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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, λ c < λ < − λ and that the critical point λ c also exists in a range of −1.5 < λ c   < −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. [ABSTRACT FROM AUTHOR]

In this study, the heat and mass transfer characteristics of nanofluid flow over a nonlinearly stretching sheet are investigated. The important effects of axisymmetric of thermal conductivity and viscous dissipation have been included in the model of nanofluids. The Buongiorno model is considered to solve the nanofluid boundary layer problem. The governing nonlinear partial differential equations have been transformed into a system of ordinary differential equations and are solved numerically via the shooting technique. The validity of this method was verified by comparison with previous work performed for nanofluids without the effects of the magnetic field and viscous dissipation. The analytical investigation is carried out for different governing parameters, namely, the Brownian motion parameter, thermophoresis parameter, magnetic parameter, Biot number, and Eckert number. The results indicate that the skin friction coefficient has a direct relationship with the Brownian motion number and thermophoresis number. Moreover, it can be seen that the Nusselt number decreases with the increase of the magnetic parameter and Eckert number. [ABSTRACT FROM AUTHOR]