(Solved): a) Water entering at \( 23^{\circ} \mathrm{C} \) is to be heated to \( 53^{\circ} \mathrm{C} \) in ...

a) Water entering at \( 23^{\circ} \mathrm{C} \) is to be heated to \( 53^{\circ} \mathrm{C} \) in a tube of \( 0.02 \mathrm{~m}- \) ID at a mass flow rate of \( 0.01 \mathrm{~kg} / \mathrm{s} \). The outside of the tube is wrapped with an insulated electric - heating element that produces a uniform flux of \( 15,000 \mathrm{~W} / \mathrm{m}^{2} \) over the surface. Neglecting any entrance effects, determine i) the film heat transfer coefficient (12 marks) ii) the length of pipe needed for the \( 30^{\circ} \mathrm{C} \) increase in average temperature (6 marks) iii) the inner tube surface temperature at the outlet. (2 marks)