The chemical entropy generation analysis is an approach to optimize the performance
of different thermal systems by investigating the related irreversibility of the system.
The influences of second-order slip with the chemical reaction on the boundary layer
flow and heat transfer of a non-Newtonian nanofluid in a non-Darcian porous medium
have been investigated numerically. Simultaneous solutions are presented for first and
second-order velocity slips. The second-order boundary conditions serve as a closure
of a system of the continuity, transport, and energy differential equations. The current
work differs from the previous studies in the application of a new second-order slip
velocity model. The Casson fluid model is applied to characterize the non-Newtonian
fluid behavior. The effect of the second slip parameter on the present physical parameters
was discussed through graphs and it was found that this type of slip is a very
important one to predict the investigated physical model. The present study provides
two fast convergent methods on the semi-infinite interval, namely Chebyshev collocation
method and optimal homotopy analysis method are used to analyze the
fluid flow, heat, and mass transport. Compared with available analytical and numerical
solutions, current methods are effective, quickly converging, and with great accuracy.
It was shown that the account for the second-order terms in the boundary conditions
noticeably affects the fluid flow characteristics and does not influence on the heat
transfer characteristics.