My daughter is a full time student, no income and not a dependent. with her tuition and book expenses, should she expect any refund?

Yes. You can still receive 40% of the American opportunity tax credit's value — up to $1,000 — even if you earned no income last year or owe no tax. 

To be eligible for AOTC, the student must: 

• Be pursuing a degree or other recognized education credential.
• Be enrolled at least half time for at least one academic period* beginning in the tax year. 
• Not have finished the first four years of higher education at the beginning of the tax year.
• Not have claimed the AOTC or the former Hope credit for more than four tax years
• Not have a felony drug conviction at the end of the tax year

For more details please see: American Opportunity Tax Credit

If this does not completely answer your question, please contact us again and provide some additional details.

It depends, mostly on her age.  If she is over 23, (or married filing a joint return),  and an undergraduate, she is eligible for the (up to) $1000 refundable AOTC tuition credit. She must not only be "not a dependent" but also not qualify as (meet the rules for being) a dependent.