Abstract
A recent paper announced that most textbooks, graduate and undergraduate, present an incorrect value for the Nusselt number in thermally developed laminar flow between isothermal parallel plates. The stated cause is flow work and/or dissipation that acts as a persistent source of heat generation. The purpose of this paper is to rehabilitate the textbook literature. I show that the commonly reported value of the thermally developed Nusselt number, 7.541, is quite acceptable for commonly encountered situations. In particular, for ideal gases, the wall heat flux is predicted exactly without accounting for these effects because they cancel one another. For liquids, I derive the channel length within which dissipation makes a negligible contribution to heat flux. This length will often span the entire range within which the bulk temperature changes in response to the wall temperature change. The residual bulk temperature rise from dissipation may amount to only millikelvin. The present results show that the Seban-Shimazaki criterion for thermally developed flow is misleading when dissipation is considered. A more direct criterion makes the flow thermally-developed when the Graetz series can be approximated by its first term. The one-term approximation provides consistent results, with or without dissipation, and follows a path routinely used in transient heat conduction. Further, the Nusselt number following a change in wall temperature should be calculated after removing the small temperature rise and heat flux caused by dissipation. Failure to do so gives a heat transfer coefficient that can be zero or singular.
