Mohammed Abdulhameed

A Modified Homotopy Perturbation Transform Method for Transient Flow of a Third Grade Fluid in a Channel with Oscillating Motion on the Upper Wall

A new analytical algorithm based on modified homotopy perturbation transform method is employed for solving the transient flow of third grade fluid in a porous channel generated by an oscillating upper wall. This method incorporates the He’s polynomial into the HPM, combined with Laplace transform. Comparison with HPM and OHAM analytical solutions reveals that the proposed algorithm is highly accurate. This proves the validity and great potential of the proposed algorithm as a new kind of powerful analytical tool for transient nonlinear problems. Graphs representing the solutions are discussed, and appropriate conclusions are drawn.

Solution of the Falkner–Skan wedge flow by a revised optimal homotopy asymptotic method

In this paper, a revised optimal homotopy asymptotic method (OHAM) is applied to derive an explicit analytical solution of the Falkner–Skan wedge flow problem. The comparisons between the present study with the numerical solutions using (fourth order Runge–Kutta) scheme and with analytical solution using HPM-Padé of order [4/4] and order [13/13] show that the revised form of OHAM is an extremely effective analytical technique.

Radiation effects on two-dimensional MHD Falkner-Skan wedge flow

Radiation effects on two-dimensional MHD Falkner-Skan boundary layer wedge have been studied. Analytical solution of nonlinear boundary-layer equations is obtained by modified homotopy perturbation method. It is observed that the magnetic field tends to decelerate fluid flow whereas radiations and thermal diffusion tend to increase fluid temperature.

Unsteady Blood Flow with Nanoparticles Through Stenosed Arteries in the Presence of Periodic Body Acceleration

The effects of nanoparticles such as Fe 3O4,TiO2, and Cu on blood flow inside a stenosed artery are studied. In this study, blood was modelled as non-Newtonian Bingham plastic fluid subjected to periodic body acceleration and slip velocity. The flow governing equations were solved analytically by using the perturbation method. By using the numerical approaches, the physiological parameters were analyzed, and the blood flow velocity distributions were generated graphically and discussed. From the flow results, the flow speed increases as slip velocity increases and decreases as the values of yield stress increases.

Existence of steady solution from unsteady flow of viscoelastic fluid due to different pressure waveform in a circular cylinder

This work is to examine theoretically unsteady flow of viscoelastic fluid in a circular cylinder and to investigate the existence of steady solutions. We consider the flow is solely due to pressure gradient in following three forms: (i) sinusoidal; (ii) square; (iii) constant. Based on the pressure gradient described, three flow situations are solved and the exact analytical solutions are given in terms of Bessel functions. In all the three problems, it is found that the variation of the unsteady and steady solution mainly depends for small time, while for large time the two solutions are identical.

An existence of trapezoidal waveform of oscillating motion from triangular pressure waveforms: The case of an Oldroyd-B model

Oscillating motion of Oldroyd-B flow in a capillary tube at a triangular sine and cosine pressure waveform is considered. An analytical solution of velocity field is obtained for an oscillating laminar flow, which can be used to determine the existence of trapezoidal waveform effect on the flow. When both triangular sine and cosine components are dominate, the oscillating flow can result in significant trapezoidal waveform performance. The dimensionless oscillating frequency, amplitude, and fluid material parameters, are primary factors affecting the flow performance of an oscillating flow in a capillary tube.

Optimal series solution for mixed convection flow of third grade viscoelastic fluid in a channel with walls transpiration

An analytical solution of mixed convection flow of viscoelastic fluid in a channel with walls transpiration is obtained by optimal homotopy asymptotic method. Comparison with previous recorded result through reduction in pertinent parameters unveils the presented optimal series solution is correct. The result valid for non-transpiration walls for the values from the pertinent flow parameters could be derived as a special case from the present analysis. The results show that the proposed method is effective and has a distinct advantage over usual approximation methods in that the approximate solution obtained here is valid not only for weakly nonlinear equations, but also for strongly nonlinear ones. Second order approximation is needed for velocity while only first order temperature is needed to obtain desired results.

Unsteady free convection flow past an oscillating wall with ramped wall temperature

In this paper, a problem of unsteady free convection of a Newtonian fluid over a flat plate with oscillating motions, starting from rest, and with ramped wall temperature is considered. The exact solutions for velocity and temperature distributions are derived using the perturbation techniques combined with Laplace transformation. The variations of velocity and temperature distributions on various physical parameters are shown graphically and analyzed while numerical values of skin friction and Nusselt number are presented in tabular form. Furthermore, the free convection flow of a Newtonian fluid has been compared with the flow of second grade fluid. It is found that the flow of Newtonian fluid is smaller than that of second grade fluid.