“…These appropriate thermal-hydraulic specifications of the VGs as a passive heat transfer enhancement technique have motivated many investigators to study and optimize the performance of these geometries in different heat exchange systems, such as circular and noncircular ducts [6][7][8][9][10][11][12], flat PFHE [13][14][15][16][17][18], tube-fin heat exchanger [19][20][21][22][23][24][25][26][27], heat sink [28,29], electronic chip [30,31], and micro-and-mini channels [32]. However, in most studies gases were often used as the heat transfer medium, and studies of liquids are very low.…”