Directed acyclic graphs are commonly used to model scientific workflows, by expressing dependencies between tasks, as well as the resource requirements of the workflow. As a special case, rooted directed trees occur in several applications. Since typical workflows are modeled by huge trees, it is crucial to schedule them efficiently. We investigate the partitioning and mapping of tree-shaped workflows on target architectures where each processor can have a different memory size. Our three-step heuristic adapts and extends previous work for homogeneous clusters. In particular, we design a novel algorithm to assign subtrees to processors with different memory sizes, and we show how to select appropriate processors when splitting or merging subtrees. The experiments demonstrate that exploiting the heterogeneity reduces the makespan significantly compared to the state of the art for homogeneous memories.