Castrol's "Syntec" oil is touted by showing an ad in which a car engine runs with all its oil drained away. Aside from the combustion parts of the engine, critical failures could occur in the journal bearings of the crankshaft as heat is generated by viscous dissipation in the fluid. A typical journal bearing is shown in Figure P10.31. Assuming the engine is idling at \(1000 \mathrm{rpm}\), that the amount of heat removed by conduction in the metal parts is negligible, and that the engine starts out at temperature of \(85^{\circ} \mathrm{C}\) :

a. How fast does the temperature rise in the oil? Assume the oil is at a uniform temperature and use a parallel plate configuration to calculate the velocity profile with a thickness between the plates of \(r_{o}-r_{i}\).

b. If oil breaks down at \(250^{\circ} \mathrm{C}\), how long before the engine dies?

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Oil Properties: p = 825 kg/m k=0.136 W/m K Bearing Data: r = 0.08 m C = 2325 J/kg K v 10.0 10 6 m/s r = 0.07993 m