Analytical and Numerical Analyses of MHD Non-Newtonian Third-Grade Nanofluid in Couette and Poiseuille Flows Using AGM

In the present study, an analytical solution for MHD flow-heat transfer highly non-linear equations of non-Newtonian third-grade nanofluid is established using the AGM method while considering the effect of the magnetic field, the radiation heat transfer, the inclination and the nanoparticles fraction. From dimensionless analysis, the main characteristic parameters are identified, specifically the viscoelastic parameter, the magnetic parameter, the gravitational parameter, the generalized pressure gradient, the thermal radiation parameter, the Brinkman number and the Hamilton number. Two classes of problems, namely, plane Couette flow and plane Poiseuille flow, are considered. Validation was conducted using results from established numerical methods, including Mathematica software, the Adomian Decomposition Method (ADM), and BVP4C solver to benchmark our findings derived via the Akbari Gangi Method. The comparative analysis reveals the reliability and accuracy of the established analytical solutions. The effect of the main parameters of water-SWCNT nanofluid on velocity and temperature profiles are graphically illustrated and discussed. The main results reveal that increasing a magnetic parameter results in a significant drop in the velocity. Furthermore, the rise in Brinkman's number and the radiation parameter affect the temperature differently. Additionally, the viscoelastic and gravitational parameters have opposite velocity and temperature effects. The results demonstrate the complex interaction between several physical characteristic parameters in the fluid dynamics and heat transfer processes. The efficient and highly accurate series-based analytical solutions for flow velocity and temperature obtained through the Akbari-Ganji Method provide valuable insights and are a powerful tool for addressing similar problems in fluid dynamics and heat transfer.