This thesis presents investigations on the heat transfer in complex heat ex- changers in general and in regenerative heat exchangers (regenerators) in par- ticular. The motivation for this work is a result of inconsistencies obeserved in the results from a series of experiments on active magnetic regenerators (AMRs) with parallel plates. The results suggest that random variations in the regenerator geometries causes maldistributed fluid flow inside the regener- ators, which affects the regenerator performance. In order to study the heat transfer processes in regenerators with non-uniform geometries, a numerical model, which simulates a single-blow operation in a parallel-plate regenerator, was developed and used to model the heat transfer under various conditions. In addition to the modeling of the heat transfer, a series of experiments on passive regenerators with non-uniform, but precisely controlled, geometries was performed. The objective of performing these experiments was in part to eval- uate the direct applicability of the model, which only simulates one half of the regenerator cycle, to a practical situation where the regenerator is running con- tinuously by comparing the results gained. Additionally, the experiments gave real comparative results, whereas the model to a certain degree more served to provide insight to the heat transfer processes taking place inside the regenera- tors, something that would be - if not impossible - then highly impractical to do experimentally. It has been found that non-uniformity in the plate spacings of non-uniform regenerators can have a significant impact on the regenerator effectiveness, particularly for regenerators with small plate spacings. The observed reduc- tions in effectiveness have furthermore been found to alter the optimim plate spacing, and decreasing the plate spacing beoynd a certain point can even hurt the performance. Inter-channel heat transfer effects - or thermal cross-talk - have also been in- vestigated and the results show that not only the size of the plate spacings, but also their mutual order, can affect the heat transfer significantly.