mperatures of gases inside the combustion chamber of a four-stroke automobile en

Question

mperatures of gases inside the combustion chamber of a four-stroke automobile engine can reach up to 1000°C. To remove this enormous amount of heat, the engine utilizes a closed liquid- cooled system which relies on conduction to transfer heat from the engine block into the liquid and then into the atmosphere by flowing coolant around the outside surface of each cylinder Assume you have a 4-cylinder engine, and each cylinder has a diameter of 8.25 cm and height of 10.1 cm and is 3.78 mmi thick. The temperature on the inside of the cylinders is 198.6°C and the temperature outside, where the coolant passes, is 131.4 C. The temperature of the incoming liquid (a mixture of water and antifreeze) is maintained at 95.0°C What volume flow rate of coolant would be required to cool this engine? Assume that the coolant reaches thermal equilibrium with the outer cylinder walls before exiting the engine. The specific heat of the coolant is 3.75 Jig. C and its density is 1.070 x103 kg/m3. The cylinder walls have thermal conductivity of 1.10 x 102 W/m "C. Assume that no heat passes through the ends of the cylinders Number cIn - 494.45

Explanation / Answer

given n = 4 cylinders
diameter of each cylinder, d = 8.25 cm
height, h = 10.1 cm
thickness, t = 3.78 mm
To = 131.4 C
Ti = 198.6 C
Toi = 95 C

heat capacity of coolant, c = 3.75 J/g C
rho = 1.070*10^3 kg/m^3
thermal conductivity of cylinder walls, k = 1.1*10^2 W/m C

for the cylinderical container, let rat of heat flow be R
then
R = kA*dT/dr
R*dr = k*2*pi*r*h*dT
R*dr/r = 2k*pih*dT
integrating
R*ln(ro/ri) = 2k*pi*h*(Ti - To)
R = 2k*pi*h(Ti - To)/ln(do/di) = 2*1.1*10^2*pi*0.101(198.6 - 131.4)/ln(8.25/(8.25-2*0.378))
R = 48808.15193 W

so in time t, energy released = Rt
this has to be absorbed by the coolant in time t
so mass of coolant required = m
mc(131.4 - 95) = R
m = 0.35756887 kg
volume = m/rho = 3.341765220*10^-4 m^3

hence volume flow rate = 334.1765220639 cm^3/s
for n = 4 cylinders. volume flow rat e= 1336.70608 cm^3/s

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