Theoretical solution for the cross-flow heat exchanger

Abstract

The theory of the cross-flow heat exchanger first was treated by Nußelt [1, 2] on the base of heat balances for the two interacting fluids over an exchanging area element. This leads to a partial differential equation. But the solution was an infinite row which could not be expressed in a compact formula. In this paper it will be shown that a compact formula for the infinite row is possible. All temperatures of the interacting fluids, for example the local fluid temperatures and the mean outlet temperatures as well as the local temperature difference and the mean temperature difference over the complete exchanger are now being available in simple formulae which have the form of an infinite sum. The summation has to be stopped at a finite value with a negligible deviation.

As all variables in the formulae are dimensionless, normalized diagrams are developed which are generally valid and give a good overview over a wide range of exchanger conditions.