ANS:B - counter flow with equal heat capacities.

In a counter flow heat exchanger with equal heat capacities, the hot and cold fluids flow in opposite directions. Here's how it works:

1. Opposite Directions: In a counter flow heat exchanger, the hot fluid enters at one end of the exchanger and flows towards the other end, while the cold fluid enters at the opposite end and flows in the opposite direction towards the first end. This arrangement maximizes the temperature difference between the two fluids along the length of the exchanger, enhancing heat transfer efficiency.
2. Equal Heat Capacities: When we say the heat capacities are equal, we mean that both fluids have the same capacity to absorb or release heat per unit mass. This ensures that the temperature changes in the two fluids are directly proportional to the heat exchanged between them.
3. Temperature Distribution: In a counter flow heat exchanger with equal heat capacities, the temperature profiles of both fluids exhibit a straight line pattern. As the hot fluid flows through the exchanger, its temperature decreases linearly from the inlet to the outlet as it transfers heat to the cold fluid. Conversely, the temperature of the cold fluid increases linearly from the inlet to the outlet as it absorbs heat from the hot fluid.
4. Efficiency: The counter flow arrangement with equal heat capacities maximizes the temperature difference between the hot and cold fluids along the length of the exchanger. This results in efficient heat transfer and allows for a more compact heat exchanger design compared to parallel flow arrangements.