Stagnation point flow over a stretching/shrinking sheet in a carbon nanotubes with slip effects

The consideration of the stagnation point flow over a stretching/shrinking sheet in carbon nanotubes (CNTs) is investigated. Mathematical models are derived for three boundary layer flow problems over a linearly, nonlinearly and exponentially stretching/shrinking sheet in CNTs with the presence of slip at the surface. Both single- and multi-wall CNTs are used along with two base fluids which are water and kerosene. Similarity transformation are used to transform the partial differential equations into a nonlinear ordinary differential equations. The stability analysis is derived for linear case by introducing the partial differential equations in unsteady case. These equations are then solved by using bvp4c solver in Matlab. Numerical results of skin friction coefficient and local Nusselt number are exhibited in forms of table and graph and also for profiles of velocity and temperature for a range of numerous parameters such as Prandtl number Pr, CNTs volume fraction φ, velocity slip parameter σ, thermal slip parameter σt, heat generation parameter Q, suction/injection parameter S, stretching/shrinking parameter ∈ and nonlinear parameter β. These parameters are observed to have a major influence on coefficient of skin friction and the local Nusselt number which illustrates the rate of heat transfer at the surface. The results show that solutions for shrinking sheet are dual solutions while unique solutions for stretching sheet. It is noticed that slip parameter, suction/injection parameter and nonlinear parameter widens the range in which the dual solutions exist. Furthermore, the first solution is found stable meanwhile the second solution is unstable and it is obtained by performing a stability analysis.

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