Analysis of a Stagnation Point Flow with Hybrid Nanoparticles over a Porous Medium

The unsteady stagnation-point flow of a hybrid nanofluid over a stretching/shrinking sheet embedded in a porous medium with mass transpiration and chemical reactions is considered.The momentum and mass transfer problems are combined to form a system of partial differential equations,which is converted into a set of ordinary differential equations via similarity transformation.These ordinary differential equations are solved analytically to obtain the solution for velocity and concentration profiles in exponential and hypergeometric forms,respectively.The concentration profile is obtained for four different cases namely constant wall concentration,uniform mass flux,general power law wall con-centration and general power law mass flux.The effect of different physical parameters such as Darcy number Da^(1-1),mass transpiration parameter V_(C),stretching/shrinking parameter (d),chemical reaction parameter(β)and Schmidt number (Sc)on velocity and concentration profile is examined.Results show that,the axial velocity will decreases as the shrinking sheet parameter increases,regardless of whether the suction or injection case is examined.The concentration decreases with an increase in the shrinking sheet parameter and the chemical reaction rate parameter.

Heat transfer study on solid and porous convective fins with temperature-dependent heat generation using efficient analytical method

A simple and highly accurate semi-analytical method, called the differential transformation method(DTM), was used for solving the nonlinear temperature distribution equation in solid and porous longitudinal fin with temperature dependent internal heat generation. The problem was solved for two main cases. In the first case, heat generation was assumed variable by fin temperature for a solid fin and in second heat generation varied with temperature for a porous fin. Results are presented for the temperature distribution for a range of values of parameters appearing in the mathematical formulation(e.g. N, εG, and G). Results reveal that DTM is very effective and convenient. Also, it is found that this method can achieve more suitable results in comparison to numerical methods.

Quantum Squeezing of Dark Solitons in Optical Fibers

在纤维的黑暗 soliton 繁殖的量子论基于 linearization 近似被学习。当时，在光子数字，阶段，位置(时间) 和使量子化的黑暗 solitons 的动量的无常是计算的。最后，压榨黑暗 soliton 被使用 homodyne 察觉并且与明亮的 soliton 大小写相比调查。

Numerical study on polymer nanofibers with electrically charged jet of viscoelastic fluid in electrospinning process

Electrospinning is a useful and efficient technique to produce polymeric nanofibers. Nanofibers of polymers are electrospun by creating an electrically charged jet of polymer solution. Numerical study on non-Newtonian and viscoelastic jets of polymer nanofibers in electrospinning process is presented in this work. In particular, the effect of non-Newtonian rheology on the jet profile during the electrospinning process is examined. The governing equations of the problem are solved numerically using the Keller-Box method. The effects of yield stress and power-law index on the elongation, velocity, stress and total force are presented and discussed in detail. The results show that by increasing the values of yield stress, the fluid elongation is reduced significantly.

Investigation of third-grade non-Newtonian blood flow in arteries under periodic body acceleration using multi-step differential transformation method

In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically. The blood is considered as the third- grade non-Newtonian fluid under the periodic body acceleration motion and the pulsatile pressure gradient. The hybrid multi-step differential transformation method （Hybrid-Ms- DTM） and the Crank-Nicholson method （CNM） are used to solve the partial differential equation （PDE）, and a good agreement between them is observed in the results. The effects of the some physical parameters such as the amplitude, the lead angle, and the body acceleration frequency on the velocity and shear stress profiles are considered. The results show that increasing the amplitude, Ag, and reducing the lead angle of body acceleration, 9, make higher velocity profiles on the center line of both arteries. Also, the maximum wall shear stress increases when Ag increases.

Quantum phase distribution and the number-phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states：solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.

Motion of a spherical particle in a fluid forced vortex by DQM and DTM

In this study, coupled equations of the motion of a particle in a fluid forced vortex were investigated using the differential transformation method （DTM） with the Pad6 approximation and the differential quadrature method （DO_M）. The significant contribution of the work is the introduction of two new, fast and efficient solutions for a spherical particle in a forced vortex that are improvements over the previous numerical results in the literature. These methods represent approximations with a high degree of accuracy and minimal computational effort for studying the particle motion in a fluid forced vortex. In addition, the velocity profiles （angular and radial） and the position trajectory of a particle in a fluid forced vortex are described in the current study.

Propulsion and launching analysis of variable-mass rockets by analytical methods

In this study,applications of some analytical methods on nonlinear equation of the launching of a rocket with variable mass are investigated.Differential transformation method(DTM),homotopy perturbation method(HPM)and least square method(LSM)were applied and their results are compared with numerical solution.An excellent agreement with analytical methods and numerical ones is observed in the results and this reveals that analytical methods are effective and convenient.Also a parametric study is performed here which includes the effect of exhaust velocity(C_(e)),bum rate(BR)of fuel and diameter of cylindrical rocket(d)on the motion of a sample rocket,and contours for showing the sensitivity of these parameters are plotted.The main results indicate that the rocket velocity and altitude are increased with increasing the C_(e) and BR and decreased with increasing the rocket diameter and drag coefficient.

Unsteady sedimentation analysis of spherical particles in Newtonian fluid media using analytical methods

Unsteady settling behavior of solid spherical particles falling in water as a Newtonian fluid is investigated using a drag coefficient of the form given by Ferreira et al.Differential transformation method(DTM),Galerkin method(GM),collocation method(CM),and numerical methods are applied to analyze the characteristics of particles motion.The influence of physical parameters on terminal velocity is discussed and moreover,comparing the techniques,it is showed that GM and CM are very efficient for solving the governing equation and DTM with Padéapproximation has the best agreement with numerical results.The novelty of this work is introducing three simple and exact analytical method for solving the nonlinear equation of sedimentation and applied it in many industrial and chemical applications。