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A steady laminar two-dimensional magnetohydrodynamic mixed-convection flow in trapezoidal enclosures filled with water-based micropolar nanofluids is investigated numerically by using the finite difference method. The left and right inclined vertical sidewalls of the trapezoidal enclosure are maintained at a low temperature. The horizontal top wall is considered adiabatic and moves at a uniform lid-driven velocity, while a part of the bottom wall is subjected to a uniform heat source and the remaining parts of it are considered adiabatic. An external magnetic field at different orientation angles is applied on the left sidewall of the enclosure. The fluid inside the enclosure is a water-based micropolar nanofluid containing different types of solid spherical nanoparticles (Cu, Ag, Al2O3, and TiO2). Parametric studies of the influence of various parameters such as the Hartmann number, Richardson number, the type of nanofluid, magnetic field orientation angle, dimensionless viscosity, dimensionless length, location of a heat source, solid volume fraction in the fluid flow, and the heat transfer rate have been conducted. Comparisons with previously published numerical works are performed and good agreement between the results is obtained. It is found that the average Nusselt number increases when the Richardson number decreases and the solid volume fraction increases, while it decreases as the heat source length increases. Moreover, it is observed that the Hartmann number, heat source location, and the dimensionless viscosity have a significant effect on the average Nusselt number.
Ahmed et al. (Mon,) studied this question.