All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
This matter should be looked at in two ways:
1- Does the system prevent the student from using the grant offered by the university in anything other than the research he is working on?
2- Is giving money to the teacher considered as spending the money on the research or not?
Therefore, if the university conditions spending the money on the research, then this condition should be fulfilled. However, if giving the money to the teacher is not included in spending it on the research, then it is not permissible in principle to give him anything. In this case the teacher has no right to demand the money, and it is not permissible for the student to accept his demand unless he fears harm from him. In this case, it is considered a bribe in regard to the teacher, and the student is permitted to give it to him for necessity. However, if the university system allows the student to give part of this money to the teacher, then it is permissible for him to do so but he may refuse to give it to him according to the benefit of his research. Also, it is permissible to benefit from the money in a research in another laboratory if it is not possible to carry out the research in the laboratory of the university.
In conclusion, the student should abide by the conditions of the university which offers this grant.
For more benefit on studying without a Mahram, please refer to Fataawa 93145 and 90269.
Allaah Knows best.