A reverse-core turbofan engine comprising: a reverse-core gas generator including a compressor section, a combustor section, and a turbine section; a propulsor section including a fan and a fan-tip turbine; and a core duct including: a first portion, disposed aft of the propulsor section, configured to receive air from the propulsor section, and direct air aft, toward an inlet of the reverse-core gas generator; and a second portion, configured to receive air from an exit of the reverse-core gas generator and direct the air forward and radially outward of the propulsor, toward the fan-tip turbine in the propulsor, thereby driving the propulsor; a third portion, configured to receive air from an exit in the fan-tip turbine and direct the air aft, toward an exit of the core duct; wherein the core duct includes at least one hollow strut disposed therein and positioned between the high pressure turbine and the fan-tip turbine; characterized in that: a heat exchanger cooled by air from an outer bypass duct is disposed on the core duct at a location axially aft of the bypass duct, which heat exchanger is operably coupled to and arranged with the compressor section such that, in operation, air is collected and extracted from the compressor section and is circulated through the heat exchanger in a direction substantially opposite to a direction of air flow through the bypass duct and the collected and extracted air is cooled by the air from the outer bypass duct; and wherein the bypass duct is radially exterior to the inlet of the core duct, and radially interior to the third portion of the core duct. a reverse-core gas generator including a compressor section, a combustor section, and a turbine section; a propulsor section including a fan and a fan-tip turbine; and a core duct including: a first portion, disposed aft of the propulsor section, configured to receive air from the propulsor section, and direct air aft, toward an inlet of the reverse-core gas generator; and a second portion, configured to receive air from an exit of the reverse-core gas generator and direct the air forward and radially outward of the propulsor, toward the fan-tip turbine in the propulsor, thereby driving the propulsor; a third portion, configured to receive air from an exit in the fan-tip turbine and direct the air aft, toward an exit of the core duct; wherein the core duct includes at least one hollow strut disposed therein and positioned between the high pressure turbine and the fan-tip turbine; characterized in that: a heat exchanger cooled by air from an outer bypass duct is disposed on the core duct at a location axially aft of the bypass duct, which heat exchanger is operably coupled to and arranged with the compressor section such that, in operation, air is collected and extracted from the compressor section and is circulated through the heat exchanger in a direction substantially opposite to a direction of air flow through the bypass duct and the collected and extracted air is cooled by the air from the outer bypass duct; and wherein the bypass duct is radially exterior to the inlet of the core duct, and radially interior to the third portion of the core duct. a first portion, disposed aft of the propulsor section, configured to receive air from the propulsor section, and direct air aft, toward an inlet of the reverse-core gas generator; and a second portion, configured to receive air from an exit of the reverse-core gas generator and direct the air forward and radially outward of the propulsor, toward the fan-tip turbine in the propulsor, thereby driving the propulsor; a third portion, configured to receive air from an exit in the fan-tip turbine and direct the air aft, toward an exit of the core duct; wherein the core duct includes at least one hollow strut disposed therein and positioned between the high pressure turbine and the fan-tip turbine; characterized in that: a heat exchanger cooled by air from an outer bypass duct is disposed on the core duct at a location axially aft of the bypass duct, which heat exchanger is operably coupled to and arranged with the compressor section such that, in operation, air is collected and extracted from the compressor section and is circulated through the heat exchanger in a direction substantially opposite to a direction of air flow through the bypass duct and the collected and extracted air is cooled by the air from the outer bypass duct; and wherein the bypass duct is radially exterior to the inlet of the core duct, and radially interior to the third portion of the core duct. a heat exchanger cooled by air from an outer bypass duct is disposed on the core duct at a location axially aft of the bypass duct, which heat exchanger is operably coupled to and arranged with the compressor section such that, in operation, air is collected and extracted from the compressor section and is circulated through the heat exchanger in a direction substantially opposite to a direction of air flow through the bypass duct and the collected and extracted air is cooled by the air from the outer bypass duct; and wherein the bypass duct is radially exterior to the inlet of the core duct, and radially interior to the third portion of the core duct.