[susan53]

First of all, you need to use phonemic script when talking about pronunciation. I imagine you are asking about the two possible pronunciations for "the" : 1) /ðiː/ - pronounced as in the word "thee" and 2) /ðə/ - which is what I think you mean by "thuh".

Also, it makes no difference if you're reading out loud or just speaking spontaneously - the pronunciation is the same.

The pronunciation /ðə/ occurs when the following word starts with a consonant sound - so eg :
the book /ðə bʊk/
the car /ðə kɑː/
and also the university - because notice that I said a consonant sound, not a letter of the alphabet. And university starts with the sound /j/ which is a consonant : /juːnɪvɜːsɪtiː/. So :
/ðə juːnɪvɜːsɪtiː/. Another example is the word usual /juːʒuːl/ :
the usual suspects /ðə juːʒuːl sʌspeks/

The pronunciation /ði:/ occurs when the following word starts with a vowel sound - so eg :
the egg /ðiː eg/
the old car /ðiː ɒld kɑː/

English hates having two vowels together though, so very often a /j/ sound is inserted to join them :
the egg /ðiːjeg/
the old car /ðiːjɒld kɑː/

It's really the same as the choice between the indefinite articles a and an. a comes before consonant sounds:
a book /ə bʊk/
and an comes before vowel sounds :
an old car /ən ɒld kɑː/

But in the case of the definite article (the) it's only the pronunciation that changes. The written word remains the same.

Hope that's clear.