Water at room temperature flows through a smooth pipe with an inner diameter of 10 cm. The flow is fully developed, and Re D = 1.5 × 10 5 . (a) Calculate the eddy diffusivity and shear stress τ rz at...

Water at room temperature flows through a smooth pipe with an inner diameter of 10 cm. The flow is fully developed, and Re_D
= 1.5 × 10⁵.

(a) Calculate the eddy diffusivity and shear stress τ_rz
at distances 3 mm and 1 cm from the wall.

(b) Find the effective thermal conductivity (k + k_tu) at the locations specified in part (a).

(c) Repeat parts (a) and (b), this time using the eddy diffusivity model of Reichardt (1951).

(d) Repeat parts (a)–(c), this time assuming that the tube wall is rough so that ε_s/D = 0.01.