Problem 2 Neglecting radiation, there is fully-developed forced convection through a cylindrical pipe with a uniform...

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Problem 2 Neglecting radiation, there is fully-developed forced convection through a cylindrical pipe with a uniform wall heat flux q". The pipe's radius is R, the pipe's length is L, the mass flowrate is m and the fluid's specific heat is c (a) Neglecting conduction, derive the differential equation which governs the mean temperature T(x). Clearly draw the differential control volume, labelling x, dx, x+dx, and all heat transfer rates, where x is the axial position in the pipe. (b) Neglecting conduction, determine the solution for T(X) as a function of the mean inlet temperature Ti (c) Neglecting conduction, determine the solution for T(x) as a function of the mean outlet temperature To (d) Including conduction, derive the differential equation which governs the mean temperature T(x). Do not specify boundary conditions, integrate or solve. Problem 2 Neglecting radiation, there is fully-developed forced convection through a cylindrical pipe with a uniform wall heat flux q". The pipe's radius is R, the pipe's length is L, the mass flowrate is m and the fluid's specific heat is c (a) Neglecting conduction, derive the differential equation which governs the mean temperature T(x). Clearly draw the differential control volume, labelling x, dx, x+dx, and all heat transfer rates, where x is the axial position in the pipe. (b) Neglecting conduction, determine the solution for T(X) as a function of the mean inlet temperature Ti (c) Neglecting conduction, determine the solution for T(x) as a function of the mean outlet temperature To (d) Including conduction, derive the differential equation which governs the mean temperature T(x). Do not specify boundary conditions, integrate or solve.