Question

Temperatures of gases inside the combustion chamber of a four‑stroke automobile engine can reach up to 1000 ∘C.1000 ∘C. To remove this enormous amount of heat, the engine utilizes a closed liquid‑cooled system that 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.

Suppose that, in a particular 55‑cylinder engine, each cylinder has a diameter of 8.50 cm,8.50 cm, a height of 10.4 cm,10.4 cm, and a thickness of 3.78 mm.3.78 mm. The temperature on the inside of the cylinders is 195.2 ∘C,195.2 ∘C, and the temperature outside, where the coolant passes, is 134.2 ∘C.134.2 ∘C. The temperature of the incoming liquid (a mixture of water and antifreeze) is maintained at 101.3 ∘C.101.3 ∘C.

What volume flow rate of coolant ??Vt 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⋅∘C3.75 J/g⋅∘C and its density is 1.070×103 kg/m3.1.070×103 kg/m3. The cylinder walls have thermal conductivity of 1.10×102 W/m⋅∘C.1.10×102 W/m⋅∘C. Assume that no heat passes through the ends of the cylinders.

??=Vt=

cm3s

Answer 1

V = 1.867*10⁶ cm³/s.

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