Nuclear (E before R)

I'm not sure I can explain this well, but I hope you understand the question anyway.
Most words don't have an "ee" sound (IPA: /i/) before r's, but it's reduced and lowered, so many transcriptions in dictionaries use IPA /ɪ/ instead.
The difference can be seen comparing "Knee" with "Near", "Fee" with "Fear", and so on.

The question is: does that happen for every combination of /i/ and /r/, becoming /ɪr/? can you think of any words that actually have /ir/? I can only think of NUCLEAR, which dictionaries say it's an exception, but I even reduce that, so "nuclear" rhymes with "clear", "near" and "happier" (/ɪr/). Thanks.

There historically was a distinction between /iːr/ and /ɪr/ in English dialects in general (such as "serious" having /iːr/ and "Sirius" having /ɪr/), but this has been lost in most North American English dialects outside the Northeast. As for "nuclear", aside from those who have /ˈnuːkjuːlər/ for it, I have never heard of it not rhyming with "clear", and in particular I have never heard of people having /iːr/ for "nuclear" but /ɪr/ for "clear".

<<I have never heard of it not rhyming with "clear">>

It certainly doesn't rhyme with "clear" for me. It's not /i:r/ versus /Ir/ though. in "nuclear" the "clear" has two syllables "nu clee er" whereas I have one syllable in "clear".

I agree that the final "ar" in "nuclear" is a bit more distinct than the final "ar" in "clear"

How about "seer"(a person that sees) though it's not a common word.

Thanks. I see you all make that distinction, apart form Travis. I'd like to know if there are other words that are generally like "nuclear", with /ir/ instead of /ɪr/. According to Merriam Webster, "theory" can be pronounced either way, for example, although I use the reduced vowel, /ɪr/.
In other words, I suspect "nuclear" is the only exception. Can anyone tell me more?

I am from California and I pronounce the "clear" portion of "nuclear" as two syllables and just plain "clear" as one syllable.

I just had to give my actual pronunciations for some reason...

"nuclear" [ˈnʲʉ̯uʔkɰɪːʁ]
"clear" [ˈkʰɰɪːʁ]
"near" [ˈnɪːʁ]
"happier" [ˈhɛ̯æʔpjʁ̩ː]