Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators

This paper aims to implement an analytical method, known as the Laplace homotopy perturbation transform technique, for the result of fractional-order Whitham–Broer–Kaup equations. The technique is a mixture of the Laplace transformation and homotopy perturbation technique. Fractional derivatives with Mittag-Leffler and exponential laws in sense of Caputo are considered. Moreover, this paper aims to show the Whitham–Broer–Kaup equations with both derivatives to see their difference in a real-world problem. The efficiency of both operators is confirmed by the outcome of the actual results of the Whitham–Broer–Kaup equations. Some problems have been presented to compare the solutions achieved with both fractional-order derivatives.

An Analytical View of Fractional-Order Fisher’s Type Equations within Caputo Operator

The present research article is related to the analytical investigation of some nonlinear fractional-order Fisher’s equations. The homotopy perturbation technique and Shehu transformation are implemented to discuss the fractional view analysis of Fisher’s equations. For a better understanding of the proposed procedure, some examples related to Fisher’s equations are presented. The identical behavior of the derived and actual solutions is observed. The solutions at different fractional are calculated, which describe some useful dynamics of the given problems. The proposed technique can be modified to study the fractional view analysis of other problems in various areas of applied sciences.

Numerical Investigation of Time-Fractional Equivalent Width Equations that Describe Hydromagnetic Waves

The present research article is related to the analytical investigation of some fractional-order equal-width equations. The homotopy perturbation technique along with Elzaki transformation is implemented to discuss the fractional view analysis of equal-width equations. For better understanding of the proposed procedure some examples related to equal-width equations are presented. The identical behavior of the derived and actual solutions is observed. The proposed technique can be modified to study the fractional view analysis of other problems in various areas of applied sciences.

Effects of Stenosis and Dilatation on Flow of Blood Mixed with Suspended Nanoparticles: A Study Using Homotopy Technique

The paper deals with a theoretical study on blood flow in a stenosed segment of an artery, when blood is mixed with nano-particles. Blood is treated here as a couple stress fluid. Stenosis is known to impede blood flow and to be the cause of different cardiac diseases. Since the arterial wall is weakened due to arterial stenosis, it may lead to dilatation /aneurysm. The homotopy perturbation technique is employed to determine the solution to the problem for the case of mild stenosis. Analytical expressions for velocity, shear stress at the wall, pressure drop, and flow resistance are derived. The impact of different physical constants on the wall shear stress and impedance of the fluid is examined by numerical simulation. Streamline patterns of the nanofluid are investigated for different situations.

Numerical Approximate Solution to Flow over a Flat Plate ( the Balusis Problem) By Perturbation Iteration- Algorithm

This paper applied perturbation iteration- algorithm (PI-A) to solve the problem of the incompressible two-dimensional laminar boundary layer flow over a flat plat as wall as called the Blasius problem (BP). BP is governed by Navier- Stokes equation (NSE) and continuity equation which were transformed into ordinary differential equation using similarity transforms. The results presented are tabulated for similarity stream function and can be seen highly of accuracy through comparable with that obtained by Ganji et al.[3] who studied BP using Homotopy perturbation technique (HPT) , Research results for the same problem using the variationally This paper applied perturbation iteration- algorithm (PI-A) to solve the problem of the incompressible two-dimensional laminar boundary layer flow over a flat plat as wall as called the Blasius problem (BP). BP is governed by Navier- Stokes equation (NSE) and continuity equation which were transformed into ordinary differential equation using similarity transforms. The results presented are tabulated for similarity stream function and can be seen highly of accuracy through comparable with that obtained by Ganja et al.[3] who studied BP using Homotopy perturbation technique (HPT) , Research results for the same problem using the variational iteration technique (VIT) before Aiyesimi and Niyi[5] and results numerical by Blasius[1]. Finally, The method that is efficient and widely applicable for solving ODE.

MHD Peristaltic Transport of Bingham Blood Fluid with Heat and Mass Transfer Through a Non-Uniform Channel

In the present work, the flow of non-Newtonian Bingham blood fluid through non-uniform channel is investigated. The fluid is electrically conducting, and the external uniform magnetic field is applied on this motion. The heat and mass transfer are taken in consideration, so, Soret and Dufour effects are studied. The problem is modulated mathematically by a system of non-linear partial differential equations which govern the velocity, temperature and concentration distributions. The system of these equations is simplified under the assumptions of long wavelength and low Reynolds number, then it is solved analytically by using homotopy perturbation technique. These distributions are obtained as a function of the physical parameters of the problem. The effects of these parameters on the obtained solutions are discussed numerically and illustrated graphically through a set of figures. These parameters play an important role to control the values of solutions. The used Bingham model is applicable for the physiological transportation of blood in arteries.

Heat and Mass Transfer Analysis of Nanofluid Flow Based on Cu, Al2O3, and TiO2 over a Moving Rotating Plate and Impact of Various Nanoparticle Shapes

The study of rotating nanofluid flows has a vital role in several applications such as in food processing, rotating machinery, cooling systems, and chemical fluid. The aims of the present work are to improve the thermophysical properties of convective flow and heat transfer for unsteady nanofluid past a moving rotating plate in the presence of ohmic, viscous dissipations, Brownian, and thermophoresis diffusion. The system is strained under the effect of strong magnetic field, and then the Hall current is considered. For this investigation, three different types of the nanoparticles Cu (copper), Al2O3 (aluminium oxide), and TiO2 (titanium dioxide) with various shapes (spherical, cylindrical, and brick) are considered, and water is used as a base nanofluid. The system governing equations are solved semianalytically using homotopy perturbation technique. In order to validate the present work, different comparisons are made under some special cases with previously published results and found an excellent agreement. It is observed that the shape of nanoparticles plays a substantial role to significantly determine the flow behaviour. Also, it can be found that the use of the cylindrical nanoparticle shape has better improvement for heat transfer rate compared with the other nanoparticle shapes.