Unused engine oil with a 100°C inlet temperature flows at a rate of 0.25 kg/sec through a 5.1-cm-ID pipe that is enclosed by a jacket containing condensing steam at 150°C. If the pipe is 9 m long, determine the outlet temperature of the oil. Also at what length of the pipe would the oil temperature be at 1100C?

Question

GIVEN

• Unused engine oil flows through a pipe enclosed by a jacket containing condensing steam.

• Oil flow rate, m

= 0.25 kg/s.

• Oil inlet temperature, Tb,in = 100°C.

• Inner or inside diameter of pipe in which oil flows, D = 5.1 cm = 0.051 m.

• Length of heated pipe (heated by condensing steam) in which oil flows, L = 9 m.

• Temperature of condensing steam, Ts = 150°C.

FIND

• Temperature of oil, Tb,out, at the outlet of the 9-m-long heated pipe.

• Length of pipe at which oil temperature will be 1100C.

ASSUMPTIONS

• Steady-state flow of oil and its heating by the condensing steam in the outer jacket.

• The temperature of condensing steam is constant and uniform across the length of pipe.

• The thermal resistance of the pipe is negligible, and hence the inside surface temperature of the

pipe is Tw = Ts, this represents a uniform pipe surface temperature condition.

SKETCH



PROPERTIES AND CONSTANTS

for unused engine oil at Tb,in = 100°C

Density, ? = 840.0 kg/m3

Thermal conductivity, k = 0.137 W/(m K)

Absolute viscosity, ?b = 17.1 × 10–3 (Ns)/m2

Prandtl number, Pr = 276

Specific heat, cp = 2219 J/(kg K)

At the pipe surface temperature of 150°C, the absolute viscosity ?s = 5.52 × 10–3 (Ns)/m2

Answer 1

The Reynolds number for oil flow inside the pipe is



The thermal entrance length is given for laminar flow, and it can be calculated as



Hence, the temperature profile is NOT fully developed, or the flow is thermally developing. Because there is a large variation in the oil viscosity at the pipe wall temperature and the bulk temperature, the effect of property (viscosity) variation has to be considered either the Hausen correlation of the Sieder and Tate correlation could be used because (?b/?s) = 3.1 (< 9.75; the limit to calculate the Nusselt number. Thus, using the more simpler Sieder and Tate correlation



The outlet temperature can now be calculated



When the oil temperature reaches 1100C,



Thus oil temperature reaches 1100C at 0.19 m.

COMMENTS

The oil flow attains the tube wall (or the condensing steam) temperature at the outlet of the 9-m-long

pipe. Also, because of the 50?C temperature difference between the inlet and the outlet, the above

calculation should be repeated after evaluating the properties at the average temperature between the

inlet and outlet.