Water enters a tube at 29°C with a flow rate of 460 kg/h. The rate of heat transfer from the tube wall to the fluid is given as qs′(W/m)=ax, where the coefficient a is 25 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 31 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.
Water enters a tube at 29°C with a flow rate of 460 kg/h. The rate of heat transfer from the tube wall to the fluid is given as qs′(W/m)=ax, where the coefficient a is 25 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 31 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, qs″ (instead of qs′=ax), would provide the same fluid outlet temperature as that determined in part 8.13b? For this type of heating, sketch the temperature distributions requested in part 8.13c.
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