Author details

we depict the profiles of velocity and shear stress for three different values of H. It is observed from these figures that the flow velocity as well as the shear stress decreases with increasing H, which corresponds to the shear thickening phenomenon. Figure 5 is sketched to show the velocity and the shear stress profiles at different values of K. It is noticeable that velocity as well as the shear stress increases by increasing K. In order to study the effects of t, we have plotted Figure 6, where it appears that the velocity is also a strong function of t of the Jeffrey fluid. It can be observed that the increase of t acts as an increase of the magnitude of velocity components near the plate, and this corresponds to the shear-thinning behavior of the examined non-Newtonian fluid. Figure 7 presents the velocity field and the shear stress profiles at different values of y. It is noticeable that velocity and shear stress both decreases

> t=6 t=7

> t=8

Figure 6. Velocity and shear stress profiles corresponding to the cosine oscillations of the duct for different values of t.

Figure 7. Velocity and shear stress profiles corresponding to the cosine oscillations of the duct for different values of y.

Other parameters are taken as x = 0.5, λ = 1.4, U = 0.2, H = 0.5, K = 0.6, d = 1, h = 2, θ = 0.6, ω = 0.5 and ν = 0.1.

Other parameters are taken as x = 0.5, λ = 1.4, U = 0.2, H = 0.5, K = 0.6, d = 1, h = 2, θ = 0.6, ω = 0.5 and ν = 0.1.

y=0.1 y=0.3

y=0.6

0 1 2 3

y

0 1 2 3

t

t=6 t=7

t=8

y=0.1 y=0.3 y=0.6

<sup>4</sup> 2 10

2 10 <sup>4</sup>

4 10 <sup>4</sup>

6 10 <sup>4</sup>

0

by increasing y.

136 Porosity - Process, Technologies and Applications

5 10 <sup>5</sup>

1 10 <sup>4</sup>

2 10 <sup>4</sup>

u

3 10 <sup>4</sup>

1 10 <sup>4</sup>

u

1.5 10 <sup>4</sup>

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>0</sup>

y

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>0</sup>

t

Amir Khan1,2\*, Gul Zaman1 and Obaid Algahtani<sup>3</sup>

\*Address all correspondence to: amir.maths@gmail.com

1 Department of Mathematics, University of Malakand, Chakdara, Dir (Lower), Khyber Pakhtunkhwa, Pakistan

2 Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, Pakistan

3 Department of Mathematics, Science College, King Saud University, Saudi Arabia
