A laundry appliance (12) includes a rotating drum (18) for processing laundry. A blower directs process air (24) through an air path (20) that includes the rotating drum (18). A heat exchanger (56) is positioned within the air path (20) that cools and dehumidifies the process air (24). A plurality of air filters (30) arranged sequentially captures lint (32) from the process air (24) at respective positions upstream of the heat exchanger (56). A filter spray system (34) has a plurality of fluid sprayers (36) that deliver fluid (38) to a surface of each air filter (30) of the plurality of air filters (30). Each fluid sprayer (36) of the plurality of fluid sprayers (36) directs captured lint (270) away from a respective air filter (30) of the plurality of air filters (30).