Analytical Study on Couple Stress Fluid in an inclined Channel

Abstract

Numerical and analytical solutions of Stokes theory of couple stress fluid under the effects of constant, space, and variable viscosity in the inclined channel are discussed here. The considered couple stress fluid is described mathematically with the definition of the stress tensor. The dimensional form of the boundary value problem is transformed into dimensionless form by defining dimensionless quantities and then solved with help of the perturbation technique. The analytical expressions of velocity and temperature of all cases based on the viscosity of the couple stress fluid are presented. For the validity of the perturbation solution, the Pseudo-Spectral collocation method is employed for each case of the viscosity model including constant, space, and Vogel's models, respectively. The solution of the perturbation method and Pseudo-Spectral methods are shown together in the graphs. The effects of couple stress parameters on velocity and temperature distributions are also elaborated with physical reasoning in the results and discussion part. It is observed that velocity and temperature of fluid escalate via the pressure gradient parameter and Brinkman number while decelerating via couple stress parameter.

Effects of Slip and Inclined Magnetic Field on the Flow of Immiscible Fluids (Couple Stress Fluid and Jeffrey Fluid) in a Porous Channel

“…A review of couple stress fluid dynamics was reported by Stokes [4] in 1984. The presence of couple stress parameter decreases the velocity of the fluid and other parameters effect on the velocity of a single couple stress fluid studied by Devakar et al [5], Ahmad [6], and Jangili et al [7].…”

Numerical Investigation of the Magnetized Reactive Viscous Couple Stress Fluid Flow Down an Inclined Riga Plate with Variable Viscosity

“…Therefore, the Chebyshev trial function provides a very good approximation for the uncoupled problem. Moreover, for the Coupled system when α = 0, tables for the comparison of the numerical solutions by spectral collocation and the Runge-Kutta-Fehlberg (RKF) integration technique are presented for Equations (12) and (13). In Tables 2 and 3, the error ranges from 10 −17 and 10 −8 for Equation (12) which means that the two results converge to one.…”

“…Yusuf et al [12] also presented a semi-analytical solution on a micropolar fluid flow over an inclined geometry with velocity slip. Very recently, Ahmad et al [13] analytically examined Stoke's theory of couple stress fluid over an inclined channel under variable viscosity.…”

The flow of non‐Newtonian fluid in an inclined channel through variable permeability

“…Multiphase flow suspended with Hafnium particles is better than the one with crystal particles. Ahmad et al 28 examined the analytical study on a couple stress fluid in an inclined channel. Finite element simulations of free convection flow inside a porous inclined cavity filled with micropolar fluid reported by Ali et al 29 The entropy analysis in the Rabinowitsch fluid model through the inclined wavy channel was explained by Nazeer et al 30 Numerical simulations of MHD flow of micropolar fluid inside a porous inclined cavity with uniform and nonuniform heated bottom studied by Nazeer et al 31 The impact of slip boundary conditions, magnetic force, and porous medium on blood flow of Jeffrey fluid discussed by Nazeer et al 32 Mathematical modelings and simulation of MHD electro‐osmotic flow of Jeffrey fluid in convergent geometry reported by Nazeer et al 33 Saleem et al 34 depicts the theoretical study of electro‐osmotic multiphase flow of Jeffrey fluid in a divergent channel with lubricated walls.…”