The problem of heat losses from a fluid moving througha

Chapter 8, Problem 8.63

(choose chapter or problem)

The problem of heat losses from a fluid moving througha buried pipeline has received considerable attention.Practical applications include the trans-Alaska pipeline,as well as power plant steam and water distribution lines.Consider a steel pipe of diameter Dthat is used to trans-port oil flowing at a rate m?othrough a cold region. Thepipe is covered with a layer of insulation of thickness tand thermal conductivity kiand is buried in soil to adepth z(distance from the soil surface to the pipe center-line). Each section of pipe is of length Land extendsbetween pumping stations in which the oil is heated toensure low viscosity and hence low pump power require-ments. The temperature of the oil entering the pipe froma pumping station and the temperature of the groundabove the pipe are designated as Tm,iand Ts, respectively,and are known.Consider conditions for which the oil (o) propertiesmay be approximated as ?o?900 kg/m3, cp,o?2000J/kg?K, ?o?8.5?10?4m2/s, ko?0.140 W/m?K, Pro?104; the oil flow rate is m?o?500 kg/s; and thepipe diameter is 1.2 m.(a) Expressing your results in terms of D, L, z, t, m?o,Tm,i, and Ts, as well as the appropriate oil (o), insula-tion (i), and soil (s) properties, obtain all the expres-sions needed to estimate the temperature Tm,oof theoil leaving the pipe.(b) If Ts??40C, Tm,i?120C, t?0.15 m, ki?0.05W/m?K, ks?0.5 W/m?K, z?3 m, and L?100 km,what is the value of Tm,o? What is the total rate ofheat transfer qfrom a section of the pipeline?(c) The operations manager wants to know the tradeoffbetween the burial depth of the pipe and insulationthickness on the heat loss from the pipe. Develop agraphical representation of this design information.