Estimate 

(a) The heat transfer coefficient for a spherical fuel droplet injected into a diesel engine at 80°C and 90 m/s. The oil droplet is 0.025 mm in diameter, the cylinder pressure is 4800 kPa, and the gas temperature is 944 K. 

(b) Estimate the time required to heat the droplet to its self-ignition temperature of 300°C.

GIVEN

• An oil droplet injected into a diesel engine
• Initial droplet temperature (T_o) = 80°C
• Injection velocity (U_d) = 90 m/s
• Droplet diameter (D) = 0.025 mm = 2.5 x 10^–5 m
• Cylinder pressure = 4800 kPa
• Gas temperature (T_∞) = 944 K = 671°C

ASSUMPTIONS

• Radiative heat transfer is negligible
• The gas has the properties of air and behaves as an ideal gas
• Only the density of the gas is affected by pressure
• Variation of the thermal conductivity of the oil with temperature is negligible
• Fuel has the same properties as unused engine oil

D-0.025 mm Gas T--871C Ug= 90 m/s