In nanotechnology research, nanofluid technology contributes many applications to engineering applications and industry, such as power generation, solar collection, heat exchangers for cooling, and many more. However, there are still a few constraints in terms of heat transfer enhancement, although nanofluid properties show the best heat transfer rate compared with conventional fluids. Thus, this study was conducted for the purpose of investigating the behaviors of flow and heat transfer of hybrid nanofluid with carbon nanotubes (CNTs) on a permeable exponentially shrinking surface, as well as investigating the effects of a magnetic field and heat source/sink. This study was conducted by developing a mathematical model, which was the Tiwari–Das model for momentum and energy equations, and then transforming the model’s partial differential equations (PDEs) to ordinary differential equations (ODEs) using a similarity solution. Next, these equations were solved numerically using the MATLAB bvp4c boundary value problem solver. The authors particularly explored these behaviors with a few variations. Based on the results obtained, it was found that dual solutions exist in a specific range of the shrinking case, and that the critical point also exists in a range of −1.5 < < −1 with different parameters. For the heat source/sink effect, the Nusselt number was higher when heat sink case ε < 0, whereas it decreased when the heat source case ε > 0. Therefore, this study deduced that the heat transfer rate of hybrid nanofluid (CNTs/Cu–water) is better than regular nanofluid (CNT–water) and conventional fluid (water). The present study took into consideration the problem of MHD flow and heat transfer analysis of a hybrid nanofluid towards an exponentially shrinking surface with the presence of heat source/sink and thermal radiation effects. The authors show that dual solutions exist within a specific range of values due to the shrinking case. The current work is predicted to have numerous benefits in equivalent real-world systems.
MHD flow and heat transfer over a porous shrinking surface with velocity slip and temperature jump