In a fanfiction, her yell could also be a call for help. Maybe she's in a dangerous situation, like being trapped in a dark alley in Diagon Alley by some Death Eaters. Her yell would be a desperate attempt to get the attention of Harry or other friendly wizards.
It might signify her strong emotions. Hermione is a passionate character. Her yell could be a sign of her anger, for instance, if someone questions her intelligence or mocks her for being a 'Mudblood'.
In Harry Potter fanfiction, 'Black Morning' could potentially signify a morning filled with dark or foreboding events. It might be related to the presence of dark magic, or perhaps a morning where the characters are facing a great threat. For example, it could be a morning when Voldemort's forces are gathering and there's a sense of impending doom in the wizarding world.
Stress and danger can also be reasons. When facing a powerful dark wizard or a difficult situation at Hogwarts, the pressure can get to them. Harry may yell out of frustration at not being able to find a solution quickly, and Hermione might yell back as she tries to keep him calm and rational. In a fanfic, this can create a lot of emotional turmoil and keep the readers engaged.
It could also be related to the treatment of Harry's friends or allies. Suppose Fudge is persecuting Dumbledore or other Order of the Phoenix members. Harry, who is loyal to his friends and those fighting against the Dark Arts, would be enraged and yell at Fudge. He wouldn't stand for any harm coming to those he cares about, and Fudge's actions in this regard would surely provoke Harry's anger.
One possible reason could be a difference in opinion regarding the safety of the characters. Maybe Molly is being overly protective in a way that Harry feels is hindering their fight against the dark forces, so he yells in frustration.
Maybe Harry finds out that Dumbledore knew more about his family's past than he let on. For instance, if Dumbledore had information about some dark secrets in the Potter family but didn't tell Harry, it could make Harry furious and prompt him to yell. Also, if Dumbledore's actions led to the death or harm of someone Harry cared about, like Sirius, Harry would likely be very angry with him.
It could also be a sign of her determination. She might be pushing herself to the limit to achieve a certain goal. For example, if she is trying to break into a magically protected place to retrieve an important object, the sweat shows how hard she is working towards that goal. In a more detailed sense, her drenched state could also be a way for the author to show her vulnerability. Even though Hermione is a very intelligent and powerful witch, she is still human (well, a witch but you get the idea). The sweat makes her more relatable and shows that she can be affected by the difficult situations she is put in. It adds depth to her character in the fanfiction.
Maybe Albus has done something dangerous or disobeyed Harry's instructions. For example, if Albus got involved with some dark magic related stuff without Harry's knowledge, that would surely make Harry yell at him.
In fanfictions, Draco may yell at Harry due to jealousy. Harry is often the center of attention and gets all the glory. Draco, who comes from a proud pure - blood family, might feel overshadowed and this could lead to him yelling in frustration.
Well, it could be in battles against dark wizards or when protecting her friends. Sometimes it's in magical duels or facing off against mythical creatures.
In the fanfiction, Harry could outsmart Hermione by understanding people better. Hermione is often very logical and book - smart, but Harry might be more in tune with the emotions and motives of others. He could use this to his advantage in a situation where they are trying to solve a mystery or deal with a difficult person. He can read between the lines and make decisions based on his gut feeling about people, while Hermione is still analyzing the facts from her books.