Free convection in a trapezoidal cavity filled with a micropolar fluid

• Natural convection in a trapezoidal cavity filled with a micropolar fluid was studied.
• Governing equations were formulated using the Boussinesq approach and Eringen theory.
• Vortex viscosity parameter dampens the convective fluid flow and heat transfer.
• Micro-gyration parameter does not lead to essential changes of analyzed parameters.

The present investigation deals with the study of steady laminar natural convective flow and heat transfer of micropolar fluids in a trapezoidal cavity. The bottom wall of the cavity is kept at high constant temperature, the inclined walls is kept at low constant temperatures while the top horizontal wall is adiabatic. Governing equations formulated in dimensionless stream function and vorticity variables has been solved by finite difference method of the second order accuracy. Comprehensive verification of the utilized numerical method and mathematical model has shown a good agreement with numerical data of other authors. Computations have been carried out to analyze the effects of Rayleigh number, Prandtl number and vortex viscosity parameter both for weak and strong concentration cases. Obtained results have been presented in the form of streamlines, isotherms and vorticity profiles as well as the variation of the average Nusselt number and fluid flow rate. It has been shown that an increase in the vortex viscosity parameter leads to attenuation of the convective flow and heat transfer inside the cavity.