I've heard that the Arab slave trade was larger than the Atlantic slave trade, so if so why is there no black people in Arabia, or what is the actual case with this?
There’s always more to say, but as a starting point, you may be interested in this older thread:
In short, many assimilated (particularly the children of female slaves and their masters—these were not all sub-Saharan Africa slaves, either, c.f. the white Circassian slaves), many had no children (particularly the male slaves), and also some Black Muslim communities still do exist in the Middle East, for instance the Afro-Turks around the Turkish city of Izmir and the so-called “Al-Akhdam” in Yemen.
Many contributing factors.
According to Bernard Lewis, the growth of internal slave populations through natural increase was insufficient to maintain slave numbers through to modern times, which contrasts markedly with rapidly rising slave populations in the New World. He writes that
a) Liberation by freemen of their own offspring born by slave mothers was "the primary drain,” and b) Liberation of slaves as an act of piety, was a contributing factor.
For a long time, until the early 18th century, the Crimean Khanate maintained a massive slave trade with the Ottoman Empire and the Middle East. Between 1530 and 1780 there were almost certainly 1 million and quite possibly as many as 1.25 million white, European Christians enslaved by the Muslims of the Barbary Coast of North Africa