A combustor for a turbomachine, the combustor comprising: a combustion chamber and a heat exchanger; the heat exchanger dividing the combustion chamber into a rich combustion zone and a low temperature zone; wherein the low temperature zone is located downstream of the rich zone, the heat exchanger comprising: a plurality of air passages; a plurality of air inlets in fluid communication with the plurality of air passages; and a plurality of combustion gas passages, each of the combustion gas passages extending between a combustion gas inlet in fluid communication with the rich combustion zone and a combustion gas outlet in fluid communication with the low temperature zone, the plurality of combustion gas passages in thermal communication with the plurality of air passages, characterized in that each combustion gas passage of the plurality of combustion gas passages extends along a curved line and the plurality of cooling air passages extend between the plurality of air inlets and a plurality of air outlets in fluid communication with the low temperature zone whereby the combustion gas passages and the air passages discharge only into the low temperature zone downstream the heat exchanger. a combustion chamber and a heat exchanger; the heat exchanger dividing the combustion chamber into a rich combustion zone and a low temperature zone; wherein the low temperature zone is located downstream of the rich zone, the heat exchanger comprising: a plurality of air passages; a plurality of air inlets in fluid communication with the plurality of air passages; and a plurality of combustion gas passages, each of the combustion gas passages extending between a combustion gas inlet in fluid communication with the rich combustion zone and a combustion gas outlet in fluid communication with the low temperature zone, the plurality of combustion gas passages in thermal communication with the plurality of air passages, characterized in that each combustion gas passage of the plurality of combustion gas passages extends along a curved line and the plurality of cooling air passages extend between the plurality of air inlets and a plurality of air outlets in fluid communication with the low temperature zone whereby the combustion gas passages and the air passages discharge only into the low temperature zone downstream the heat exchanger. a plurality of air passages; a plurality of air inlets in fluid communication with the plurality of air passages; and a plurality of combustion gas passages, each of the combustion gas passages extending between a combustion gas inlet in fluid communication with the rich combustion zone and a combustion gas outlet in fluid communication with the low temperature zone, the plurality of combustion gas passages in thermal communication with the plurality of air passages, characterized in that each combustion gas passage of the plurality of combustion gas passages extends along a curved line and the plurality of cooling air passages extend between the plurality of air inlets and a plurality of air outlets in fluid communication with the low temperature zone whereby the combustion gas passages and the air passages discharge only into the low temperature zone downstream the heat exchanger.