Water enters a tube at 27C with a flow rate of450 kg/h.

Chapter 8, Problem 8.12

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Water enters a tube at 27C with a flow rate of450 kg/h. The heat transfer from the tube wall to thefluid is given as q?s(W/m)?ax, where the coefficient ais 20 W/m2and x(m) is the axial distance from the tubeentrance.(a) Beginning with a properly defined differential con-trol volume in the tube, derive an expression for thetemperature distribution Tm(x) of the water.(b) What is the outlet temperature of the water for aheated section 30 m long?(c) Sketch the mean fluid temperature, Tm(x), and thetube wall temperature, Ts(x), as a function of dis-tance along the tube for fully developed anddevel-oping flow conditions.(d) What value of a uniform wall heat flux, qs(insteadof q?s?ax), would provide the same fluid outlettemperature as that determined in part (b)? For thistype of heating, sketch the temperature distribu-tions requested in part (c).