natbib not working with elsarticle-num bibstyle

(this answer merely summarizes and combines some of the the comments made by various contributors)

  • The chief reason why the OP couldn't create a formatted bibliography using natbib, BibTeX, and the elsarticle-num bibliography style was that the bibliography style file, elsarticle-num.bst, was not present in the OP's TeX distribution.

  • The solution consisted in downloading the file from the following URL:

    https://www.elsevier.com/__data/assets/file/0011/56846/elsarticle-num.bst
    

    Once the bst file was properly installed, no further obstacles stood in the way of creating the formatted bibliography.

  • To facilitate the typesetting of long URL strings and, in particular, to allow easy line-breaking of long URL strings, a further suggestion was made to load the xurl package immediately prior to loading the hyperref package.

  • One or more of the OP's advisers appear to have major hangups about the need to achieve "formatting consistency" in the typeset bibliography. (For instance, the output produced by the unsrtnat bibliography style was not acceptable to them because it lacked formatting consistency.) To accommodate such rather strong views, it definitely helps to make the hyperlinked material "blend in" into the surroundings. Adding the instruction

    \hypersetup{colorlinks,urlcolor=black}
    

    in the preamble, after loading the hyperref package, certainly helps meet this objective. The hyperlinks will still be there -- you just wouldn't know it solely from looking at the formatted bibliographic entries.