Mercury at an inlet bulk temperature of 90°C flows through a 1.2-cm-ID tube at a flow rate of 4535 kg/h. This tube is part of a nuclear reactor in which heat can be generated uniformly at any desired rate by adjusting the neutron flux level. Determine the length of tube required to raise the bulk temperature of the mercury to 230°C without generating any mercury vapor, and determine the corresponding heat flux. The boiling point of mercury is 355°C.

Question

GIVEN

• Mercury flow in a tube

• Inlet bulk temperature (Tb,in) = 90°C

• Inside tube diameter (D) = 1.2 cm = 0.012 m

• Flow rate (m ) = 4535 kg/h = 1.26 kg/s

• Outlet bulk temperature (Tb,out) = 230°C

• Boiling point of mercury = 355°C

FIND

(a) The length of tube (L) required to obtain Tb,out without generating mercury vapor

(b) The corresponding heat flux (q/A)

ASSUMPTIONS

• Steady state

• Fully developed flow

SKETCH



PROPERTIES AND CONSTANTS

for mercury at the average bulk temperature of 160°C

Density (?) = 13,240 kg/m3

Thermal conductivity (k) 11.66 W/(m K)

Absolute viscosity (?) = 11.16 × 10–4 (Ns)/m2

Prandtl number (Pr) = 0.0130

Specific heat (c) = 140.6 J/(kg K)

Answer 1

The Reynolds number is



Therefore, can be applied to calculate the Nusselt Number





(b) The maximum allowable heat flux is determined by the outlet conditions. The outlet wall

temperature must not be higher than the mercury boiling point



(a) The length of the tube required can be calculated from the following



Solving for the length



COMMENTS

Note that L/D = 0.419 m/0.012 m = 35 > 30, therefore, the assumption of fully developed flow and

use is valid.