tables and graphs results reveal the complete reliability, efficiency and accuracy of the proposed methods.

Parameters Approach Applied on Nonlinear Oscillators

We applied an approach to obtain the natural frequency of the generalized Duffing oscillator and a nonlinear oscillator with a restoring force which is the function of a noninteger power exponent of deflection . This approach is based on involved parameters, initial conditions, and collocation points. For any arbitrary power of , the approximate frequency analysis is carried out between the natural frequency and amplitude. The solution procedure is simple, and the results obtained are valid for the whole solution domain.

A comparison between numerical methods for solving Fuzzy fractional differential equations

Abstract In this paper, numerical simulation of linear and nonlinear fuzzy initial value problems of fractional order has been done. A modificaton in the improved Euler’s method for fuzzy fractional order is proposed and utilized. Also, the two component homotopy perturbation method also known as a modified homotopy perturbation method (MHPM) is employed to solve the considered problems. The results obtained from the considered techniques are compared. These methods are illustrated by solving several examples. Effciency and exactness of results worked out from MHPM is examined from the tables and comparatively it is found that MHPM is more accurate and closer to the exact solutions than the existing methods.

Investigation of combined heat and mass transfer betweenvertical parallel plates in a two-layer flow of couple stressnanofluid

Abstract This study is an investigation of fully-developed laminar flow in a two-layer vertical channel; one part filled with couple stress nanofluid and the other part with clear couple stress fluid. The flow is examined for combined heat and mass transfer using uniform wall temperature and concentration boundary conditions. Optimal homotopy analysis method (OHAM) is used to solve the nonlinear coupled ordinary differential equations (ODEs) governing the flow in each region. This method is based on the homotopy analysis method (HAM)which is an effective method to analytically approximate the solution of highly nonlinear problems. The influence of pertinent parameters is observed on velocity, temperature, and concentration distributions, specifically, the effect of Brownian parameter on couple stress fluid is mentioned.

A note on soliton solutions of Klein-Gordon-Zakharov equation by variational approach

Abstract In this paper, an investigation has been made to validate the variational approach to obtain soliton solutions of the Klein-Gordon-Zakharov (KGZ) equations. It is evident that to resolve the non-linear partial differential equations are quite complex and difficult. The presented approach is capable of achieving the condition for continuation of the solitary solution of KGZ equation as well as the initial solutions selected in soliton form including various unknown parameters can be resolute in the solution course of action. The procedure of attaining the solution reveals that the scheme is simple and straightforward.

3D stagnation point flow of Maxwell fluid towards an off-centered rotating disk

Purpose – The purpose of this paper is to study the three dimensional, steady and incompressible flow of non-Newtonian rate type Maxwell fluid, for stagnation point flow toward an off-centered rotating disk. Design/methodology/approach – The governing partial differential equations are transformed to a system of non-linear ordinary differential equations by conventional similarity transformations. The non-perturbation technique, homotopy analysis method (HAM) is employed for the computation of solutions. And, the solution is computed by using the well-known software Mathematica 10. Findings – The effects of rotational parameter and Deborah number on radial, azimuthal and induced velocity functions are investigated. The results are presented in graphical form. The convergence control parameter is also plotted for velocity profiles. The comparison with the previous results is also tabulated. The skin friction coefficients are also computed for different values of Deborah number. Originality/value – This pap...