Energy Transfer
Consider the total thermal energy carried by the fluid as
Now image this same amount of energy is carried by a body of fluid with the same mass flow rate but at a uniform mean temperature Tm. Therefore Tm can be defined as
Consider Tm as the reference temperature of the fluid so that the total heat transfer between the pipe and the fluid is governed by the Newtons cooling law as: qs=h(Ts-Tm), where h is the local convection coefficient, and Ts is the local surface temperature. Note: usually Tm is not a constant and it varies along the pipe depending on the condition of the heat transfer.