No, this is not part of the Sunnah. You can supplicate and pray to Allah during your sujood.

Is it right to pray nafil salah for some work…in hopes the work will become easy (salaat ul hajaat)

Prayer | March 26, 2014 4:51 pm
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Is it right to pray nafil salah for thankfulness or just prostration is allowed?
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Is it right to combine all your prayers because you are about to travel or to shorten your dhuhr,asr and maghrib prayers from 4 to 2 raka’ah’s when you arrive at your destination?