is there any way to submit a design for a new apple product to apple

Appe has a corporate policy of not accepting - or even reading - unsolicited ideas. The best you can do is to become an Apple employee, and go from there.

Here is Apple's official statement on the subject:

http://www.apple.com/legal/intellectual-property/policies/ideas.html

They'll take suggestions via their feedback pages, but by submitting that way you give up any and all rights to the idea as well as any possibiliity of credit or compensation for said ideas.

Regards.