Water enters a tube at 27 C with a flow rate of 450 kg/h.

Chapter , Problem 8.12

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Water enters a tube at 27 C with a flow rate of 450 kg/h. The heat transfer from the tube wall to the fluid is given as q s(W/m) ax, where the coefficient a is 20 W/m2 and x (m) is the axial distance from the tube entrance. (a) Beginning with a properly defined differential control volume in the tube, derive an expression for the temperature distribution Tm(x) of the water. (b) What is the outlet temperature of the water for a heated section 30 m long? (c) Sketch the mean fluid temperature, Tm(x), and the tube wall temperature, Ts(x), as a function of distance along the tube for fully developed and developing flow conditions. (d) What value of a uniform wall heat flux, q s (instead of q s ax), would provide the same fluid outlet temperature as that determined in part (b)? For this type of heating, sketch the temperature distributions requested in part (c).