A pipe, 2cm diameter at $40^0C$ is placed in

(i) an air flow at $50^0C$ with $h = 20W/m^2K OR in (ii) water at $30^0C$ with $h = 70 W/m^2K$.

Find the heat transfer per unit length of the pipe and comment on the results in both cases.

Given,

d = 2cm = 0.02m (Diameter of pipe)

t1 = 40℃ = 313K (Temperature of pipe)

t2 = 50℃ = 323K (Surrounding temperature)

h = 20W/m2K (Convective heat transfer coefficient of surrounding medium)

l = 1m (Length of pipe)

Find: (1) Q (Heat transfer rate)

Solution:

Heat transfer rate

Q = dtR = t1 - t21h. As = 313 - 323120 × π × 0.02 × 1

Q = -12.566 W (-ve sign indicates that heat flows from surrounding medium to pipe)

Case 2

Given,

d = 2cm = 0.02m (Diameter of pipe)

t1 = 40℃ = 313K (Temperature of pipe)

t2 = 30℃ = 303K (Surrounding temperature)

h = 70W/m2K (Convective heat transfer coefficient of surrounding medium)

l = 1m (Length of pipe)

Find: (1) Q (Heat transfer rate)

Solution:

Heat transfer rate

Q = dtR = t1 - t21h. As = 313 - 303170 × π × 0.02 × 1

Q = 43.982 W (+ve sign indicates that heat flows from pipe to surrounding medium)