Hello my name isXXXXX will be glad to assist you, In the 8/3 you ran new to this unit, you should have 4 wires, black and red for hots, neutral and ground, the ground and neutral should be isolated from each other in a sub panel meaning the ground should have its own independent bar with only ground tied to it with a connection to the box itself. the neutral should be connected to the buss on either side of the panel, front or back buss will not matter for the neutral, it is important that ground wires and neutral wires are seperated on to different buss bars. (let me know if this makes sense) Now the most likely cause for the main feed breaker tripping would be a loose connection you may want to begin in the sub panel checking to be sure all the main feed wire connections are tight (with main feed breaker off of course) you may also want to be sure all other connections are tight in this panel as well while you have power off. Then check at the breaker feeding the sub panel, check for loose connections here as well at neutral and grounds that feed the sub panel, you may also want to remove the breaker and check for damage, arcing or burning evidence. ( if breaker shows signs of damage also check buss bar on the panel for damage, and you would also need to replace breaker) Be sure sub panel feed breaker fits tight into the panel as well. Once you have checked these likely causes, we will continue if this does not resolve the problem. The delayed tripping is caused likely by a build up of heat, when you have a loose connection it will arc causing this heat build up and thus causing the breaker to trip, especially under a big load like a dryer.