The proficiency of hybrid nanofluid from Cu-Al₂O₃/water formation as the heat transfer coolant is numerically analyzed using the powerful and user-friendly interface bvp4c in the Matlab software. For that purpose, the Cu-Al₂O₃/water nanofluid flow between two parallel plates is examined where the lower plate can be deformed while the upper plate moves towards/away from the lower plate. Other considerable factors are the wall mass suction/injection and the magnetic field that applied on the lower plate. The reduced ordinary (similarity) differential equations are solved using the bvp4c application. The validation of this novel model is conducted by comparing a few of numerical values for the reduced case of viscous fluid. The results imply the potency of this heat transfer fluid which can enhance the heat transfer performance for both upper and lower plates approximately by 7.10% and 4.11%, respectively. An increase of squeezing parameter deteriorates the heat transfer coefficient by 4.28% (upper) and 5.35% (lower), accordingly. The rise of suction strength inflates the heat transfer at the lower plate while the presence of the magnetic field shows a reverse result.

An investigation has been done on the hybrid nanofluid slip flow in the existence of heat generation over an exponentially stretching/shrinking permeable sheet. Hybridization of alumina and copper with water as the base fluid is considered. The mathematical model is simplified through the similarity transformation. A numerical solver named bvp4c in Matlab software is utilized to facilitate the problem-solving process and dual solutions are attained. The influences of several pertinent parameters on the main physical quantities of interest and the profiles are scrutinized and presented in the form of graphs. Through the stability analysis, only the first solution is considered as the physical solution. As such, the findings conclude that the upsurges of volume fraction on the copper nanoparticle could enhance the skin friction coefficient and the local Nusselt number.

The present work highlights the stagnation point flow with mixed convection induced by a Riga plate using a Cu-Al ${}_2$ O ${}_3$ /water hybrid nanofluid. The electromagnetohydrodynamic (EMHD) force generated from the Riga plate was influential in the heat transfer performance and applicable to delay the boundary layer separation. Similarity transformation was used to reduce the complexity of the governing model. MATLAB software, through the bvp4c function, was used to compute the resulting nonlinear ODEs. Pure forced convective flow has a distinctive solution, whereas two similarity solutions were attainable for the buoyancy assisting and opposing flows. The first solution was validated as the physical solution through the analysis of flow stability. The accretion of copper volumetric concentration inflated the heat transfer rate for the aiding and opposing flows. The heat transfer rate increased approximately up to an average of 10.216% when the copper volumetric concentration increased from 0.005 $(0.5\%)$ to 0.03 $(3\%)$ .