Statistical and Stability Analysis of MHD Nanofluid Flow Over a Stretching Surface With Melting and Slip Effects

This research investigates the stability of dual solutions for magnetohydrodynamic (MHD) flow of Ree–Eyring nanofluid with base fluid water and alumina nanoparticles in a melting stretching sheet. The heat transfer effects due to the extension of the melting surface in the occurrence of thermal radiation, magnetic fields, and the effects of heat sources/sinks are also considered in this investigation. The present study is novel because it simultaneously considers velocity slip, thermal slip, melting heat transfer, and Ree–Eyring rheology, along with a stability analysis of dual solutions. By suitable similarity transformations, the governing partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs). The numerical solution of the boundary value problem is carried out using the bvp4c solver in MATLAB for computation and graphical presentation. The governing highly nonlinear PDEs were solved computationally, and the resulting physical quantities like skin friction coefficient and Nusselt number were further examined using linear regression analysis. Residual plots and predicted actual comparisons were used to estimate the precision and stability of the obtained solutions. The statistical findings show an excellent correlation among predicted and real values, with coefficients of correlation greater than 0.93 for skin friction and 0.97 for the Nusselt number in the first solution. The findings show that the mathematical framework accurately forecasts the heat transfer properties of the nanofluid system. The graphical results show that the velocity profile decreased with the increase in the Ree–Eyring fluid (REF) parameter and velocity slip parameter; however, the temperature profile amplified with the larger values of the magnetic parameter, REF parameter, and heat generation parameter. The numerical results reveal that with escalation in suction parameter and stretching parameters, the skin friction coefficient decreased, but the Nusselt number showed the opposite trend. The eigenvalues disclose that the first solution is stable and the second solution is unstable. The results seem to be of valuable significance in the high precision industrial coating processes. To the best of the authors’ knowledge, this study is the first time when all aspects of Ree–Eyring nanofluid rheology, melting heat transfer, velocity and thermal slip impacts, and dual solutions stability analysis have been integrated. The current work thus delivers a unified and complete study of the physical and stability properties of the system.