Water, at a temperature of 10°C, flows in a hydraulically smooth tube that has an inner diameter of 5 cm, with a mean velocity of 1.05 m/s (see Figure P7.8). At location A, where the flow is...

Water, at a temperature of 10°C, flows in a hydraulically smooth tube that has an inner diameter of 5 cm, with a mean velocity of 1.05 m/s (see Figure P7.8). At location A, where the flow is hydrodynamically fully developed, a wall heat flux of 2 × 10⁴
W/m²
is imposed on the tube

a. Find the location of point B, where the fluid mean temperature reaches 30°C. Is the flow thermally developed at that location?

b. Assuming that the flow at location B is thermally developed, find the local heat transfer coefficient, wall friction factor, and wall temperature, using appropriate constantproperty correlations.

c. Calculate the eddy diffusivity and the mixing length at location B, at a distance of 1 mm from the wall.

d. Calculate the mean (i.e., time-averaged) fluid temperature at location B, at 1 mm distance from the wall.

 e. Improve the results in Part b for the effect of temperature on properties.

For simplicity, assume that water is incompressible. Also, for Part d, use the universal temperature profile for a flat surface as an approximation.