Direct numerical simulation of forced air convection with variable physical properties*

We present a theoretical framework for predicting friction and heat transfer coefficients in variable-properties forced air convection. Drawing from concepts in high-speed wall turbulence, which also involves significant temperature, viscosity, and density variations, we utilize the mean momentum balance and mean thermal balance equations to develop integral transformations

that account for the impact of variable fluid properties. These transformations are then applied inversely to predict the friction and heat transfer coefficients, leveraging the universality of passive scalars transport theory. Our proposed approach is validated using a comprehensive dataset from direct numerical simulations, covering both heating and cooling conditions up to a friction Reynolds number of approximately $\Rey_\tau\approx 3200$. The predicted friction and heat transfer coefficients closely match DNS data with an accuracy margin of 1-2\%, representing a significant improvement over the current state of the art. Compared to empirical formulas that are based on experimental data fitting, the present approach reveals to be more general and reliable as it is rooted in the fundamental equations. Another important advange is that the method also provides the mean velocity and temperature profiles with accuracy comparable to DNS, which can be used as wall functions in simulations employing wall-modeling approaches. The proposed framework is available online at www.thermoturb.com.