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.