Should a PhD student use his academic affiliation for his publications which are not related to his thesis?

Yes.

The affiliation serves two purposes: acknowledgement and identification.

Even if it is not part of your thesis research, if you are receiving resources of any kind from your institution, you should list them as your affiliation. These resources include money (whether directly related to your research or not), computing equipment, internet access, printer access, electricity, phones, faculty and student colleagues (whether coauthors or not), library access (either physical or electronic), whiteboards, local coffee shops/bars, and the general intellectual atmosphere that encourages you to do research in the first place. You can afford to be generous.

Also, the affiliation helps identify you as an author, especially if you have a common name, or you publish other papers with the same affiliation.

First step: Ask your (1) advisor or (2) the department head or (3) both. Since you are not faculty, you may have to get permission to use the departmental affiliation for something that is outside your project. As long as this involves ethical and legitimate research I am sure it is not a problem. The department or university may have guidelines for publishing ethics which you may want to check as well. So, although there may not even be a problem, it is better to be safe than sorry.