Air at 30°C enters a rectangular duct 1-m-long and 4 mm by 16 mm in cross-section at a rate of 0.0004 kg/s. If a uniform heat flux of 500 W/m2 is imposed on both of the long sides of the duct, calculate (a) the air outlet temperature (b) the average duct surface temperature, and (c) the pressure drop.

Question

GIVEN

• Air flowing through a rectangular duct

• Inlet bulk air temperature (Tb,in) = 30°C

• Duct length (L) = 1 m

• Duct height (H) 4 mm = 0.004 m

• Duct width (w) = 16 mm = 0.016 m

• Air mass flow rate ( m ) = 0.0004 kg/s

• Uniform heat flux (q/A) = 500 W/m2 on the long sides

FIND

(a) Air outlet temperature (Tb,out)

(b) The average duct surface temperature (Ts)

(c) The pressure drop (? p)

ASSUMPTIONS

• The short sides of the duct are insulated

• Entrance effects are negligible

SKETCH

Answer 1

(a) The total rate of heat transfer to the air



The specific heat (cp) ? 1000 J/(kg K), therefore, Tb,out ? 70°C. the specific heat at the approximate average bulk temperature of 50°C is 1016 J/(kg K).



(b) The average duct surface temperature is given by



The heat transfer coefficient can be obtained from the proper correlation.

The hydraulic diameter of the duct is



Therefore, entrance effects will be neglected.

The Reynolds number is



Therefore, the flow is laminar.

The Nusselt number for this geometry is given in



The average surface temperature is



for 2b/2a = 1/4, fReD = 72.93



The pressure drop is given by