A One-Dimensional Model for Heat Transfer in Engine Exhaust Systems

This paper presents a one-dimensional model for heat transfer in exhaust systems. Convective heat transfer in pipe flows under steady-state and transient conditions is studied. Analytical solution of the governing equation for steady-state condition is obtained. Effects of turbulent, laminar and transition flow regimes on heat transfer are allowed for. Influences of various parameters, i.e. inlet mass flow rate & temperature, wall temperature, pipe length and pipe diameter, on heat transfer are assessed quantitatively. Efforts are made to explain the physics of heat transfer process from basic principles. It is proven mathematically that in turbulent flow regime, the pipe outlet temperature increases with increasing pipe diameter and mass flow. For transient condition, the governing equations are derived, and a warm-up process is simulated. Effects of inlet condition, pipe geometry, external heat transfer and wall thickness on outlet temperature are discussed. The initial pipe outlet temperature increases with increasing pipe diameter, while the rate of change of temperature decreases with diameter. Comparison between the simulation and measurement is made, showing good agreement. Instantaneous heat transfer during an engine cycle at a cold start condition is simulated. Gas temperature distribution in exhaust port over time and space domains is obtained and characterized. It is found that there is a strong correlation between heat transfer and mass flow rate. The heat transferred to the exhaust port and runner wall is mainly in the phases of exhaust gas blow-down and piston displacement, while the heat loss from the stationary gas during closed valve period is relatively small despite the long period. It is shown that the one-dimensional model is capable of quantifying many thermal behaviours of exhaust systems.