Theoretical solution for the cross-flow heat exchanger

The theory of the cross-flow heat exchanger first was treated by NuBelt [1, 2] on the base of heat balances for the two interacting fluids over an exc hanging area element. This leads to a partial differential equation. But th e solution was an infinite row which could not be expressed in a compact fo rmula. In this paper it will be shown that a compact formula for the infini te row is possible. All temperatures of the interacting fluids, for example the local fluid temperatures and the mean outlet temperatures as well as t he local temperature difference and the mean temperature difference over th e 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 va lue with a negligible deviation. As all variables in the formulae are dimen sionless, normalized diagrams are developed which are generally valid and g ive a good overview over a wide range of exchanger conditions.