$[$Internal flow$]$ Water at $25C$ with a mass flow rate of $0\mathrm{.}6$ th will be heated to $65C$ by using saturated steam at $2$ bars in a double pipe heat exchanger. The heat exchanger has an inner pipe $($outside diameter of $18$ mm $,$ wall thickness $1$ mm $)$ and an outer pipe $($outside diameter of $35$ mm $,$ wall thickness $2$ mm $).$ Water stream flows inside the annulus, while steam condenses inside the inner pipe. The outer surface of the outer pipe is well insulated, and the thermal resistance of the inner wall is negligible. Calculate:

a$)$ The average convective film transfer coefficient of water

b$)$ The heat flux from the inner tube

c$)$ The mass flow rate of steam and the length of the annulus needed.