What is comes down to is surface area.
In an object of a fixed size, the only way to increase the amount of it in contact with the environment is to make it more convoluted and wrinkly. Higher surface areas interact more with their environment.
In the case of a heat sink, the high surface area allows for more heat to dissipate.
Other examples of high surface area are sponges. They use extra surface area to absorb water. Your intestines are wrinkly on the inside to better absorb nutrients. Your lungs have lots of little pockets to better absorb oxygen.
Sometimes the opposite is true, and something is smooth to conserve heat. This is why we don’t have wrinkly thermoses and tea kettles.
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