3. Turbulent Flow

Momentum transfer: \[\frac{\tau}{\rho} = (\nu + \varepsilon_m)\frac{dv}{dy}\]

Heat transfer: \[\frac{q}{\rho C_P} = -(\alpha+\varepsilon_h)\frac{dT}{dy}\] where \(y\) is the distance measured from the tube wall. \(\varepsilon\) is eddy diffusivity (turbulent).