Question

Gas with a thermal conductivity of k = 0.04 W/mk and prandtl number of 0.7 is flowing at anaverage velocity of 0.5 m/s through a 2 mm diameter tube at a Reynolds number of 50. The heat capacity rate for the gas flowing through the tube is 0.001 kJ/s. The inlet temperature of the gas is 20C. There is a constant heat flux of 200 W/m^2 transferred from the tube wall into the gas.

a) What is the Nu at a distance of 8 mm into the pipe?

b) How does h vary with x downstream of this point?

Answer 1

a) Since Re < 2000, it is a case of laminar flow.

For laminar flow the entrance length number

where l_e is length to fully developed velocity profile

and d = tube or duct diameter = 2mm(Given)

since given distance = 8mm > entrance length(6 mm), the flow is fully developed at this point.

For laminar fully developed flow and constant heat flux condition the Nusselt number is constant and given by:

b) since Nu is constant for fully developed flow, and k,D are also constants, hence 'h' remains constant with x downstream of this point.