Heat and mass transfer conduct in an unsteady two- dimensional stream between parallel sheets

In the present research, an effort has been made to analytically solve heat and mass linear/ nonlinear as well as steady/ unsteady equations in a viscous nanofluid squeezed between parallel sheets. Using Python and the SymPy library, the nanofluid with viscous properties between parallel sheets has been analyzed to symbolically solve flow, heat, and mass transfer effects equations through the Homotopy Perturbation Method and Akbari-Ganji Method approaches. The two nanofluids selected to conduct this study are Copper as well as $A{l}_2{O}_3$, whose sizes are 29 nm and 47 nm respectively. The provided details encompass the outcomes of active variables on flow and the transfer of heat coupled with mass. The Homotopy Perturbation and Akbari-Ganji methods have resulted in top-of-the-line consequences compared to analytical and numerical approaches. This research study highlights a faster and more accurate computation to conduct the analytic section of the study. The outcome shows that the increase of the Prandtl number and the Eckert number will increase Nusselt. However, skin friction increases with the increase in the Schmidt number. Furthermore, a rise in Schmidt number and parameters related to chemical reactions leads to an elevated Sherwood number. The outcomes of the study presented here provide a more innovative and precise insight, and the comparison with the available literature also proves there is a well-agreed numerical calculation. Microchips in engineering and medical-related industries would enjoy the outcomes obtained from this study. This study proves that the maximum and minimum amounts of heat transfer in respect occur at $\eta =$0 and $\eta =1$. Moreover, the maximum and minimum amounts of error are equal to 0.0001 and 0.00001, respectively. The maximum and minimum amounts of concentration occur at $\eta =$1 and $\eta =0$ in order. Finally, the maximum and minimum amounts of error are equal to 0.000016 and 0.000002, respectively.