This study investigates the heat augmentation and hydromagnetic flow of water-based carbon nanotubes (CNTs) inside a partially heated rectangular fin-shaped cavity. A thin heated rod is placed within the cavity to create a resistance or to provide a source for heat transfer. The obstacle is tested for the heated case, while the right side of the horizontal tip is tested for three different temperatures (adiabatic, cold, and heated). The left vertical side of the cavity is partially heated with temperature T_h, and the rest of the sides are kept cold at temperature T_c except the right tip. Two different thermal boundary conditions (prescribed temperature and adiabatic) are employed on the fin tip. The CNTs and water are assumed to be in thermal equilibrium with no-slip velocity. The magnetic field and thermal radiation are introduced in the momentum and energy equations, respectively. The governing equations are obtained in dimensionless form by means of dimensionless variables. The numerical computation is performed via the finite element method using the Galerkin approach. The substantial effects of emerging parameters on the streamlines, isotherms, dimensionless velocities, and temperature are reported graphically and discussed. In the case of a cold or adiabatic fin-tip, a drop to minimum is found in the dimensionless temperature. The components of velocity are perceived maximum at a vertical corner while minimum at the horizontal corner. It is demonstrated that the local Nusselt numbers are increased by introducing both solid volume fraction of CNTs and radiation effects, while the Nusselt number noticed maximum at the corners.

The constructal design-based model is reported to analyze the thermal control and heat augmentation inside a split lid-driven square cavity. A Y-shaped obstacle is placed within the cavity, which is filled with Al₂O₃–Cu–water hybrid nanofluids. The concept of the split-lid-driven cavity is utilized for the first time. The governing flow mathematical structure is obtained in terms of a system of partial differential equations and converted to a non-dimensional form through dimensionless variables. The numerical experiments are performed by employing a Galerkin finite element scheme for different values of involved physical parameters. The effects of pertinent parameters on the streamlines, isotherms, dimensionless temperature, and Nusselt numbers are investigated for different values of the Richardson number. Due to the simultaneous motion of the split-lids, the streamlines and isotherms show symmetrical distribution. The local Nusselt number increases with the moving split-lids and attains the maximum value when both lids meet. The average Nusselt number decreases with an increase in the Richardson number. It is important to note that the Y-shaped obstacle enhances the heat transfer rate in the cavity.