In an industrial refrigeration system, brine (10 % NaCl by weight) having a viscosity of 0.0016 (Ns)/m2 and a thermal conductivity of 0.85 W/(m K) is flowing through a long 2.5-cm-ID pipe at 6.1 m/s. Under these conditions, the heat transfer coefficient was found to be 16,500 W/(m2 K). For a brine temperature of –1°C and a pipe temperature of 18.3°C, determine the temperature rise of the brine per meter length of pipe if the velocity of the brine is doubled. Assume that the specific heat of the brine is 3768 J/(kg K) and that its density is equal to that of water.

Question

GIVEN

• Brine flowing through a pipe

• Brine properties

? Viscosity (?) = 0.0016 Ns/m2

? Thermal conductivity (k) = 0.85 W/(m K)

? 10% NaCl by weight

? Specific heat (c) = 3768 J/(kg K)

• Pipe inside diameter (D) = 2.5 cm = 0.025 m

• Brine velocity (V) = 6.1 m/s

• Heat transfer coefficient ( h c) = 16,500 W/(m2 K)

• Brine temperature (Tb) = –1°C

• Pipe temperature (Ts) = 18.3°C FIND

• Temperature rise of the brine per meter length (?Tb/m) if the velocity is doubled (V = 12.2 m/s) ASSUMPTIONS

• Steady state

• Fully developed flow

• Constant and uniform pipe wall temperature

• Density of the brine is the same as water density

SKETCH



PROPERTIES AND CONSTANTS

density (?) of water ? 1000 kg/m3

Answer 1

The Reynolds number at the original velocity is



The thermal conductivity of the fluid can be calculated from the given heat transfer coefficient using

the Dittus-Boelter correlation





The Prandtl number is



The Reynolds number for the new velocity is twice the original Reynolds number:

ReD = 190,626. For fully developed flow



The temperature after one meter is given