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.

This study is to investigate the magnetohydrodynamic (MHD) stagnation point flow and heat transfer characteristic nanofluid of carbon nanotube (CNTs) over the shrinking surface with heat sink effects. Similarity equations deduced from momentum and energy equation of partial differential equations are solved numerically. This study looks at the different parameters of the flow and heat transfer using first phase model which is Tiwari-Das. The parameter discussed were volume fraction nanoparticle, magnetic parameter, heat sink/source parameters, and a different type of nanofluid and based fluids. Present results revealed that the rate of nanofluid (SWCNT/kerosene) in terms of flow and heat transfer is better than (MWCNT/kerosene) and (CNT/water) and regular fluid (water). Graphically, the variation results of dual solution exist for shrinking parameter in range λc<λ≤−1 for different values of volume fraction nanoparticle, magnetic, heat sink parameters, and a different type of nanofluid. However, a unique solution exists at −1<λ<1, and no solutions exist at λ<λc which is a critical value. In addition, the local Nusselt number decreases with increasing volume fraction nanoparticle when there exists a heat sink effect. The values of the skin friction coefficient and local Nusselt number increase for both solutions with the increase in magnetic parameter. In this study, the investigation on the flow and heat transfer of MHD stagnation point nanofluid through a shrinking surface with heat sink effect shows how important the application to industrial applications.