Question

Can the temperature of the cold fluid rise above the inlet temperature of the hot fluid at any location in a heat exchanger? Explain.

Short answer

Answer: No, the temperature of the cold fluid cannot rise above the inlet temperature of the hot fluid in a heat exchanger due to the principle of energy conservation and the temperature relationships in the heat exchanger.

Step-by-step solution

Heat Exchanger Principle

In a heat exchanger, two fluids are separated by a solid wall, where one fluid transfers heat energy to the other fluid without any direct contact or mixing between the two fluids. The cold fluid gains thermal energy from the hot fluid, causing its temperature to rise while the hot fluid's temperature decreases.

Conservation of Energy

The principle of energy conservation states that energy cannot be created or destroyed, only converted from one form to another. In a heat exchanger, the total energy input equals the total energy output. This means that the thermal energy lost by the hot fluid must be equal to the thermal energy gained by the cold fluid.

Temperature Relationships

In a heat exchanger, the hot fluid's inlet temperature (T_{hi}) must always be higher than the cold fluid's inlet temperature (T_{ci}) for heat transfer to occur. As the fluids flow through the exchanger, heat is transferred from the hot fluid to the cold fluid, causing the hot fluid's exit temperature (T_{ho}) to be lower than its inlet temperature, and the cold fluid's exit temperature (T_{co}) to be higher than its inlet temperature. We have the following relationships: 1. T_{hi} > T_{ci} 2. T_{ho} < T_{hi} 3. T_{co} > T_{ci}

Cold Fluid's Temperature Rising Above Hot Fluid's Inlet Temperature

Based on the principle of energy conservation and temperature relationships in the heat exchanger, the cold fluid's exit temperature cannot rise above the hot fluid's inlet temperature. This is because the hot fluid will always lose thermal energy to the cold fluid, hence its exit temperature will always be lower than the inlet temperature. Therefore, T_{co} can never be greater than T_{hi}. In conclusion, the temperature of the cold fluid cannot rise above the inlet temperature of the hot fluid at any location in a heat exchanger.