A cylindrical storage tank with a diameter of 4 m and a leng

A cylindrical storage tank with a diameter of 4 m and a length of 10 m will hold a fluid whose temperature must be maintained at 347 K. In order to size the heater required for the tank, the following worst-case scenario is considered: Ambient air temperature = -20degree C Wind speed = 20 m/s \'lank wall temperature = 347 K What size (kW) healer will be needed?

Solution

At mean film temperature, t_f=(-20+74)/2=27 C, thermo physical properties of air.

v=15.761*10^-6 m²/s, k=0.02619 W/(m-deg), P_r=0.7123

V=wind speed=20m/s

R_e=V*d/v = 20*4/(15.761*10^-6) = 5075820 (laminar)

N_u=h*d/k = 0.664*(R_e)^0.5 * (P_r)^0.33 = 0.664*2252.958*0.8940849 = 1337.52

h=N_u*k/d = 1337.52*0.02619/4 = 8.7574 W/m²-deg

Convective heat loss,

Q=h A t = h (3.14*d*l) t = 8.7574 (3.14*4*10) 94 = 103.4 kW