A well-insulated shell-and-tube heat exchanger is used to...

A well-insulated shell-and-tube heat exchanger is used to heat water $\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)$ in the tubes from 20 to $70^{\circ} \mathrm{C}$ at a rate of $4.5 \mathrm{~kg} / \mathrm{s}$. Heat is supplied by hot oil $\left(c_{p}=2.30 \mathrm{~kJ} /\right.$ $\mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$ ) that enters the shell side at $170^{\circ} \mathrm{C}$ at a rate of $10 \mathrm{~kg} / \mathrm{s}$ Disregarding any heat loss from the heat exchanger, determine $(a)$ the exit temperature of oil and $(b)$ the rate of exergy destruction in the heat exchanger. Take $T_{0}=25^{\circ} \mathrm{C}$.

A well-insulated shell-and-tube heat exchanger is used to heat water $\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)$ in the tubes from 20 to $70^{\circ} \mathrm{C}$
at a rate of $4.5 \mathrm{~kg} / \mathrm{s}$. Heat is supplied by hot oil $\left(c_{p}=2.30 \mathrm{~kJ} /\right.$ $\mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$ ) that enters the shell side at $170^{\circ} \mathrm{C}$ at a rate of $10 \mathrm{~kg} / \mathrm{s}$
Disregarding any heat loss from the heat exchanger, determine $(a)$ the exit temperature of oil and $(b)$ the rate of exergy destruction in the heat exchanger. Take $T_{0}=25^{\circ} \mathrm{C}$.

Key Concepts

Exergy Destruction

Exergy destruction, also known as irreversibility, represents the loss of potential to perform work due to irreversible processes such as friction, mixing, or heat transfer across finite temperature differences. Quantifying exergy destruction in a system, like a heat exchanger, is important for assessing its performance and guiding improvements towards more efficient energy utilization. It is a key measure linking the first and second laws of thermodynamics.

Exergy Analysis

Exergy analysis is a thermodynamic tool used to evaluate the quality or potential usefulness of energy in a process. It involves quantifying the maximum useful work that can be obtained from a system as it reaches equilibrium with its environment. Exergy analysis helps identify where energy degradation occurs and thus can be used to pinpoint inefficiencies within a system.

Energy Balance

Energy balance is a fundamental concept in thermodynamics that involves accounting for the energy entering and leaving a system. It ensures that the energy lost by one part of a system is gained by another, following the principle of conservation of energy. In heat exchanger problems, calculating the energy transfer between the hot and cold streams by equating the heat lost by one stream to the heat gained by the other is a typical application.

Heat Exchanger

A heat exchanger is a device designed to efficiently transfer heat between two or more fluids without mixing them. The design and analysis of heat exchangers are essential in various engineering applications, as they provide a means to recover energy, control process temperatures, and improve overall system efficiency. Understanding the working principles, such as countercurrent or parallel flow configurations, is key to their effective operation.

Specific Heat Capacity

Specific heat capacity is a material property that indicates the amount of energy required to raise the temperature of a unit mass of a substance by one degree. It plays a crucial role in determining the energy exchange in thermal systems. In heat exchanger problems, the specific heat capacity of the fluids is used to calculate the heat transferred based on the mass flow rates and temperature changes.

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