Emad H. Aly

Exact Analytical Solution of the Peristaltic Nanofluids Flow in an Asymmetric Channel with Flexible Walls and Slip Condition: Application to the Cancer Treatment

In the cancer treatment, magnetic nanoparticles are injected into the blood vessel nearest to the cancers tissues. The dynamic of these nanoparticles occurs under the action of the peristaltic waves generated on the flexible walls of the blood vessel. Studying such nanofluid flow under this action is therefore useful in treating tissues of the cancer. In this paper, the mathematical model describing the slip peristaltic flow of nanofluid was analytically investigated. Exact expressions were deduced for the temperature distribution and nano-particle concentration. In addition, the effects of the slip, thermophoresis, and Brownian motion parameters on the temperature and nano-particle concentration profiles were discussed and further compared with other approximate results in the literatures. In particular, these results have been obtained at the same values of the physical examined parameters that was considered in Akbar et al., “Peristaltic flow of a nanofluid with slip effects,” 2012. The results reveal that remarkable differences are detected between the exact current results and those approximately obtained in the literatures for behaviour of the temperature profile and nano-particles concentration. Accordingly, the current analysis and results are considered as optimal and therefore may be taken as a base for any future comparisons.

Advances in the Adomian decomposition method for solving two-point nonlinear boundary value problems with Neumann boundary conditions

A new straightforward approach for solving ordinary and partial second-order boundary value problems with Neumann boundary conditions is introduced in this research. This approach depends mainly on the Adomian decomposition method with a new definition of the differential operator and its inverse, which has been modified for Neumann boundary conditions. The effectiveness of the proposed approach is verified by several linear and nonlinear examples.

Exact Analytical Solution for Suction and Injection Flow with Thermal Enhancement of Five Nanofluids over an Isothermal Stretching Sheet with Effect of the Slip Model: A Comparative Study

We introduced a direct and effective approach to obtain the exact analytical solution for the nanoparticles-water flow over an isothermal stretching sheet with the effect of the slip model. In particular, we examined and compared the effect of the existence of five metallic and nonmetallic nanoparticles, namely, Silver, Copper, Alumina, Titania, and Silicon Dioxide, in a base of water. The most interesting physical parameters were then discussed in the presence of no-slip model, first order slip, and second order slip parameters. It is found that, with no-slip effect, the present exact solutions are in a very good agreement with the previous published results. On the other hand, with the effect of the slip model, increase in the nanoparticle volume friction decreases the velocity for the high density of nanoparticles, increases it for the low density of them, and increases the temperature for all investigated nanoparticles. Further, increase in the wall mass decreases the velocity and temperature; however, it increases the local skin friction. Furthermore, increase in the slips slows down the velocity, increases the temperature with an impressive effect in the injection case, and decreases the local skin friction and the reduced Nusselt number. It was also demonstrated that, as the nanoparticle becomes heavier, this results in increase and decrease in reduced skin friction coefficient and reduced Nusselt number, respectively, with significant effect in the presence of the second slip. Finally, Silver is the suitable nanoparticle if slowing down the velocity and increasing the temperature are needed; Silicon Dioxide is the appropriate nanoparticle if different behavior is to be considered.

Study of electrical and optical properties of Cd1 − xZnxS thin films

Thin films of Cd0.9Zn0.1S and CdS were prepared by thermal evaporation under vacuum of 10−6 Torr and with deposition rate of 60 nm/min. X ray diffraction studies confirm the hexagonal structure of both CdS and Cd0.9Zn0.1S films. The effect of heat treatments with or without CdCl2 enhances the grain size growth and improves the crystalline of the films. Moreover, the activation energy is decreased by heat treatment with or without CdCl2 for all thin films. The optical absorption coefficient of Cd0.9Zn0.1S thin films were determined from measured transmittance and reflectance in the wavelength range of 300 to 2500 nm. The optical absorption spectra reveal the existence of direct energy gap for these films. It was found that the optical energy gap decreases upon annealing or CdCl2 treatments.

New Analytical and Numerical Solutions for Mixed Convection Boundary-Layer Nanofluid Flow along an Inclined Plate Embedded in a Porous Medium

Two different analytical and numerical methods have been applied to solve the system describing the mixed convection boundary-layer nanofluids flow along an inclined plate embedded in a porous medium, namely, homotopy perturbation method (HPM) and Chebyshev pseudospectral differentiation matrix (ChPDM), respectively. Further, ChPDM is used as a control method to check the accuracy of the results obtained by HPM. The analytical method is applied using a new way for the deformed equations, and the resulted solution was expressed in terms of a well-known entire error function. In addition, using only two terms of the homotopy series, the approximate analytical solution is compared with the numerical solution obtained by the accurate ChPDM approach. The results reveal that good agreements have been achieved between the two approaches for various values of the investigated physical parameters.

On the Exact Analytical and Numerical Solutions of Nano Boundary-Layer Fluid Flows

The nonlinear boundary value problem describing the nanoboundary-layer flow with linear Navier boundary condition is investigated theoretically and numerically in this paper. The -expansion method is applied to search for the all possible exact solutions, and its results are then validated by the Chebyshev pseudospectral differentiation matrix (ChPDM) approach which has been recently introduced and successfully used. This numerical technique is firstly applied and, on comparing with the other recent work, it is found that the results are very accurate and effective to deal with the current problem. It is then used to examine and validate the present analytical analysis. Although the -expansion method has been used widely to solve nonlinear wave equations, its application for nonlinear boundary value problems has not been discussed yet, and the present paper may be the first to address this point. It is clarified that the exact solutions obtained via the -expansion method cannot be obtained by using some of the other methods. In addition, the domain of the physical parameters involved in the current boundary value problem is also discussed. Furthermore, the convex, vicinity of zero, and asymptotic solutions are deduced.

Radiation and MHD Boundary Layer Stagnation-Point of Nanofluid Flow towards a Stretching Sheet Embedded in a Porous Medium: Analysis of Suction/Injection and Heat Generation/Absorption with Effect of the Slip Model

In existence of the velocity slip model, suction/injection, and heat source/sink, the boundary layer flow near a stagnation-point over a heated stretching sheet in a porous medium saturated by a nanofluid, with effect of the thermal radiation and magnetic field, has been studied. The governing system of partial differential equations was transformed into a system of nonlinear ordinary equations using the appropriate similarity transforms. Then, the obtained system has been numerically solved by the Chebyshev pseudospectral differentiation matrix (ChPDM) approach. It was found that, at some special cases, the current results are in a very good agreement with those presented in the literature. In addition, the flow velocity, surface shear stress, temperature, and concentration are strongly influenced on applying the slip model, which is, therefore, extremely important to predict the flow characteristics accurately in the nanofluid mechanics. It was proved that this velocity slip condition is mandatory and should be taken into account in nanoscale research; otherwise, false results and a spurious physical sight are to be gained. Further, it was deduced that the influence of the stream velocity and shear stress reaches very rapidly the stable manner for both cases of the velocity ratio. However, when this ratio is equal to one, the skin friction coefficient, reduced Nusselt number, and reduced Sherwood number are constant and equal to zero, 0.721082, and 3.06155, respectively. Furthermore, it was proved that the reduced Nusselt number decreases with increase of Brownian motion and thermophoresis; has a very weak effect on increasing Lewis number; increases with increase of Prandtl number; and is higher in the cases of suction, velocity ratio > 1 and heat source in comparison with injection, velocity ratio 1 in comparison with injection and velocity ratio < 1, respectively; and is approximately the same in the heat source and heat sink cases. Finally, it was shown that the most effective region for radiation effect is .

Effect of the Velocity Second Slip Boundary Condition on the Peristaltic Flow of Nanofluids in an Asymmetric Channel: Exact Solution

The problem of peristaltic nanofluid flow in an asymmetric channel in the presence of the second-order slip boundary condition was investigated in this paper. To the best of the authors’ knowledge, this parameter was here incorporated for the first time in such field of a peristaltic flow. The system governing the current flow was found as a set of nonlinear partial differential equations in the stream function, pressure gradient, nanoparticle concentration, and temperature distribution. Therefore, this system has been successfully solved exactly via a very effective procedure. These exact solutions were then proved to reduce to well-known results in the absence of second slip which were published very recently in the literature. Effect of the second slip parameter on the present physical parameters was discussed through graphs and it was found that this type of slip is a very important one to predict the investigated physical model. Moreover, the variation of many physical parameters such as amplitudes of the lower and upper waves, phase difference on the temperature distribution, nanoparticle concentration, pressure rise, velocity, and pressure gradient were also discussed. Finally, the present results may be viewed as an optimal choice for their dependence on the exact solutions which are obtained due to the highly complex nonlinear system.

Analysis of fluid motion and heat transport on magnetohydrodynamic boundary layer past a vertical power law stretching sheet with hydrodynamic and thermal slip effects

The present model is committed to the study of MHD boundary layer flow and heat transfer past a nonlinear vertically stretching porous stretching sheet with the effects of hydrodynamic and thermal slip. The boundary value problem, consisting of boundary layer equations of motion and heat transfer, which are nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, with the aid of similarity transformation. This problem has been solved, using Runge Kutta fourth order method with shooting technique. The effects of various physical parameters, such as, stretching parameter m, magnetic parameter M, porosity parameter fw, buoyancy parameter λ, Prandtl number Pr, Eckert number Ec, hydrodynamic slip parameter γ, and thermal slip parameter δ, on flow and heat transfer characteristics, are computed and represented graphically.