Nitrogen at 30°C and atmospheric pressure enter a triangular duct 0.02 m on each side at a rate of 4 × 10–4 kg/s. If the duct temperature is uniform at 200°C, estimate the bulk temperature of the nitrogen 2 m and 5 m from the inlet.

Question

GIVEN

• Atmospheric nitrogen flowing through a triangular duct

• Bulk inlet temperature (Tb,in) = 30°C

• Width of each side of the duct (w) = 0.02 m

• Mass flow rate (m ) = 4 × 1–4 kg/s

• Duct temperature (Ts) = 200°C (uniform)

FIND

• The bulk temperature

(a) 2 m from the inlet and,

(b) 5 m from the inlet

SKETCH

Answer 1

(a) Assuming the outlet temperature is 70°C, then the average bulk temperature is 50°C, for nitrogen

Specific heat (cp) = 1042 J/(kg K) Thermal conductivity (k) = 0.0278 W/(m K) Absolute viscosity (?) = 18.79 × 10–6 (Ns)/m2 Prandtl Number (Pr) = 0.71 The hydraulic diameter of the duct is



The length from the entrance at which the velocity and temperature profiles become fully developed

can be obtained



Therefore, the flow is fully developed over most of the duct length.

for fully developed flow in triangular cross-section duct: NuD= 2.47



Rearranging



With this outlet temperature, the average bulk temperature will be 100°C. This is far enough from the

initial guess that another iteration is warranted



The bulk temperature at x = 2 m is 176°C.

(b) The same procedure can be used to find the bulk temperature at x = 5 m. Let Tb,out = 190°C.

Average bulk temperature = 110°C



The bulk temperature a x = 5 m is about 199°C.