This is the hose running to the inlet on the heater core connector on the firewall of E30 318i (M10), E30 M3, and E31 840i/850i models.
Rubber hoses are ideal when new, as they allow some movement and flexibility during driving. The only problem is that they begin to degrade as they age, and can eventually fail, leaving you with the potential for loss of control from coolant spilling and/or an overheating situation. Replace your radiator hoses as a preventative measure before they fail in order to save you from further headaches and expenses.
This is a Genuine BMW heater hose with a two year warranty. Buying a Genuine part will usually be more expensive than an OEM or aftermarket brand but you are assured that it meets BMW's designs for fitment, performance, and longevity. It will also be the very latest design, incorporating any updates or revisions that an aftermarket brand typically will ignore.
E30 (84-91) > 318i
E30 (84-91) > M3
E31 (91-97) > 840Ci
E31 (91-97) > 850CSi
E31 (91-97) > 850Ci