Air at an average temperature of 150°C flows through a short square duct 10 × 10 × 2.25 cm at a rate of 15 kg/h. The duct wall temperature is 430°C. Determine the average heat transfer coefficient, using the duct equation with appropriate L/D correction. Compare your results with flow-over-flat-plate relations.

Question

GIVEN

• Air flowing through a short square duct

• Average air temperature (Ta) = 150°C

• Duct dimensions = 10 × 10 × 2.25 cm = 0.1 × 0.1× 0.0225 m

• Duct wall surface temperature (Ts) = 430°C

• Mass flow rate (m ) = 15 kg/h

FIND

The average heat transfer coefficient ( h c) using (a) The duct equation with appropriate L/D correction (b) The flow-over-flat-plate relation

ASSUMPTIONS

• Constant and uniform duct wall temperature

SKETCH



PROPERTIES AND CONSTANTS

for dry air at the average temperature of 150°C

Thermal conductivity (k) = 0.0339 W/(m K)

Absolute viscosity (?b) = 23.683 × 10–6 (Ns)/m2

Prandtl number (Pr) = 0.71 At the surface temperature of 430°C,

the absolute viscosity (?s) = 33.66 × 10–6

Answer 1

The hydraulic diameter of the duct is



The Reynolds number is



Therefore, the flow is laminar.

(a) Using the Hausen correlation, Equation (7.41) to estimate the Reynolds number with

D/L = DH/L = 10/2.25 = 4.44



(b) Applying the flow-over-flat-plate relation of