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

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).

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.

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.