Question

Under what conditions can the overall heat transfer coefficient of a heat exchanger be determined from \(U=\) \(\left(1 / h_{i}+1 / h_{o}\right)^{-1} ?\)

Short answer

Answer: The formula can be used when the heat exchanger is simple, operating at steady-state, has fully developed flow in both inside and outside regions, has heat transfer due to convection only, and is free of additional factors such as fouling or temperature-dependent fluid properties.

Step-by-step solution

Recap on heat transfer coefficients

A heat transfer coefficient is a parameter that quantifies the rate of heat transfer across a surface due to a temperature difference across that surface. The heat transfer coefficient represents the convective heat transfer between the fluid and the surface. There are two heat transfer coefficients in the given formula: \(h_{i}\) (the inside surface) and \(h_{o}\) (the outside surface).

Discuss what affects the overall heat transfer coefficient

The overall heat transfer coefficient (U) is dependent on several factors, such as the type of heat exchanger, fluid properties and flow rates, surface conditions, and the presence of any additional resistances (like thermal resistance due to fouling or wall conduction). The provided formula assumes that all these factors are incorporated in the heat transfer coefficients.

Identify when the provided formula can be utilized

The formula \(U=\) \(\left(1 / h_{i}+1 / h_{o}\right)^{-1}\) can be used to determine the overall heat transfer coefficient (U) of a heat exchanger under the following conditions: - The heat exchanger is simple and has no additional complexities or features that would affect the overall heat transfer. - The flow is steady-state and fully developed in both the inside and outside regions. - Heat transfer is only due to convection, and other modes of heat transfer (e.g., radiation and conduction) can be neglected. - There is no significant fouling present in the heat exchanger that would affect the overall heat transfer coefficient. - Fluid properties are not significantly affected by temperature or local conditions. In summary, the formula can be used to determine the overall heat transfer coefficient for a heat exchanger, provided that the heat exchanger is relatively simple, operating at steady-state, and free of additional factors such as fouling or temperature-dependent fluid properties.

Key concepts

Heat Exchanger Design

Heat exchanger design involves the systematic planning of equipment used to transfer heat between two or more fluids. These devices are crucial in many industries, such as chemical processing, power generation, and air conditioning.
Designing a heat exchanger requires understanding the specific requirements of the process, including:

• The type of heat exchanger (e.g., shell-and-tube, plate, or finned tube).
• Material selection to withstand operating temperatures and pressures.
• Calculations for surface area to ensure efficient heat transfer.

Many factors influence the design, including the type and properties of fluids involved, flow patterns, and desired temperature changes.
Ultimately, an effective design minimizes costs while maximizing thermal efficiency and ensuring safety.

Convective Heat Transfer

Convective heat transfer refers to the transfer of heat between a solid surface and a fluid moving over or through it.
The process occurs due to the motion of the fluid, which carries energy with it. This can be seen in everyday examples like air flowing over a hot surface or water moving through pipes.
For convective heat transfer, a key parameter is the heat transfer coefficient, denoted by the symbol \(h\).
It quantifies the efficiency of this transfer, depending on:

• The nature of the fluid (e.g., air or water).
• The surface area involved.
• Flow dynamics, including velocity and turbulence.

In many applications, maximizing \(h\) ensures more effective heat exchange, making it important to select appropriate materials and design configurations.

Fluid Dynamics

Fluid dynamics is the study of fluids in motion and is essential for the analysis and design of heat exchangers. Understanding fluid dynamics helps predict how fluids behave when under the influence of forces, crucial for setting up efficient heat exchange processes.
Key concepts in fluid dynamics include:

• Flow rate and velocity, both of which impact heat transfer rates.
• Laminar vs. turbulent flow: Turbulent flow typically enhances mixing and heat transfer.
• Pressure drops, which can affect overall system performance.

In heat exchangers, optimizing these factors ensures that fluids flow evenly and efficiently, enhancing the overall thermal performance of the system.

Thermal Resistance

Thermal resistance is a concept that describes the resistance to heat flow through a material or system. It can be thought of as an obstacle that slows down the transfer of heat.
The overall thermal resistance of a system is determined by all the individual resistances it encounters, such as those in materials and surfaces involved in the process. In heat exchangers, thermal resistance is accounted for in calculating the overall heat transfer coefficient, \(U\).
The formula \(U= \left(1 / h_{i}+1 / h_{o}\right)^{-1}\) represents the inverse sum of resistances from the inside and outside surface heat transfer coefficients (\(h_i\) and \(h_o\)). A lower thermal resistance (higher \(U\)) means more efficient heat transfer.
Minimizing fouling and ensuring clean surfaces can significantly reduce thermal resistance.

Steady-State Flow Conditions

Steady-state flow conditions refer to a situation where the fluid flow parameters (such as flow rate, pressure, and temperature) remain constant over time. In heat exchanger systems, it implies that these factors are stable and predictable, ensuring consistent performance and output.
This condition is critical for applying certain simplified calculations, like determining the overall heat transfer coefficient using the formula \(U= \left(1 / h_{i}+1 / h_{o}\right)^{-1}\).Steady-state flow benefits include:

• Predictability in system operation.
• Ease in monitoring and maintenance.
• Ability to apply standard models and equations accurately.

In practice, maintaining steady-state conditions can avoid operational fluctuations, leading to more efficient and reliable heat exchange processes.