non-Newtonian Second Grade Fluid Research Articles

Stagnation point flow of a second-grade hybrid nanofluid induced by a Riga plate

PurposeThis paper aims to accentuate the behavior of second-grade hybrid Al2O3–Cu nanofluid flow and its thermal characteristics driven by a stretching/shrinking Riga plate.Design/methodology/approachThe second-grade fluid is considered with the combination of Cu and Al2O3 nanoparticles. Three base fluids namely water, ethylene glycol (EG) and methanol with different Prandtl number are also examined. The formulation of the mathematical model of second-grade hybrid nanofluid complies with the boundary layer approximations. The complexity of the governing model is reduced into a simpler differential equations using the similarity transformation. The bvp4c solver is fully used to solve the reduced equations. The observation of multiple solutions is conducted for the assisting (stretching) and opposing (shrinking) cases.FindingsThe impact of suction parameter, second-grade parameter, electromagnetohydrodynamics (EMHD) parameter, velocity ratio parameter and the volumetric concentration of the alumina and copper nanoparticles are numerically analyzed on the velocity and temperature profiles, skin friction coefficient and local Nusselt number (thermal rate) of the second-grade Al2O3–Cu/water. The solution is unique when (static and stretching cases) while dual for a specific range of negative in the presence of suction effect. Based on the appearance of the first solution in all cases of, it is physically showed that the first solution is stable. Further examination reveals that the EMHD and suction parameters are the contributing factors for the thermal enhancement of this non-Newtonian working fluid. Meanwhile, the viscosity of the non-Newtonian fluid also plays a significant role in the fluid motion and heat transfer rate based on the finding that the EG base fluid produces the maximum heat transfer rate but the lowest critical value and skin friction coefficient.Originality/valueThe results are novel and contribute to the discovery of the hybrid nanoparticles’ performance in the non-Newtonian second-grade fluid. Besides, this study is beneficial to the researchers in this field and general audience from industries regarding the factors, which contributing to the thermal enhancement of the working fluid.

A class of exact solutions of second grade fluid

This paper describes a class of exact solutions of the equations of motion for an unsteady, incompressible non-Newtonian second grade fluid in the Cartesian co-ordinates. The exact solutions of non-linear equations governing the flow of second grade fluids are obtained through generalized separation variables method by assuming certain form of stream functions. The expressions for velocity profile and vorticity stream function are constructed. Key words: Exact solutions, vorticity functions, second grade fluids, separation of variables.

Exact solutions of non-Newtonian fluid flows with prescribed vorticity

The equations of motion of a non-Newtonian second-grade fluid flow are highly nonlinear partial differential equations. For this reason, there exists only a limited number of exact solutions. Due to the complexity of the equations, inverse methods described by Nemenyi [1] have become attractive in the study of non-Newtonian fluids. In these methods, certain physical or geometrical properties of the flow field are assumed a priori. Lin and Tobak [2] studied steady plane viscous incompressible flows for a chosen vorticity function by decomposing the nonlinear fourth-order partial differential equation in the streamfunction. This excellent approach yielded two second-order linear partial differential equations in the streamfunction. Hui [3] used this approach to study unsteady plane viscous incompressible flows. During the past decade, there has been substantial interest in flows of viscoelastic liquids due to the occurrence of these flows in industrial processes. In this paper, we study the steady and unsteady incompressible viscous non-Newtonian second-grade fluid flows in which the vorticity is proportional to the streamfunction perturbed by a uniform stream. The solutions obtained are exact solutions and represent various non-parallel flows of second-grade fluids. The plan of this paper is as follows: In Sect. 2, the equations of motion of an unsteady plane incompressible second-grade fluid are given, and the vorticity function is assumed to be∇ 2 ψ=A(ψ−Ux−BUy 2). In Sect. 3, solutions for the steady flow are obtained. In Sect. 4, solutions for unsteady flow are obtained.