Problem 3: In a molten-salt nuclear reactor, radioactive liquid is flowing through a cylindrical pipe of diameter D. Fission in the liquid results in a uniform internal heat generation of å W/m³. The pipe wall also has a heater on it that can provide a uniform surface heating rate of q"W/m². The radioactive liquid has a specific heat capacity of C, J/kg-K, a mass flow rate of m kg/s, and an inlet temperature of Tmi.Conduction in the fluid in the x-direction can be assumed to be negligible, conduction through the pipe wall is negligible, and the flow in the pipe is steady and fully developed. Using a differential control volume in the pipe, perform an energy balance to obtain a differential equation that describes the variation of the bulk temperature (Tm) as a function of x-distance along the pipe. What is the boundary condition? DO NOT SOLVE the differential equation.

Fig: 1