Nadeem Alam Khan

Numerical Simulation for the Unsteady MHD Flow and Heat Transfer of Couple Stress Fluid over a Rotating Disk

The present work is devoted to study the numerical simulation for unsteady MHD flow and heat transfer of a couple stress fluid over a rotating disk. A similarity transformation is employed to reduce the time dependent system of nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). The Runge-Kutta method and shooting technique are employed for finding the numerical solution of the governing system. The influences of governing parameters viz. unsteadiness parameter, couple stress and various physical parameters on velocity, temperature and pressure profiles are analyzed graphically and discussed in detail.

Fractional-order Riccati differential equation: Analytical approximation and numerical results

The aim of this article is to introduce the Laplace-Adomian-Padé method (LAPM) to the Riccati differential equation of fractional order. This method presents accurate and reliable results and has a great perfection in the Adomian decomposition method (ADM) truncated series solution which diverges promptly as the applicable domain increases. The approximate solutions are obtained in a broad range of the problem domain and are compared with the generalized Euler method (GEM). The comparison shows a precise agreement between the results, the applicable one of which needs fewer computations.

Solutions of the Force-Free Duffing-van der Pol Oscillator Equation

A new approximate method for solving the nonlinear Duffing-van der pol oscillator equation is proposed. The proposed scheme depends only on the two components of homotopy series, the Laplace transformation and, the Pade approximants. The proposed method introduces an alternative framework designed to overcome the difficulty of capturing the behavior of the solution and give a good approximation to the solution for a large time. The Runge-Kutta algorithm was used to solve the governing equation via numerical solution. Finally, to demonstrate the validity of the proposed method, the response of the oscillator, which was obtained from approximate solution, has been shown graphically and compared with that of numerical solution.

Heat and Mass Transfer of Thermophoretic MHD Flow of Powell–Eyring Fluid over a Vertical Stretching Sheet in the Presence of Chemical Reaction and Joule Heating

Abstract The present paper deals with the effect of surface heat and mass transfer on magnetohydrodynamic flow of Powell–Eyring fluid over a vertical stretching sheet. The effects of thermophoresis, Joule heating and chemical reaction are also considered. The governing non-linear partial differential equations of the model are transformed into coupled non-linear ordinary differential equations using a similarity transformation and solved numerically by Runge–Kutta method and analytically by homotopy analysis method (HAM). The convergence is carefully checked by plotting ℏ

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

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Parameters Approach Applied on Nonlinear Oscillators

-curves. For different dimensionless parameters, numerical and analytical calculations are carried out and an investigation of the obtained results shows that the flow field is influenced considerably by the buoyancy ratio and thermal radiation, chemical reaction and magnetic field parameters. A totally analytical and consistently applicable solution is derived which agrees with numerical results.

MHD nonaligned stagnation point flow of second grade fluid towards a porous rotating disk

e approximation was effectively used in this method to capture the essential behavior of solutions for the mathematical model of accumulated effect of toxins on a population living in a closed system. The behavior of the solutions and the effects of different values of fractional-order α are indicated graphically. The study outlines significant features of this method as well as sheds some light on advantages of the method over the other. The results show that this method is very efficient, convenient, and can be adapted to fit a larger class of problems.

Swirling flow of couple stress fluid due to a rotating disk

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.