This tool predicts the fully-developed laminar Nusselt number (Nu) and friction factor (represented as fRe, a product of Fanning friction factor and Reynold's number) for any cross-sectional shape of a flow channel. The Nusselt number prediction is available for two different constant heat flux boundary conditions, H1 and H2. H1 is the case where the flux is constant along the flow direction but the temperature is constant along the circumference of the channel at any cross-section. H2 is the case where the heat flux is constant along both, the axial and the circumferential directions.

The input to the tool is the shape of the cross-section, the other boundary of which is represented in radial coordinates at equiangular locations separated by one degree. The center of mass of the shape is centered at the origin, and the area of the shape is 1 square unit. Thus, the input is a (1x360) dimensional vector of radial coordinates. The starting point of the radial coordinates does not matter as the final Nu and fRe predicted is an average across 360 different rotations of the shape. The output of the tool is the predicted Nu_H1, Nu_H2, and fRe.

The tool also presents a demo for a couple of different cross-sections (e.g circle, ellipse, rectangle, equilateral triangle).

Saeel S. Pai, Justin A. Weibel

Financial support for this work provided by members of the Cooling Technologies Research Center, a graduated National Science Foundation Industry/University Cooperative Research Center at Purdue University, is gratefully acknowledged.

Researchers should cite this work as follows:

• Saeel Shrivallabh Pai, Justin A. Weibel (2022), "ML-based Surrogate Models for Nusselt Number and Friction Factor Prediction in Constant Cross-Section Channels," https://nanohub.org/resources/mlmodels2d. (DOI: 10.21981/0MJE-TQ48).

  BibTex | EndNote

1. friction factor
2. internal flow
3. laminar flow
4. machine learning
5. Nusselt number