Which formula represents the relationship between heat transfer coefficients in a heat exchanger?

The formula that represents the relationship between heat transfer coefficients in a heat exchanger is based on how heat transfer occurs across different surfaces. In a typical heat exchanger, heat is conducted through a solid wall between two fluids, each with its own heat transfer coefficient.

The overall heat transfer coefficient (U) quantifies the efficiency of heat transfer across the entire surface of the heat exchanger. The relationship is reciprocal, which means that the total resistance to heat transfer is the sum of the individual resistances on either side of the heat exchanger.

This is accurately represented by the formula where the overall heat transfer coefficient U is calculated by the reciprocal of the sum of the reciprocal of the individual heat transfer coefficients (h_inside for the fluid inside the heat exchanger and h_outside for the fluid outside). This reflects how each coefficient contributes to the total thermal resistance: higher resistance from either side leads to a lower overall heat transfer efficiency.

Therefore, the expression showing that the inverse of U equals the sum of the inverses of the individual heat transfer coefficients captures this relationship effectively. This means that as one side's heat transfer coefficient increases, the overall heat transfer coefficient U increases, leading to better heat exchanger performance.