Counter-flow with equal heat capacity

In a heat exchanger, the temperature distribution of the hot and cold fluids is an important factor to consider. The temperature distribution determines the effectiveness of the heat transfer process and is influenced by the flow arrangement and the heat capacity rates of the fluids.

Counter-flow is a type of flow arrangement in a heat exchanger where the hot and cold fluids flow in opposite directions. In this arrangement, the hot fluid enters from one end of the exchanger and the cold fluid enters from the other end. As they flow through the exchanger, heat is transferred from the hot fluid to the cold fluid.

Equal heat capacity refers to the heat capacity rates of the hot and cold fluids being the same. Heat capacity rate is a measure of the amount of heat energy a fluid can absorb or release per unit time. When the heat capacity rates of the hot and cold fluids are equal, it means that they have the same ability to absorb or release heat.

- Parallel-flow with unequal heat capacity: In this arrangement, the hot and cold fluids flow in the same direction. The temperature distribution is not a parallel straight line pattern because the fluids have different heat capacity rates. This means that they absorb or release heat at different rates, causing the temperature difference between the fluids to vary along the length of the exchanger.

- Counter-flow with unequal heat capacity: In this arrangement, the hot and cold fluids flow in opposite directions. The temperature distribution is not a parallel straight line pattern because the fluids have different heat capacity rates. The temperature difference between the fluids will vary along the length of the exchanger.

- Parallel flow with equal heat capacity: In this arrangement, the hot and cold fluids flow in the same direction. The temperature distribution is a parallel straight line pattern because the fluids have the same heat capacity rates. This means that they absorb or release heat at the same rate, resulting in a uniform temperature difference between the fluids along the length of the exchanger.

- Counter-flow with equal heat capacity: In this arrangement, the hot and cold fluids flow in opposite directions. The temperature distribution is a parallel straight line pattern because the fluids have the same heat capacity rates. This means that they absorb or release heat at the same rate, resulting in a uniform temperature difference between the fluids along the length of the exchanger.

Therefore, the correct answer is option B - Counter-flow with equal heat capacity. In this arrangement, both the hot and cold fluids flow in opposite directions and have equal heat capacity rates, resulting in a parallel straight line pattern of temperature distribution for both fluids.