Despite a surge collection of XAI methods, users still struggle to obtain required AI explanations. Previous research suggests chatbots as dynamic solutions, but the effective design of conversational XAI agents for practical human needs remains under-explored. This paper focuses on Conversational XAI for AI-assisted scientific writing tasks. Drawing from human linguistic theories and formative studies, we identify four design rationales: "multifaceted", "controllability", "mix-initiative", "context-aware drill-down". We incorporate them into an interactive prototype, ConvXAI, which facilitates heterogeneous AI explanations for scientific writing through dialogue. In two studies with 21 users, ConvXAI outperforms a GUI-based baseline on improving human-perceived understanding and writing improvement. The paper further discusses the practical human usage patterns in interacting with ConvXAI for scientific co-writing.