A heat exchanging arrangement is integrated within a gas turbine engine case that at least partially encloses a gas turbine engine. The gas turbine engine has an upstream end and a downstream end which are defined by a core fluid flow through the gas turbine engine. The heat exchanging arrangement includes at least one flow passage defined within the gas turbine engine case having an inlet port and an outlet port. The at least one flow passage is configured to direct at least a portion of a fluid flowing through the gas turbine engine from between a downstream position and an upstream position while traveling between the inlet port and the outlet port.