물론(mul-ron, mulron)
An expression used to positively respond to someone's question or expectation
When to use
positive answer to question, meeting expectation, casual conversation
The nuance
물론 is used to affirmatively answer when someone asks or expects something, meaning 'definitely' or 'of course'.
당연히(dang-yeon-hi, dangyeonhi)
An expression used to emphasize logical, moral inevitability or something that is naturally expected
When to use
logical inevitability, moral obligation emphasis, formal situations
The nuance
당연히 is used when something is logically or morally proper or inevitable.