Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
You are allowed to recite the Quran in your mind, although involving our tongues and moving our lips would be better than doing it mentally.
When we involve each of our limbs (tongue, lips, mouth, heart, and mind) in reciting the Quran ion, we stand to gain multiple rewards as each of these limbs is involved in the noblest of deeds.
Having said this, it is fine to alternate: recite aloud in such a way you can hear it yourself sometimes, while doing so silently in your mind, at other times.
Almighty Allah knows best.