The answer to this question isn't as clear as you would hope it to be. The exact time frames have not been calculated, but they do depend on a few things.
"My hero was captured and the execution time period has ran out, but my hero has not been released. When will it be released? "
The execution time has expired there is still additional time you need to wait before your Hero can escape.
Your hero will attempt to escape after the execution time period, but his escape time is dependent on the captor's Prison level and your Hero level.
I am not sure of the exact time periods, because there are a lot of time variation since they are many combinations of Prison level and Hero level.
I'm sorry I can't give you guys real time periods! Just know that as you level up your Hero he/she can't be held for as long. Also, don't worry too much about your Hero been captured or killed, he/she won't lose any experience unless you don't Resurrect your Hero for 7 days. Take some time to relax, hang out with your Alliance, and plan your next KvK!
Enjoy!
Navi