Temperatures of gases inside the combustion chamber of afour‑stroke automobile engine can reach up to 1000 ∘C.1000 ∘C. Toremove this enormous amount of heat, the engine utilizes a closedliquid‑cooled system that relies on conduction to transfer heatfrom the engine block into the liquid and then into the atmosphereby flowing coolant around the outside surface of each cylinder.

Suppose that, in a particular 55‑cylinder engine, each cylinderhas a diameter of 8.50 cm,8.50 cm, a height of 10.4 cm,10.4 cm, anda thickness of 3.78 mm.3.78 mm. The temperature on the inside ofthe 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 ofthe incoming liquid (a mixture of water and antifreeze) ismaintained at 101.3 ∘C.101.3 ∘C.

What volume flow rate of coolant ??Vt would be required to coolthis engine? Assume that the coolant reaches thermal equilibriumwith the outer cylinder walls before exiting the engine. Thespecific heat of the coolant is 3.75 J/g⋅∘C3.75 J/g⋅∘C and itsdensity is 1.070×103 kg/m3.1.070×103 kg/m3. The cylinder walls havethermal conductivity of 1.10×102 W/m⋅∘C.1.10×102 W/m⋅∘C. Assumethat no heat passes through the ends of the cylinders.

??=Vt=

cm3s