Atmospheric air enters the heated section of a

Chapter 8, Problem 8.18

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Atmospheric air enters the heated section of a circulartube at a flow rate of 0.005 kg/s and a temperature of20C. The tube is of diameter D?50 mm, and fullydeveloped conditions with h?25 W/m2?K exist overthe entire length of L?3m.(a) For the case of uniform surface heat flux at qs?1000 W/m2, determine the total heat transferrate qand the mean temperature of the air leavingthe tube Tm,o. What is the value of the surface tem-perature at the tube inlet Ts,iand outlet Ts,o? Sketchthe axial variation of Tsand Tm. On the same figure,also sketch (qualitatively) the axial variation of Tsand Tmfor the more realistic case in which the localconvection coefficient varies with x.(b) If the surface heat flux varies linearly with x, suchthat qs(W/m2)?500x(m), what are the values ofq, Tm,o, Ts,i, and Ts,o? Sketch the axial variation ofTsand Tm. On the same figure, also sketch (qualita-tively) the axial variation of Tsand Tmfor the morerealistic case in which the local convection coeffi-cient varies with x. c) For the two heating conditions of parts (a) and (b),plot the mean fluid and surface temperatures, Tm(x)and Ts(x), respectively, as functions of distancealong the tube. What effect will a fourfold increasein the convection coefficient have on the tempera-ture distributions?(d) For each type of heating process, what heat fluxesare required to achieve an air outlet temperature of125C? Plot the temperature distributions.