Because I've no data, and haven't been on campus for 40 years, the following is speculation:
- Humanities: English professors probably have very little. I can't think of a reason for them to do business with the world of business. The visual arts may have more--contact with art galleries, appraisals, and such. History (if you count it as a humanity), very little. The occasional expert witness in a lawsuit (I maintain membership in two historical groups, and vaguely remember something), writing company histories, etc.
- Area studies: things like black history, gender studies, American studies, etc. would be similar to humanities, although the opportunity for "talking heads" on TV is greater.
- Social sciences: probably more than humanities, a minority of professors could be consultants, do work within private companies, organizations, consulting, etc. Economists might be most linked.
- Physical sciences, including life sciences: the most interaction.
- New fields: things like IT, management, etc. probably have the most--indeed, my impression is there's a regular revolving door in IT.