Search

Based on the Riemann-Liouville fractional derivative, the time-fractional nonlinear Fokas-Lenells equation is analyzed in this paper. The extended simplest equation method is implemented to construct several kinds of solitons such as singular and combo soliton solutions of the present model. The existence criteria of the obtained soliton solutions are also reported. Moreover, it has been shown that the results in the literature are special cases of the present ones when the fractional-order of differentiation becomes unity. [ABSTRACT FROM AUTHOR]

In the presence of a magnetic field, the Couette–Poiseuille flow of a pair stress fluid between two parallel plates was thoroughly examined. The flow was caused by uniform motion of the top plate and an axial pressure gradient. The effect of Hafnium particles, both in spherical and homogeneous form, was investigated by heating the wall. For this purpose, Reynolds' model was employed. The modeled equations are highly nonlinear partial differential equation which are transformed to convectional differential equation using the similarity transformation. The resulting non-linear system of equations was solved by recourse to the efficient bvph2 scheme along with homotopy analysis method (HAM). The innovative fragment of the present study is to scrutinize the magnetized the Couette–Poiseuille nanofluid flow of a pair stress fluid between two parallel plates is thoroughly examined with variable viscosity, still not has been elaborated in the available works to date. Consequently, in the restrictive sense, the existing work is associated with available work reported by Makinde and Onyejekwe [39] and originated in exceptional agreement. An inverse relation was found to exist between velocity and Hartman number. The reason behind this is that the increase in temperature enfeebles the viscous forces which, consequently, results in reduction of velocity. However, it was noticed that temperature profile is adversely affected by raising the viscosity parameters and consequently the velocity is enhanced. It is possible to investigate diphase flows in various geometries using inertial particles suspended in an incompressible turbulent flow with Newtonian and non-Newtonian base fluids, which might be one of the proposed model's future uses. [ABSTRACT FROM AUTHOR]

Effects of conjugate buoyant generalized heat transport in water-based nanofluids with different nanoparticles are studied. The nanofluid flows in an infinite vertical annular channel with differently heated cylindrical surfaces. The generalized Cattaneo law of thermal flux is formulated in terms of time-fractional Caputo derivative. The annulus space is formed by a solid annular wall heated on the inner surface and an isothermal exterior cylindrical tube. Analytical solutions in the Laplace domain for the temperature in the solid wall, nanofluid temperature, and nanofluid velocity are determined. The solutions in the real domain are obtained using the numerical inversion algorithm for the Laplace transforms. The results corresponding to fractional models are compared with those of the ordinary models described by the classical Cattaneo law. It has found that the heat flux given by the fractional equation leads to the decrease of heat transfer in the solid wall because the values of the temperature gradient are attenuated by the weight function in the heat flux expression. The temperature in the nanofluid has a different evolution concerning the fractional parameter. In the area close to the solid wall, the temperature increases concerning the fractional parameter. The temperature decreases with the thermal memory parameter in the region close to the outer wall. For large values of time, it is observed that the fractional model leads to an improvement of heat transfer. [ABSTRACT FROM AUTHOR]

Hybrid modeling is a term that has recently been used to describe the mixture of liquids. Hybrid models are important in a variety of systems, including medical treatments, manufacturing, experimental instrument design, aerosol particle processing, and naval academies, among others. With the presence of the Buoyancy force and Boussinesq second-order thermal variation, the nonlinear, linear, and quadratic Roseland approximations on three-dimensional flow characteristics were considered. In addition, ternary solid nanoparticles of various shapes and densities were included. With appropriate transformation, the resulting ruling partial differential system is changed into a governing ordinary differential system, and a solution with three mixture compositions is supplied (Case-I, Case-II and Case-III). CNTs (Spherical), GNT (Cylindrical), and Al 2 O 3 (Platelet) with water as a base fluid at 0 °C, Case-II mixture of CNT (Spherical), GNT (Cylindrical), and Al 2 O 3 (Platelet) with water as a base fluid at 10 °C, and Case-III mixture of CNTs (Spherical), GNP (Cylindrical) and Al 2 O 3 (Platelet) with water as a base fluid at 50 °C, there are numerous variations in three mixing compositions as follows as well as the flow's linear, quadratic, and nonlinear thermal radiation situations. In comparison to Case-I and Case-III ternary combinations, the temperature distribution in Case-II ternary mixtures is wider. Case-2 CNTs (Spherical), GNP (Cylindrical), and Al 2 O 3 (Platelet) with water as a base fluid at 10 °C has a higher conductivity than Case-1 CNTs (Spherical), GNP (Cylindrical), and Al 2 O 3 (Platelet) with water at 0 °C, and Case-3 CNTs (Spherical), GNP (Cylindrical), and Al 2 O 3 (Platelet) With water as a base fluid at 50 °C. The skin friction coefficient is more in case-1 compared to case-2 and case-3. [ABSTRACT FROM AUTHOR]