This is the oven I mentioned as making life astern so unpleasant. It's called the "tryworks". It's basically a brick rectangle with an open top and two massive iron pots suspended over the fire.
When a whale was caught, it would be stripped of blubber, the sheets of which (called "the blanket") would be lowered into the ship. There, they'd be cut into managable chunks, called "the horse pieces." The horse pieces would then be brought up on deck and rendered (or "tried out") into whale oil here in the tryworks.
Remember that whaling ships would go out to sea for years - however long it took to fill the hold with barrels of whale oil. After awhile everything onboard would be coated with oily black soot: the decks, the rigging, your clothes, yourself, your food... Suddenly that little fo'c'stle (upwind of the tryworks) seems like the sweet place to be.