a turbine engine cooling arrangement according to an example of the present disclosure includes , among other things , a core passage for receiving a core flow for combustion , a first airflow source including a first passage adjacent the core passage for conveying a first airflow , a second airflow source including a second passage adjacent the first passage for conveying a second airflow , and a heat exchanger that is thermally connected with the first passage and the second passage for transferring heat between the first airflow and the second airflow . the first airflow and the second airflow stream over the heat exchanger in a parallel radial direction and a parallel axial direction . an engine inlet divides inlet air into the core flow , the first airflow , and the second airflow . a method of providing cooling air is also disclosed .