Question

Air at 40°C flows over a long, 25-mm-diameter cylinder with an embedded electrical heater. In a series of tests, measurements were made of the power per unit length, P’, required to maintain the cylinder surface temperature at 300°C for different free stream velocities u of the air. The results are as follows:
Air velocity, u (m/s) 1 2 4 8 12
Power, P’ (W/m) 450 658 983 1507 1963

(a) Determine the convection coefficient for each velocity, and display your results graphically.
(b) Assuming the dependence of the convection coefficient on the velocity to be of the form h = Cu n , determine the parameters C and n from the results of part (a)

Answer 1

Answer:

a) See attachment

b) C = 21.626 W / m^2 .K , n = 0.593

Explanation:

a)

dT = 300 - 40 = 160 K

A = pi*D*l where D = 0.025 m

Power = P' * l = h * dT * A

P' l = h * pi * D * l* dT

Hence,

h = P' / (pi*D*dT)

We will use the above equation to compute for respective values of P'

Note: The results are tabulated and attached

b)

Assuming the dependence of the convection coefficient on the velocity to be of the form h=CV^n, determine the parameters C and n from the results of part (a).

Taking logarithm on both sides:

Ln (h) = Ln(C) + n*Ln(V)

n = (Ln(h2) - Ln(h1)) / (Ln(V2) - Ln(V1))

n = (Ln (32.223/22.037)) / Ln(2))

n = 0.593

Using regression we can compare:

C = 21.626 W/m^2 . K