is there a word in the english language that does not have a vowel
There are very few lexical words (that is, not counting interjections) without vowel letters. The longest such lexical word is tsktsks, pronounced /ˌtɪskˈtɪsks/. The mathematical expression nth /ˈɛnθ/, as in delighted to the nth degree, is in fairly common usage. Another mathematical term without vowel letters is rng /ˈrʌŋ/, derived from ring by deleting the letter ⟨i⟩. A more obscure example is ln.
English words without vowels