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The purpose of this paper is to obtain the nonlinear Schrodinger equation (NLSE) numerical solutions in the presence of the first-order chromatic dispersion using a second-order, unconditionally stable, implicit finite difference method. In addition, stability and accuracy are proved for the resulting scheme.

The conserved quantities such as mass, momentum and energy are calculated for the system governed by the NLSE. Moreover, the robustness of the scheme is confirmed by conducting various numerical tests using the Crank-Nicolson method on different cases of solitons to discuss the effects of the factor considered on solitons properties and on conserved quantities.

The Crank-Nicolson scheme has been derived to solve the NLSE for optical fibers in the presence of the wave packet drift effects. It has been founded that the numerical scheme is second-order in time and space and unconditionally stable by using von-Neumann stability analysis. The effect of the parameters considered in the study is displayed in the case of one, two and three solitons. It was noted that the reliance of NLSE numeric solutions properties on coefficients of wave packets drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws. Accordingly, by comparing our numerical results in this study with the previous work, it was recognized that the obtained results are the generalized formularization of these work. Also, it was distinguished that our new data are regarding to the new communications modes that depend on the dispersion, wave packets drift and nonlinearity coefficients.

The present study uses the first-order chromatic. Also, it highlights the relationship between the parameters of dispersion, nonlinearity and optical wave properties. The study further reports the effect of wave packet drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws.

The purpose of this paper is to study the Blasius flat plate with viscous dissipation in the presence of suction or injection effects in the boundary layer of a viscoelastic fluid.

The governing partial differential equations are derived as a first order ordinary differential equation using similarity (Blasius) variables. Velocity profiles, temperature profiles, skin friction parameters, and heat transfer parameters are computed numerically for various values of the viscoelastic parameter K, the suction or injection parameter f _w , the Prandtl number Pr, the Eckert number Ec, and the moving parameter λ.

The effects of the viscoelastic, moving, and suction/injection parameters on the skin friction and heat transfer of the flat plate are studied. The effects of these parameters on the velocity and temperature profiles are also presented for 0≤Pr≤3.

To the best of the authors' knowledge, this important classical problem has not been studied before for the case of a viscoelastic fluid. Thus, the results are original and new for this type of fluid.

This paper aims to examine the unsteady stagnation-point flow, heat and mass transfer of upper-convected Oldroyd-B nanofluid along a stretching sheet. The thermal conductivity is taken in a temperature-dependent fashion. With the aid of Cattaneo–Christov double-diffusion theory, relaxation-retardation double-diffusion model is advanced, which considers not only the effect of relaxation time but also the influence of retardation time. Convective heat transfer is not ignored. Additionally, experiments verify that with sodium carboxymethylcellulose (CMC) solutions as base fluid, not only the flow curve conforms to Oldroyd-B model but also thermal conductivity decreases linearly with the increase of temperature.

The suitable pseudo similarity transformations are adopted to address partial differential equations to ordinary differential equations, which are computed analytically through homotopy analysis method (HAM).

It is worth noting that the increase of stagnation-point parameter diminishes momentum loss, so that the velocity enlarges, which makes boundary layer thickness thinner. With the increase of thermal retardation time parameter, the nanofluid temperature rises that implies heat penetration depth boosts up and the additional time required for nanofluid to heat transfer to surrounding nanoparticles is less, which is similar to the effects of concentration retardation time parameter on concentration field.

This paper aims to explore the unsteady stagnation-point flow, heat and mass transfer of upper-convected Oldroyd-B nanofluid with variable thermal conductivity and relaxation-retardation double-diffusion model.

The purpose of this note is to provide general solutions for radiative magnetohydrodynamic natural convection flow.

To obtain exact solutions for such motions of Newtonian fluids, as seen in the existing literature, the Laplace transform technique is used.

General solutions are obtained for temperature, velocity and Nusselt number in the presence of heat source and shear stress on the boundary. They can generate exact solutions for any motion with technical relevance of this type. Fluid velocity is presented as the sum of mechanical and thermal components. Influence of physical parameters on temperature and velocity is graphically underlined for ramp-type heating plate that applies a constantly accelerating shear stress to the fluid. Thermal and mechanical effects are significant and must be taken into consideration.

For illustration, as well as for a check of results, three special cases with applications in engineering are considered and some known results are recovered.

Obtained solutions are presented in the simplest forms. In addition, the solutions corresponding to cosine oscillatory heating and oscillating shear are presented so that they can be immediately reduced to those corresponding to constant heating and uniform shear if the oscillations’ frequency becomes zero. Heat transfer characteristics with thermal radiation are graphically illustrated using one parameter only for such motions.

The boundary-layer analysis is required to reveal the fluid flow behavior in several industrial processes and enhance the products’ effectiveness. Therefore, this research aims to investigate the buoyancy or mixed convective stagnation-point flow (SPF) and heat transfer of a micropolar fluid filled with hybrid nanoparticles over a vertical plate. The nanoparticles silver (Ag) and titanium dioxide (TiO₂) are scattered into various base fluids to form a new-fangled class of (Ag-TiO₂/various base fluid) hybrid nanofluid along with different shape factors.

The self-similarity transformations are used to reformulate the leading requisite partial differential equations into renovated non-linear dimensionless ordinary differential equations. The numerical dual solutions are gained for the transmuted requisite equations with the help of the bvp4c built-in package in MATLAB software. The results are validated by comparing them with previously available published data for a particular case of the present study.

The impact of various pertaining parameters such as nanoparticle volume fraction, material parameter, shape factor and mixed convective on temperature, heat transfer, fluid motion, micro-rotation and drag force are visualized and scrutinized through tables and graphs. It is observed that dual or non-uniqueness outcomes are found for the case of buoyancy assisting flow, whereas the solution is unique in the buoyancy opposing flow case. Additionally, the fluid motion and micro-rotation profiles decelerate in the presence of nanoparticle volume fraction, while the temperature augments.

The mixed convective stagnation point flow conveying TiO₂/Ag hybrid nanofluid with micropolar fluid with various shape factors is the significant originality of the current investigation where multiple outcomes are obtained for the assisting flow. The various base fluids such as glycerin, water and water–ethylene glycol (50%:50%) are considered in the present problem. The bifurcation values of the considered problem do not exist, probably because of various base fluids. To the best of the authors’ knowledge, this work is new and original which were not previously reported.