Final answer:
In a steady-state system with no internal heat generation, the heat flux into the pipe wall must be equal to the heat flux out of the pipe wall, satisfying the principle of conservation of energy.
Step-by-step explanation:
The student has asked about heat transfer in a steady-state condition with no heat generation for a pipe carrying hot water that is experiencing an external cross-flow of cold air. According to the principles of thermodynamics, specifically the conservation of energy, for a system in steady state and with no internal heat generation, the heat flux into the pipe wall must be equal to the heat flux out of the pipe wall. This satisfies the requirement that the energy entering a system must also leave the system when it is at a steady state, ensuring the total energy within the system remains constant.