Abstract
AbstractThe unsteady convective boundary layer flow of a nanofluid along a permeable shrinking/stretching plate under suction and second-order slip effects has been developed. Buongiorno’s two-component nonhomogeneous equilibrium model is implemented to take the effects of Brownian motion and thermophoresis into consideration. It can be emphasized that, our two-phase nanofluid model along with slip concentration at the wall shows better physical aspects relative to taking the constant volume concentration at the wall. The similarity transformation method (STM), allows us to reducing nonlinear governing PDEs to nonlinear dimensionless ODEs, before being solved numerically by employing the Keller-box method (KBM). The graphical results portray the effects of model parameters on boundary layer behavior. Moreover, results validation has been demonstrated as the skin friction and the reduced Nusselt number. We understand shrinking plate case is a key factor affecting non-uniqueness of the solutions and the range of the shrinking parameter for which the solution exists, increases with the first order slip parameter, the absolute value of the second order slip parameter as well as the transpiration rate parameter. Besides, the second-order slip at the interface decreases the rate of heat transfer in a nanofluid. Finally, the analysis for no-slip and first-order slip boundary conditions can also be retrieved as special cases of the present model.
Highlights
The unsteady convective boundary layer ow of a nano uid along a permeable shrinking/stretching plate under suction and second-order slip e ects has been developed
In Ref. [29], Rosca and Pop inquire another condition involving second order slip condition to examine surface heat ux. They found the high in uence of second order slip on the properties of ow and heat transfer. Considering these facts, the authors of this paper studied the e ects of second-order slip on unsteady convective boundary layer ow of a nano uid on a permeable shrinking/stretching sheet with suction in surface and to include the e ects of Brownian motion and thermophoresis for the nano uids, the two-component nonhomogeneous equilibrium model of Buongiorno is used
(38) We have to solve a complex boundary value problem that has been represented in Eqs. (23)-(26) with nine governing parameters such as unsteadiness parameter (A), shrinking parameter (λ), mass suction velocity (Vw), thermophoresis parameter (Nt), Brownian motion parameter (Nb), rstorder slip parameter (m), second-order slip parameter (n), Lewis number (Le) and Prandtl number (Pr)
Summary
Abstract: The unsteady convective boundary layer ow of a nano uid along a permeable shrinking/stretching plate under suction and second-order slip e ects has been developed. The graphical results portray the e ects of model parameters on boundary layer behavior. We understand shrinking plate case is a key factor a ecting non-uniqueness of the solutions and the range of the shrinking parameter for which the solution exists, increases with the rst order slip parameter, the absolute value of the second order slip parameter as well as the transpiration rate parameter. The second-order slip at the interface decreases the rate of heat transfer in a nano uid. The analysis for no-slip and rst-order slip boundary conditions can be retrieved as special cases of the present model
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