All perfect praise be to Allah, The Lord of The Worlds, and may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
One is allowed to give Zakah (Obligatory charity) to his/her blood-relative student, but with the following conditions:
First: The student is hard-working and doesn`t have time to make a living; whereas, a lazy student shouldn`t be given from the Zakah money. Al-Khateeb Ashirbini said, "If he was busy learning one of the Sharia sciences, and that prevented him from making a living, then he is considered poor and becomes eligible to receive Zakah because his attainment of that knowledge is a collective duty. However, a lazy student shouldn`t be given from Zakah if he was capable of making a living." {Moghni al-Mohtaj, vol.4 pp.175}.
Second: The knowledge that he is seeking is a collective duty, whether it was in the domain of Sharia such as jurisprudence (Fiqh) and Quranic exegesis (Tafseer), or any of the worldly sciences such as medicine, economics, chemistry and the like.
Third: The student isn`t among the dependents of the Zakah giver, if he was then he shouldn`t be given from that Zakah. Al-Khateeb ash-Shirbini said, "It is a condition that the Zakah recipient isn`t among the dependants of the Zakah giver." {Moghni al-Mohtaj,vol.4 pp.183}.
In conclusion, supporting one`s brother isn`t obligatory. And Allah knows best.