Numerical study of the heater length effect on the heating of a solid circular obstruction centered in an open cavity

The steady vortex formation and thermal behavior in a two-dimensional square ventilated cavity is numerically studied. The governing equations of mass, momentum and energy are solved with a finite element method combined with an operator splitting scheme. We analyze the flow occurring inside the enclosure with a centered circular obstruction and a heater plate located at the center of the lower wall of the cavity. The size of the heater is varied for five different lengths. The simulations are obtained for Richardson and Prandtl numbers of 0.01 to 10.0 with a Reynolds number of 400. Results are reported in the form of streamlines, isotherms, average Nusselt number, average bulk fluid and obstruction temperatures. The effects of the heater length, Richardson number and Prandtl number on the hydrodynamics and thermal behavior have been investigated. Four vortex formation mechanisms are identified: (a) the inertial effect of the inlet jet which moves from the lower left sidewall to the upper right sidewall, (b) the detachment of the boundary layer from the wall located above of the entrance of the cavity and from the obstruction, (c) the rolling up of the fluid when this meets with the corners of the cavity and (d) the thermal boundary layer formed on the heater which originates a thermal plume with instabilities traveling upward. It is observed that for low Prandtl numbers with large heater sizes and high Richardson numbers the temperature of the obstruction is increased.