There is one primary external conflict in the story and one internal conflict, but quite cleverly, each manifests itself in two opposite ways. The external conflict is between husband and wife, while the internal conflict is one of freedom versus the imprisonment of the marriage. In fact, it would not be unreasonable to say that the external and internal conflict are the same.
As the story begins, the wife, Mrs. Mallard, hears of the supposed death of her husband, which the reader is led to believe might be the conflict in the story because the wife suffers from a heart condition, and the news might kill her. But as the story proceeds, we see the wife as a bird in a gilded cage, someone for whom the husband's death would provide freedom from what we begin to see as conflict between husband and wife. The wife, we begin to understand, has been trapped in a marriage in which her husband dominated her, which has created a conflict within her, wanting freedom and being caught in the marriage, simultaneously internal and external conflict.
But as the story ends, we learn that Mr. Mallard is alive, and this is the external conflict that kills Mrs. Mallard, who saw, for a brief moment, a vision of a solution to her internal conflict, the freedom that Mr. Mallard's death would have brought her. It is the cessation of that dream that is responsible for her death, a conflict between the hopefulness and the sudden restoration of hopelessness.
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