An air heater in a large coal-fired steam generator heats...

An air heater in a large coal-fired steam generator heats fresh air entering the steam generator by cooling flue gas leaving the steam generator. One million lbm/hr of air at $100^{\circ} \mathrm{F}$ and 1.1 million lbm/hr of flue gas at $720^{\circ} \mathrm{F}$ enters the air heater. The flue gas leaves at $310^{\circ} \mathrm{F}$. Flue gas has $c_{p}=0.26 \mathrm{Btu} / \mathrm{lbm}^{\circ} \mathrm{F}$ and $k=1.39 .$ Pressure changes are small and may be neglected. Calculate the temperature of the air leaving the air heater and the total entropy change for the process.

Key Concepts

Energy Balance

The energy balance is the principle of conservation of energy applied to a system. In heat exchangers, it involves equating the energy lost by the hot stream to the energy gained by the cold stream, accounting for any work or losses. This approach is fundamental for determining unknown outlet temperatures in thermal systems.

Heat Exchanger Analysis

Heat exchanger analysis involves studying the transfer of energy between two fluids at different temperatures without mixing them. It requires understanding the counterflow or parallel flow arrangements, determining driving temperature differences, and applying the overall energy conservation principles. This analysis is essential in designing systems that optimize thermal efficiency.

Specific Heat Capacity

Specific heat capacity is a material property that quantifies the amount of heat required to raise the temperature of a unit mass of a substance by one degree. In thermal processes, it is used to calculate the change in enthalpy or sensible heat exchange, and is a key parameter when applying energy balances in systems with heat transfer.

Entropy Change and Entropy Generation

Entropy change is a measure of the disorder or randomness in a system and is central to the second law of thermodynamics. In a heat exchanger, the total entropy change includes contributions from both streams, and additional entropy generation indicates the irreversibility of the process. Evaluating entropy change helps in assessing the thermodynamic performance and efficiency limitations of thermal systems.

Second Law of Thermodynamics

The second law of thermodynamics governs the direction of natural processes and states that entropy in an isolated system never decreases. It is used to evaluate the irreversibility of processes and to quantify the minimum possible losses in energy conversions. In heat exchanger problems, the second law analysis is critical for determining the feasibility and efficiency of heat transfer mechanisms.

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