Temperatures of gases inside the combustion chamber of a four-stroke automobile

Question

Temperatures of gases inside the combustion chamber of a four-stroke automobile engine can reach up to 1000 degree 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 5-cylinder engine, and each cylinder has a diameter of 8.50 cm and height of 10.4 cm and is 3.78 mm thick. The temperature on the inside of the cylinders is 191.8 degree C and the temperature outside, where the coolant passes, is 134.2 degree C. The temperature of the incoming liquid (a mixture of water and antifreeze) is maintained at 101.3 degree 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 J/g degree C and its density is 1.070 times 10^3 kg/m^3. The cylinder walls have thermal conductivity of 1.10 times 10^2 W/m- degree C. Assume that no heat passes through the ends of the cylinders.

Explanation / Answer

The mode of heat trasfer here is conduction

Law of conduction stats :

Q' = -kAdT/dx

A= Conduction AREA = 2rh = 2x3.141x0.0425x0.104 = 0.0277 m2

dT = temperature differance = 191.8 - 134.2 = 57.6

dx = length along which het flows = 3.78x10^-3 m

Heat trasfer from cylinder:

Q = 1.10x10^2 x 0.0277x57.6/3.78x10^-3

= 0.464 x 10^5 Joules/sec

Ths same heat(provided by 5 cylinders) is absorbed by the coolant leading to its temperature increase:

Qt = 2.32 x10^5 Joules

Q = mCdT ......(i)

here dt = (134.2 - 101.3)

=32.9

C=3.75 j/g/C

density = 1.070 x10^3 kg/m3

Putting the values in equation-(i)

2.32 x10^5 = m'x3.75x32.9

m' = 1880.4 g/sec

m' = 1.880 kg/sec

V' = 1.880/1.070 x10^3

=1.757x10^-3 m3

= 1.757 x10^3 cm3/s Answer

note' the concept is heat given by clyinder raises the temperature of coolant

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