Analytical and numerical solutions of squeezing nanofluid flow between parallel plates: A comparison of IRPSM and HPM

The nanofluid flow between two parallel plates has many applications across various fields of engineering. The addition of nanoparticles to conventional fluids can improve the rheological properties of nanofluids, enhance the heat transfer rate, and have other beneficial characteristics. Therefore, a squeezing flow problem between two parallel plates has been investigated in this article. The nanofluid flow is composed of alumina (Al 2 O 3 ) nanoparticles and water, which is used as a base fluid. This study is featured according to the recommendations of a previous study to implement the improved residual power series method (IRPSM). The mathematical model is presented in the form of partial differential equations (PDEs), which are then transformed into ordinary differential equations (ODEs) by means of similarity variables. The considered problem is solved by two analytical methods called IRPSM, the homotopy perturbation method (HPM), and a numerical method (NDSolve). The residual errors of both applied techniques are compared to verify the validation of a new method. The comparison of both applied analytical techniques is conducted at the 17th order of approximations. From the obtained results, we confirmed that both techniques are in great agreement and have a very close relationship. The results of both methods are compared with the numerical method, and it was found that the absolute error between the IRPSM and numerical techniques is much more significant than the absolute error between the HPM and numerical techniques. Also, we have seen that the residuals of IRPSM are quite significant in terms of less residual errors than those of HPM. We confirmed that the IRPSM is a more powerful method than the HPM in terms of solving such types of mathematical problems.