This part is listed by BMW as BMW part number 17117540810 (17 11 7 540 810) and is described as URO Parts Power Steering Cooler for E82/E88 135i 1M (2008-2013) and E90/E92/E93 335i, 335is 335ix (2007-2013).
This is the fluid cooler used in the power steering system. BMW calls it a radiator or a loop. The cooler runs fluid from the steering rack back to the reservoir and is exposed to airflow to cool the fluid. Leaks here are uncommon unless the pipes have been damaged by debris or corrosion.
BMW Fitments:
1 Series
E82 / E88 (08-13) > 135i N54 (08-10)
E82 / E88 (08-13) > 135i N55 (11-13)
E82 / E88 (08-13) > 135is N55 (11-13)
E82 / E88 (08-13) > 1M (11-12)
3 Series
E90 / E91 / E92 / E93 (06-13) > 335i N54 (07-10)
E90 / E91 / E92 / E93 (06-13) > 335i N55 (11-13)
E90 / E91 / E92 / E93 (06-13) > 335is N54
E90 / E91 / E92 / E93 (06-13) > 335xi N54 (07-10)
E90 / E91 / E92 / E93 (06-13) > 335xi N55 (11-13)
