Tutorial
UEME4363: Internal Combustion Engines Tutorial No. 3
1. (a) Show that the temperature of the gases along a cylindrical exhaust pipe is given by the following expression:
hπ d T − Tw = (To − Tw ) exp − x mC & p where Tw is the wall temperature assumed to be constant along the pipe, To is the gas temperature at the inlet to the exhaust pipe, h is the convective surface heat transfer coefficient, d is the diameter of the pipe, m is the mass flow rate of the exhaust gasses, Cp is the mean specific heat of the exhaust gasses, x is the distance from the exhaust pipe inlet (b) Hence show that the heat loss from the exhaust gasses to the exhaust pipe is given by:
hπ d & Q = mC p (To − Tw )1 − exp − L mC & p where L is the total length of the exhaust pipe. ( c) Evaluate the total heat loss to the exhaust pipe if the convective heat transfer coefficient h may be obtained from the formula:
Nu = 0.023 Re 0.8 Pr 0.3
For pulsating flow, assume h is 2 times the value obtained from this formula. Prandtl Number Pr = 0.6 Mass flow rate of exhaust gasses = 0.250 kg/s Internal diameter of exhaust pipe = 6 cm Cp of exhaust gasses 1.08 kJ/kg K Density of exhaust gasses = 0.494 kg/m3 Dynamic viscosity of exhaust gasses = 3.32E-5 kg/m s Thermal conductivity of exhaust gasses = 5.26E-5 kW/m K Total length of exhaust pipe = 1.8 m Initial exhaust gas temperature = 483o C Temperature of exhaust pipe wall = 200o C
1. (a) Show that the temperature of the gases along a cylindrical exhaust pipe is given by the following expression:
hπ d T − Tw = (To − Tw ) exp − x mC & p where Tw is the wall temperature assumed to be constant along the pipe, To is the gas temperature at the inlet to the exhaust pipe, h is the convective surface heat transfer coefficient, d is the diameter of the pipe, m is the mass flow rate of the exhaust gasses, Cp is the mean specific heat of the exhaust gasses, x is the distance from the exhaust pipe inlet (b) Hence show that the heat loss from the exhaust gasses to the exhaust pipe is given by:
hπ d & Q = mC p (To − Tw )1 − exp − L mC & p where L is the total length of the exhaust pipe. ( c) Evaluate the total heat loss to the exhaust pipe if the convective heat transfer coefficient h may be obtained from the formula:
Nu = 0.023 Re 0.8 Pr 0.3
For pulsating flow, assume h is 2 times the value obtained from this formula. Prandtl Number Pr = 0.6 Mass flow rate of exhaust gasses = 0.250 kg/s Internal diameter of exhaust pipe = 6 cm Cp of exhaust gasses 1.08 kJ/kg K Density of exhaust gasses = 0.494 kg/m3 Dynamic viscosity of exhaust gasses = 3.32E-5 kg/m s Thermal conductivity of exhaust gasses = 5.26E-5 kW/m K Total length of exhaust pipe = 1.8 m Initial exhaust gas temperature = 483o C Temperature of exhaust pipe wall = 200o C