This varies considerably with the style standard you follow, or are required to follow by the target publication.
Now, if you follow the guidelines set out by the Chicago Manual of Style , then parts of a book, including numbered chapters, should be lowercase when referenced (per CMOS). See CMOS 8.178 and 8.177.
8.178 Numbered chapters, parts, and so on
The words chapter, part, appendix, table, figure, and the like are
lowercased and spelled out in text (though sometimes abbreviated in
parenthetical references). Numbers are given in arabic numerals,
regardless of how they appear in the original. If letters are used,
they may be upper- or lowercase (following the original) and are
sometimes put in parentheses. See also 9.27–29.
This matter is discussed in chapters 4 and 5.
The Latin text appears in appendix B.
The range is presented numerically in table 4.2 and diagrammed in
These connections are illustrated in table A3.
Turn to section 5(a) for further examples.
The Chicago Manual of Style
If you write consistently following Chicago, spare yourself some headaches by buying the $40/year online subscription, to have access to the online edition and to its extremely useful forum.
Now, there are other style guides, e.g. the
APA (American Psychological Association) style is most commonly used to cite sources within the social sciences. An introduction is available at Purdue OWL (Online Writing Laboratory).
Also, first obtain and become familiar with the guide style of the journal you want to publish in.