This article is focused on the research of passive cooling beams and increasing their cooling capacity. A passive cooling beam with four tubes was chosen as a model. A mathematical model was built using the corresponding criterion equations to capture the behavior of a passive cooling beam. This mathematical model can be used to optimize geometrical parameters (the distance between the ribs, rib height and thickness, and diameter and number of tubes), by changing these geometric parameters we can increase the cooling performance. The work includes a mathematical model for calculating the boundary layer, which has a significant influence on the cooling performance. The results obtained from the created mathematical model show that the model works correctly and can be used to optimize the cooling performance of passive cooling beams. To better understand the behavior of a passive cooling beam in a confined space, the entire device was numerically simulated, as was the flow in the intercostal space.