Falkner–Skan Problem for a Stretching or Shrinking Wedge With Nanoparticle Aggregation

The Falkner–Skan problem for stretching or shrining wedge is generalized for nanoparticle aggregation effects. The model is developed in the presence of the magnetic field, thermal radiation, and suction/injection effects. For the inclusion of nanoparticle aggregation effects, modifications of the Krieger-Dougherty model and Maxwell and Bruggeman models are used to predict effective viscosity and thermal conductivity of titania–ethylene glycol (TiO₂/EG) nanofluid, respectively. These models are already tested experimentally in the past and are known to predict the true values for the TiO₂/EG nanofluid with aggregated nanoparticles. The system of equations depicting the Falkner–Skan problem for a wedge with nanoparticle aggregation effects is transformed via similarity transformations and solved via the “bvp4c” function, which is accessible by matlab software. The validation of results is done through a comparison of results with published literature and a comparison of present results with the “bvp5c” function and RKF-Shooting Technique. As suggested by the previously published experimental studies, it is observed that the nanoparticle aggregation effects are strong even when the nanoparticle concentration is low. The heat transmission rate of TiO₂/EG nanofluid is seen as higher with nanoparticle aggregation effects in comparison to its absence. The streamlines become denser and more intense with the presence of a magnetic field. The results of this study apply to several thermal systems, engineering, and industrial process, which utilize nanofluid for cooling, and heating processes.