Water at 20°C enters a 1.91-cm-ID, 57-cm-long tube at a flow rate of 3 gm/s. The tube wall is maintained at 30°C. Determine the water outlet temperature. What error in the water temperature results if natural convection effects are neglected?

Question

GIVEN

• Water flowing through a tube

• Entering water temperature (Tb,in) = 20°C

• Tube inside diameter (D) = 1.91 cm = 0.0191 m

• Tube length (L) = 57 cm = 0.57 m

• Mass flow rate (m) = 3 gm/s = 0.003 kg/s

• Tube wall surface temperature (Ts) = 30°C

FIND

(a) The water outlet temperature (Tb,out)

(b) Percent error in water temperature rise if natural convection is neglected

ASSUMPTIONS

• Steady state

• Tube temperature is uniform and constant

• The tube is horizontal

SKETCH



PROPERTIES AND CONSTANTS

for water at 20°C

Specific heat (c) = 4182 J/(kg K)

Thermal conductivity (k) = 0.597 W/(m K)

Kinematic viscosity (?) = 1.006 × 10–6 m2/s

Prandtl number (Pr) = 7.0

Absolute viscosity (?b) = 993 × 10–6 (Ns)/m2

Thermal expansion coefficient (?) = 2.1 × 10–4 1/K At 30°C ?s = 792 × 10–6 (Ns)/m2

Answer 1

The Reynolds number is



The Graetz number is



The Grashof number will be based on the diameter since the tube is horizontal



For this value and ReD = 200, a indicates that the flow is in the ‘mixed convection laminar

flow’ region.



(a) The Nusselt number can be estimated using



The outlet temperature can be calculated



The average bulk temperature is 23°C. Another iteration is therefore not warranted because the

change in property values will not affect the result appreciably.

(b) Natural convection can be neglected for the Nusselt number



The error in outlet temperature is