Length of the Longest Palindromic Substring
Brachylog, 9 bytes
{s.↔}ᶠlᵐ⌉

Try it online!
Explanation
{   }ᶠ       Find all…
 s.            …substrings of the input…
  .↔           …which are their own reverse
      lᵐ     Map length
        ⌉    Max