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In this research, the analytical methods of the differential transform method (DTM), homotopy asymptotic method (HAM), optimal homotopy asymptotic method (OHAM), Adomian decomposition method (ADM), variation iteration method (VIM) and reproducing kernel Hilbert space method (RKHSM), and the numerical method of the finite difference method (FDM) for (analytical-numerical) simulation of 2D viscous flow along expanding/contracting channels with permeable borders are carried out. The solutions for analytical method are obtained in series form (and the series are convergent), while for the numerical method the solution is obtained taking into account approximation techniques of second-order accuracy. The OHAM and HAM provide an appropriate method for controlling the convergence of the discretization series and adjusting convergence domains, despite having a problem for large sizes of obtained results in series form; for instance, the size of the series solution for the DTM is very small for the same order of accuracy. It is hard to judge which method is the best and all of them have their advantages and disadvantages. For instance, applying the DTM to BVPs is difficult; however, solving BVPs with the HAM, OHAM and VIM is simple and straightforward. The extracted solutions, in comparison with the computational solutions (shooting procedure combined with a Runge–Kutta fourth-order scheme, finite difference method), demonstrate remarkable accuracy. Finally, CPU time, average error and residual error for different cases are presented in tables and figures. Full article

This work explains the cooling capabilities of ethylene glycol (EG)-based nanofluid containing aluminum oxide (Al₂O₃) as nanoparticles. Because of its enhanced thermophysical properties, Nanofluids are used in many application areas of mechanical and engineering in the form of nanofluid coolants such as electronics and vehicle cooling, transformer, and computer cooling. Depending on the heating and cooling systems, it is also used as an anti-freezing agent, which lowers the freezing point but enhances boiling point and temperature coolant. After using appropriate similarity transformation, the present Koo–Kleinstreuer–Li model for solving the boundary value problem (BVP) is tackled analytically. A comparison is made with a purely analytical approach by a modified version of the semi-analytical Adomian Decomposition Method (ADM), which is introduced by Duan and Rach (Duan–Rach Approach) and shooting technique. Analytical and graphical treatment of the flow regime is carried out, and the behavior of the leading parameters on the velocity, temperature, concentration profile with the behavior of physical quantities i.e., skin friction coefficient, local Nusselt number, and local Sherwood number are illustrated. This study confirms that, due to extraction in width the flow moves away from the lower plate whereas it moves towards near the upper plate and a rapid decrease in temperature is marked when alumina–EG nanofluids are taken into account. Full article