Heat Transfer and Entropy Generation in a Lithium-Ion Battery Pack Against Battery Spacing and Discharge Rate

Three-dimensional continuity, momentum, and energy equations have been solved in a battery pack of a unit module with 3 x 3 x 3 and 4 x 4 x 4 Li-ion cells to obtain the flow field and temperature distribution around the batteries. The battery spacing to hydraulic diameter ratio in x, y, and z directions have been varied in a wide range from 0.04458 to 0.08172, 0.00833 to 0.07133, and 0.007496 to 0.08052 for 4 x 4 x 4 cells, and 0.06 to 0.11, 0.0111 to 0.09649, 0.01 to 0.11 for 3 x 3 x 3 to obtain the optimum configuration for maximum heat transfer and minimum entropy generation. Air is pumped through the battery pack as a transport medium for heat transfer with Reynolds number (Re) varying in the laminar range from 400 to 2000. The results are plotted in terms of the average surface Nu over the battery surface and average volumetric temperature of the battery and air. It is found that the temperature of the battery pack remains almost constant against Sx. However, a significant rise in battery temperature is observed when we increase Sy. The scenario becomes different when spacing is varied in the z-direction. An optimum spacing for the minimum temperature of the battery pack is obtained at Sz/Dh = 0.03. The temperature variation trend is almost identical in 3 x 3 x 3 and 4 x 4 x 4 cells; however, the absolute temperature inside the pack is lower in 3 x 3 x 3 cells. In each case, the maximum temperature is seen on the batteries located at the top and bottom corners of the outlet. Among all the cases, the maximum temperature of 355 K has been found in 4 x 4 x 4 cells with a 3.6C discharge rate at Sy/Dh of 0.07133. Different discharging rates (1C, 2C, 3.6C, and 4C) have been considered to generate different amounts of heat inside the battery. However, it is numerically and theoretically proved that Nu and the nondimensional volumetric average temperature inside the pack are independent of the heat generation rate inside the battery pack.