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Closing on wall functions - part 6: viscous dissipation

Posted April 24, 2022 at 10:20 by sbaffini (NuTBox)
Updated June 1, 2022 at 12:28 by sbaffini

One thing which is missing in the previous derivations is the viscous dissipation term in the temperature equation. Let's reconsider the initial temperature equation when it is present:

\frac{d}{dy}\left[C_p\left(\frac{\mu}{Pr}+\frac{\mu_t}{Pr_t}\right)\frac{dT}{dy}\right]=F_T - \frac{d}{dy}\left[\left(\mu+\mu_t\right)U\frac{dU}{dy}\right]

A first integration leads to:

\left(\frac{C_p \mu}{Pr}\right)\left(1+\frac{Pr}{Pr_t}\frac{\mu_t}{\mu}\right)\frac{dT}{dy}=q_w+...
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