Question

A long 8-cm-diameter steam pipe whose external surface temperature is 90°C passes through some open area that is not protected against the winds. Determine the rate of heat loss from the pipe per unit of its length when the air is at 1 atm pressure and 7°C and the wind is blowing across the pipe at a velocity of 47 km/h. The properties of air at 1 atm and the film temperature of (Ts + T∞)/2 = (90 + 7)/2 = 48.5°C are k = 0.02724 W/m·°C, ν = 1.784 × 10-5 m2 /s, and Pr = 0.7232. (Round the final answer to the nearest whole number.)

The heat transfer rate is ______ (W/m)

Answer 1

Diameter D = 8 cm x 1m/100cm = 0.08 m

Velocity V = 47 km/h x 1h/3600s x 1000m/km

= 13.055 m/s

Reynolds number = diameter x velocity x density /viscosity

= diameter x velocity / Kinematic viscosity

= 0.08 m x 13.055 m/s / (1.784 x 10^-5 m2/s)

= 58542.60

Flow is turbulent

Nusselt number can be determined

Nu = 0.3 + (134.65/1.137)*(1.289)

Nu = 152.95

hD/k = 152.95

heat transfer coefficient h = 152.95 x 0.02724 W/m·°C / 0.08 m

= 52.08 W/m2-°C

Heat transfer by convection

Q = h x A x (T - Ts) = h x 3.14 x D x L x (T - Ts)

Q/L = h x 3.14 x D x (T - Ts)

= 52.08 W/m2-°C x 3.14 x 0.08 m x (90 - 7)°C

= 1085.84 W/m