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The study presented gives a succinct overview of the effect of partially applied magnetic field on natural convective heat transfer in a differentially heated inclined cavity. The left and right sidewalls are differentially heated such that their temperatures are maintained (at T h and T c respectively), while the top and bottom walls have been assumed to be adiabatic, such that heat transfer through those walls can be neglected. The results are supposed to elucidate the effect of changing Rayleigh number (Ra), Hartmann number (Ha), and cavity inclination angle (f ) on the thermo-fluid phenomena. The analysis is carried out numerically utilizing finite volume based computing code. The results have been demonstrated in the form of streamlines, isotherms, and average Nusselt number. From the analysis, it is found that the flow structure and associated heat transfer characteristics are severely influenced by the studied range of governing parameters.

We numerically investigate the effect of electrohydrodynamics on a non-Newtonian droplet pair suspended in a Newtonian medium. The leaky dielectric model is implemented to study the response of emulsion drops in an externally applied electric field. Subsequently, the non-Newtonian drop behavior is incorporated using the power law model, whereby three different fluid behaviors are considered for the drops: Newtonian, Shear thinning, and Shear thickening. We validated our numerical model with the available literature data, and the results are in good agreement. The droplets' deformation and net motion are investigated for a range of electrical permittivity ratios of the droplet medium with respect to the surrounding fluid. In this study, four distinct regimes are identified based on the net drop pair motion and the circulation pattern that develops due to the electric stresses inside and around the drops. Furthermore, it is observed that the droplet deformation and their net motion are fastest for the pseudo-plastic drops and slowest for dilatant drops. We devised a simple ratio-based model to understand this behavior. The inferences drawn from this study will help contribute to a better understanding of the behavior of nonlinear fluids under an electric field.