Author details

and also for both type of flows. It is further depicted that skin friction is maximum for kerosene

Figures 9 and 10 are plotted to see the variations in Nusselt number against nanoparticle volume

It is observed that the magnitude of Nusselt number is minimum at φ= 0. And it significantly increases with increasing the magnitude of nanoparticle volume fraction. The nanoparticle and base fluids are considered as SWCNT and kerosene respectively in Figure 9. Figure 9a illustrates that Nusselt number diminishes with increasing the magnitude of viscosity parameter for both type of flows at fixed values n = Gr = 0.5. Figure 9b shows that Nusselt number increases with increasing the power index both type of flows at fixed values α = Gr = 0.5. Figure 9c reveals that Nusselt number increases with increasing the Grashof number for assisting flow however it reduces with increasing the Grashof number for opposing flow at fixed values α = n = 0.5. Figure 10(a and b) are plotted to see the effects of Kerosene, Ethylene glycol and Engine oil and also effects of SWCNT and MWCNT on Nusselt number at fixed values α = Gr = 0.5, n = 2 for both types of flows (Figure 10a and b). A very minor variation in Nusselt number for SWCNT and MWCNT nanoparticles is noted for assisting and opposing flows. A significant variation in Nusselt number for Kerosene, Ethylene glycol and Engine oil is pointed out where the Nusselt

and minimum for engine oil for both types of CNTs and also for both types of flows.

number is largest for Engine oil and smallest for Kerosene for both type of flows.

The stream lines are plotted through the Figure 11(a–c) to see the effects of power law index at fixed values α = 0.4, Gr = 3,φ= 0.3 for assisting flow where SWCNT as nanoparticle and Kerosene as base fluid are considered. It is noted that stream lines go closer to each other with

A numerical investigation for boundary layer flow of CNTs nanofluids with temperature dependent viscosity over a circular stretching sheet is presented. Effects of Three types of base fluids, power law index, viscosity parameter, nanoparticle volume fraction and Grashof number on flow characteristics, and also skin friction coefficient and Nusselt number are discussed appropriately with numerical computations. The concluding remarks of present discussions

• The nature of velocity and temperature profiles for assisting and opposing flows are

• The velocity boundary layer thickness elaborates with increasing the magnitude of nanoparticle volume fraction, viscosity parameter and power law index for both type of flows.

• The thermal boundary layer thickness expands with reducing the magnitude of viscosity parameter, power law index and nanoparticle volume fraction for both type of flows. • The magnitude of skin friction coefficient enhances with increasing the nanoparticle volume fraction and power law index and it also enhances with decreasing the viscosity

similar for all values of pertinent parameters except Grashof number.

fraction both types of flows.

284 Numerical Simulations in Engineering and Science

increasing the power law index.

5. Concluding remarks

parameter for both type of flows.

are précised as:

Noreen Sher Akbar<sup>1</sup> \*, Dharmendra Tripathi2 and Zafar Hayat Khan<sup>3</sup>

\*Address all correspondence to: noreensher@yahoo.com


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