The hybrid nanofluids have efficient thermal networking due to the trade-off between the pros and cons of the more than one type of suspension. In the current study, water-based hybrid nanofluid is used to investigate mixed convection in a squared enclosure heated with a circular center heater. The cavity is placed inclined under the uniform inclined magnetic field. The squared cavity comprises of two adiabatic vertical walls and two cold horizontal walls. The governing equations are normalized using a suitable set of variables and are solved with the finite element method. A comparison is provided with previously reported results at limiting case. The grid independence is examined for the Nusselt number at the central heater. The analysis reveals the effective role of the concentration of hybrid nanofluid particles in enhancing the heat spread. The results indicate that adding 2% concentration of Ag-MgO hybrid nanoparticles causes an 18.3% uprise in the Nusselt number at the central heater. The heat transfer rate enhances for increasing Hartmann number between 0 and 10 but decreases over 10. For better heat transfer augmentation, a heater with a smaller radius is recommended for the free convection. In contrast, a heater with a larger radius serves the purpose in case of forced convection.

The magnitude of shear stress at the ciliated wall is considered as the measure of efficiency of cilia beatings as it describes the momentum transfer between the medium and the cilia. Under high shear rate, some non-Newtonian fluids behave as visco-inelastic fluids. We consider here a ciliated channel coated with Prandtl fluid, a visco-inelastic fluid, with Hartmann layer under momentum and thermal slip effects. The flow in the channel is produced due to beatings of cilia that obey an elliptic path of motion in the flow direction. An entropy analysis of the flow is also conducted in wave frame. After introducing lubrication approximations in the governing equation, the perturbation solutions are calculated. The data for pressure rise per metachronal wavelength and frictional force at the ciliated wall are obtained by numerical integration. The analysis reveals that the higher values of cilia length and velocity slip parameters support fluid flow near the channel wall surface. Fluid temperature is an increasing function of thermal slip but a decreasing function of cilia length and slip parameters. Entropy in the channel can be minimized with an increase in cilia length and slip effect at the boundary. The magnitude of the heat transfer coefficient decreases by taking the substantial slippage and tiny cilia in length at the microchannel wall.