Paper Number
PO22                         My Program 

Session
Poster Session

Title
Viscous heating limit lines for experimental prediction and qualification

Presentation Date and Time
October 22, 2025 (Wednesday) 6:30

Track / Room
Poster Session / Sweeney Ballroom E+F

Authors (Click on name to view author profile)

1. Temple, Abby K. (University of Illinois Urbana-Champaign, Mechanical Science & Engineering)
2. Ewoldt, Randy H. (University Of Illinois Urbana-champaign, Mechanical Science and Engineering)

Author and Affiliation Lines (in printed abstract book)
Abby K. Temple and Randy H. Ewoldt
Mechanical Science & Engineering, University of Illinois Urbana-Champaign, Urbana, IL 61801

Speaker / Presenter 
Temple, Abby K.

Keywords
experimental methods; theoretical methods; rheometry

Text of Abstract
Viscous heating is a nonlinear phenomenon caused by fluid friction, resulting in the apparent shear rate dependence of viscosity of even Newtonian fluids in steady shear. Although the Nahme-Griffith number [1] has been used to neglect viscous heating [2], or with certain assumptions, has itself been plotted as a limit line [3], the bulk dimensionless number does not account for spatial variations in temperature and viscosity and therefore cannot be directly used to predict viscous heating effects in experiments. In this work, we derive a viscous heating limit line to be co-plotted with viscosity vs shear rate data which accurately predicts a prescribed deviation in viscosity during a flow sweep, with only prior knowledge of geometry and fluid properties. Through an approximate analytical solution to the coupled heat and momentum equations – as began by Rudolf Nahme in the 1940s [4] – we determine an expression for the apparent viscosity measured by parallel plate non-isothermal Couette flow of a Newtonian fluid. Experimental results show good agreement between model-predicted viscosity and that which is measured by a parallel plate rotational rheometer, especially concerning the sooner onset of viscous heating with a larger gap. The proposed limit line may be used to predict viscous heating in experiments and qualify existing data, as well as give insight into viscous heating effects in industrial flows.

[1] Ockendon, H. et al., “Variable-viscosity flows in heated and cooled channels,” J. Fluid Mech., 83(1), 177-190 (1977). https://doi.org/10.1017/S002211207700113X.
[2] Johnston, M. et al., “Precision rheometry,” J. Rheol. 57(6), 1515-1532 (2013). https://doi.org/10.1122/1.4819914.
[3] Schuh, J. et al., “Asymmetric surface textures decrease friction with Newtonian fluids in full film lubricated sliding contact,” Tribol. Int. 97, 490-498 (2016). https://doi.org/10.1016/j.triboint.2016.01.016.
[4] Nahme, R., "Beiträge zur hydrodynamischen Theorie der Lagerreibung," Ing. Arch, 11(3), 191-209 (1940).