Improvement in performance of multi-pass laminar counterflow heat exchangers with external refluxes

A study on improvement in performance of multi-pass rectangular heat exchangers with uniform wall temperature and with external refluxes has been carried out under counterflow operations. An orthogonal expansion technique for solving such a conjugated Graetz problem is developed and applied to investigate a substantially improving heat transfer. A description of the average Nusselt number and the outlet dimensionless temperature is given. It is shown that for asymptotic average Nusselt numbers exit in counterflow as in single-flow operations. Numerical values of asymptotic average Nusselt numbers are reported for a wide range of Graetz numbers. Comparisons of analytical results are made with single-flow operations of the same size (without sheets inserted and without recycle). Considerable improvement in the heat transfer rate for large Graetz numbers is obtainable by introducing the recycle-effect concept in designing such double-pass operations. The effect of sheet location on the enhancement of heat transfer efficiency as well as on the increment of power consumption has been also discussed.