Parimah Kazemi, Numerical Analyst

HTRI continues to expand our research capabilities to bring our members the latest information about heat transfer and process technology. Our Research & Technology Center (RTC) houses physical test units, while our computational fluid dynamics (CFD) simulations complement our experimental program and identify and resolve operational issues of heat exchangers. A new component of our research program involves the application of neural networks to heat transfer predictions.

What is a neural network?

Most people know something about how our brains process information, creating maps or pathways through the neurons in the tissue. The more complex the information, the more pathways the brain creates, helping with memory, use of language, etc. Neural networks act in a similar way to find relationships among data and are an essential and maturing tool in the big data revolution.

Neural networks are often thought of as a series of interconnected neurons coupled with training algorithms. This analogy does not fully explain what a neural net is under the hood, nor does it explore the totality of scenarios in which neural nets can be used to improve operations.

How do neural nets work?

An ideal scenario for applying a neural net model is one in which

  • first-principles modeling, a model that requires the relationship between variables be explicitly known and stated, becomes overly complex
  • information about the relationship among variables is sparse and ambiguous
  • the computational resources needed to solve a posed first-principles model are expensive

In settings where data acquisition is relatively inexpensive and comprehensive data sets are readily available, a neural net provides a predictive model to the user at a fraction of the cost of first-principles modeling.

In the absence of comprehensive data, a neural network can provide an accurate model in applications with a narrow scope. In cases where the available data set is sparse with regard to the scenarios of interest, supplementary information is often available in the form of expert derived models or first-principles models. Physics-informed neural networks allow empirical models to be incorporated into the neural network structure.

How is HTRI applying neural nets?

HTRI recently assessed the accuracy of a neural network to predict Nusselt number for laminar flow using a comprehensive set of open literature data assembled by HTRI. The trained network performed better than several open literature correlations for Nusselt number.

neural network comparison model results
Comparison of model results

HTRI members work with heat transfer data sets that are large and comprehensive and with smaller targeted datasets. Using neural networks as a modeling tool to predict heat transfer can yield a more accurate and cost-effective way to obtain predictive analytics.


  1. C. A. Hieber, Laminar mixed convection in an isothermal horizontal tube: Correlation of heat transfer data, Intl. J. Heat Mass Transfer 25, 1737 – 1764 (1982).
  2. A. J. Ghajar and L. M. Tam, Heat transfer measurements and correlations in the transition region for a circular tube with three different inlet configurations, Exp. Thermal Fluid Sci. 8(1), 79 – 90 (1994).

Read more

A technical paper presented at the 7th Thermal and Fluids Engineering Conference is available to purchase from the ASTFE Digital Library.

Members with access to HTRI reports can read S-ST-1-17 Using Neural Networks for Predicting Nusselt Number for Intube Laminar Flows.