Thermal characterization of hybrid nanofluid with impact of convective boundary layer flow and Joule heating law: Dual solutions case study

This study emphasizes the dual exposition of the impact of convective condition and the significant effects of magnetic field, heat source and velocity slip on hybrid nanofluid flow over the exponentially shrinking sheet. The hybrid nanofluid is regarded as a contemporary variety of nanofluid; consequently, it is utilized to enhance the efficiency of heat transfer. By applying the Tiwari–Das model, the key objective of the current research is to investigate the impact of involving factors Biot number, Eckert number, volume fraction, magnetohydrodynamic (MHD), slip and suction on the temperature and velocity profiles. In addition, the Nusselt number and skin friction variations have been explored against the suction effect on the solid volume fraction of copper [Formula: see text] [1–3%] and the Biot number [Formula: see text] [1–3%]. The nonlinear partial differential equations are converted to a set of an ordinary differential equations by incorporating exponential similarity vectors. Eventually, ordinary differential equations are rectified utilizing MATLAB bvp4c solver. The results demonstrate the presence of dual exposition for suction with varying values of copper volume fraction and the Biot number. The heat transmission rate is observed to escalate in both cases as the strength of the Biot and Eckert numbers intensifies in the range of 1–3%. In summary, the results show that duality and non-unique solutions occur in the aiding flow situation when the suction [Formula: see text], while there is no flow and unique solutions of hybrid nanofluid feasible when [Formula: see text].