Final answer:
A nuclear reactor core meltdown requires high temperature, high pressure, and the loss of coolant, as demonstrated by historical incidents like the Three Mile Island accident.
Step-by-step explanation:
The acute melting of a nuclear reactor core, commonly referred to as a meltdown, can occur under specific conditions. For melting to happen, the following are required: high temperature, high pressure, and loss of coolant.
Examples of these conditions include the incident at Three Mile Island where the reactor overheated due to the failure of the cooling system. The temperature reached at least 2200 °C, the high-pressure environment exacerbated the situation, and the loss of coolant accelerated the core's damage.