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', (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, t,(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", (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).