Mixed convection heat transfer and entropy generation of water inside a square vented enclosure with and without four vibrating cylinders in horizontal and vertical directions

The control and improvement of heat transfer in enclosures is very important in several engineering applications. In the current two-dimensional numerical study, the mixed convection and entropy generation of water flowing inside a square vented enclosure that contains four vibrating cylinders with relatively low frequencies fr = 1, 2, 3, 5 Hz in the vertical and horizontal directions are reported. The effects of Reynolds and Richardson numbers, vibration frequency, vibration amplitude, and the direction of the cylinders' vibration on heat transfer and entropy generation are presented for various cases. The horizontal walls of the enclosure are kept adiabatic while the vertical left and right walls are hot and cold, respectively. The linear regression analysis was used to reveal the rate of increase in the Nusselt number with the Reynolds and Richardson numbers number for each cases. Series of analyses show that the existence and the vibration of the cylinders increases heat transfer but the vibration in the horizontal direction is more effective since the top and bottom walls of the enclosure are adiabatic. It is found that the entropy generation due to heat transfer is low at the center of the enclosure. The direct relationship between the heat transfer and both Reynolds and Richardson numbers is reported. In terms of heat transfer, it is found that the critical vibration frequency and amplitude are fr = 4 and A = 0.05L and 0.075L.