Table 1 Comparison of Previous Studies vs. Present Work.
Aspect | Previous Studies | Present Study |
|---|---|---|
Numerical Method | Most studies employ shooting methods, Runge–Kutta, or MATLAB’s bvp4c solver, Homotopy Analysis, or Spectral collocation methods. For example, Kanwal et al.20 used bvp4c for nanofluid flow with activation energy and radiation | Applies the Successive Over-Relaxation (SOR) method—a robust finite-difference scheme offering rapid and stable convergence for the strongly nonlinear boundary-layer equations encountered |
Thermal Radiation | Nonlinear thermal radiation occasionally included in hybrid-nanofluid rotating-disk studies (e.g., Mishra et al.54, Panda et al.55 & Farooq et al.67 considered hybrid nanofluid with nonlinear radiation) | Integrates nonlinear \(T^{4}\) thermal radiation, more accurate under high temperature differences, into the hybrid nanofluid model, enhancing realism for heat-transfer scaling |
Chemical Effects | Limited inclusion of Arrhenius kinetics. Only few studies examined Arrhenius activation energy in Darcy–Forchheimer rotating-disk flow using shooting methods | Incorporates Arrhenius activation energy into the rotating disk hybrid nanofluid model by incorporating SOR technique, enabling realistic modeling of temperature sensitive reactive transport relevant in catalytic and biochemical applications |
Nanoparticle Types | Typical works focus on bi-hybrid suspensions with spherical particles. Acharya et al.64 & Azhar et al.65 examined a hybrid nanofluid flow with metal oxide pairs | Studies a hybrid system (SWCNT-\(TiO_{2}\) & MWCNT-\(CoFe_{2} O_{4} \,\)), combining anisotropic (brick & cylinder) and magnetic CNT/oxide composites, a unique formulation in rotating-disk nanofluid research |
Shape Factor | Some works assess nanoparticle shape, e.g., Azhar et al.65 examined Axisymmetric transport of MoS₂–SiO₂ nanocomposites in ethylene glycol with sphericity-based evaluation of nanoscale particles | Explicitly includes nanoparticle shape factors (e.g., brick and cylindrical morphology of SWCNT-\(TiO_{2}\) & MWCNT-\(CoFe_{2} O_{4} \,\)) in effective property modeling, which significantly influences conductivity and viscosity in hybrid systems |
Application Relevance | Focus on academic modeling; limited industrial linkage | Model relevance extended to catalytic reactors, polymer processing, thermal management, and energy systems due to combined radiation reaction nanoparticle effects |
