Natural convection in enclosure with heating and cooling by sinusoidal temperature profiles on one side

A numerical study has been carried out in rectangular enclosures, which have a vertical active wall with all the other walls insulated. The equally divided active sidewall is heated and cooled with sinusoidal temperature profiles. Two cases have been considered: the first is the lower part is heated while the upper part is cooled and the second, the upper part is heated and lower part is cooled. Steady state heat transfer by laminar natural convection has been studied by numerically solving equations of mass, momentum and energy, to determine the thermal penetration in the enclosures and heat transfer as a function of Rayleigh number, the aspect ratio and the position of side heating with respect to side cooling. Rayleigh number was varied from 103 to 106 and the aspect ratio from 0.2 to 5, and the results are presented in the form of streamlines and isotherms, local and average Nusselt number, and heat penetration length. It is found that the penetration approaches to 100% at high Rayleigh numbers when the lower part is heated while the higher part is cooled. In the case of the higher part is heated and the lower part is cooled, the penetration is limited to 70% passing through maxima at Rayleigh number below 106.