Natural convection in an open square cavity with discrete heaters at their optimized positions

In this article, we determined optimum positions of discrete heaters by maximizing the conductance and then studied heat transfer and volume flow rate with discrete heaters at their optimum positions. Continuity, Navier–Stokes and energy equations are solved by finite difference – control volume numerical method. The relevant governing parameters were: the Rayleigh numbers, Ra from 103 to 107, the cavity aspect ratio, A=H/L=1, the heater size h/L from 0.05 to 0.20 and number of heaters from 1 to 3. We found that the global conductance is as an increasing function of the Rayleigh number, the heater size and the number of heaters. Best thermal performance is obtained by positioning the discrete heaters closer to the bottom and closer to each other at the beginning of fluid flow. The configuration is not equidistance but follows a function of the Rayleigh number. The Nusselt number and the volume flow rate in and out the open cavity are also increasing functions of the Rayleigh number, the heater size and the number of heaters.