Heat Transfer · Thermal radiation and enclosure exchange
Turbulent water flow (Re_D = 4.6 × 10⁴, Pr = 5.4) enters a 20 mm i.d
Problem
Turbulent water flow (Re_D = 4.6 × 10⁴, Pr = 5.4) enters a 20 mm i.d. circular tube whose wall temperature is suddenly raised and then held uniform. The hydrodynamic field is already fully developed at the start of heating. Using L_t/D = 10 for turbulent thermal development, determine the heated length required for the local Nusselt number to be within the fully developed regime, and compute that fully developed Nu_D from the Dittus–Boelter heating correlation Nu_D = 0.023 Re_D^{0.8} Pr^{0.4}.
Hint
Turbulent thermal development with a fully developed velocity profile is complete after about ten diameters.
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