Final answer:
The double pipe heat exchanger where the fluids flow in opposite directions is known as a counter-flow heat exchanger, which is distinct from parallel and cross flow configurations and typically offers higher efficiency.
Step-by-step explanation:
The type of the double pipe heat exchanger where one fluid flows through a pipe and another fluid flows through a larger pipe that surrounds the first pipe and in which the fluids flow in opposite directions is known as a counter-flow heat exchanger. This design typically results in higher efficiency because the temperature gradient between the fluids is more uniform over the length of the exchanger, which drives heat transfer. The counter-flow arrangement is not to be confused with parallel flow, where fluids flow in the same direction, or cross flow, where they move perpendicular to each other.