Closure to “Discussion of ‘Friction Numbers and Viscous Dissipation Heating for Laminar Flows of Water in Microtubes’” (2008, ASME J. Heat Transfer, 130, p. 082405)

Abstract

The derivation in our paper is for liquid (water) flow in a microtube, with a slip at the wall. For this problem, in the paper by El-Genk and Yang, a stationary microlayer, δ, whose thickness depends of the jump distance, β, separates the fluid flow from the wall of the microtube. In fact, the boundary of the flow field near the wall (r = R − δ) moves with the slip velocity relative to the stationary adiabatic wall. Under this condition, the viscous dissipation and, hence, the temperature gradient at the wall would be negligible, justifying omitting of the volumetric conduction term in Eq. (3) in the commentary offered by Asako. With no-slip at the wall, viscous dissipation could be important in some cases, e.g., for high viscosity fluids and gasses, but not when the effect on the fluid temperature is small. This is certainly truer as Reynolds number increases.