Question

The power delivered to the wheels of a vehicle (w) as a function of vehicle speed (V) is given by: w = 0.01417[hp/mph2]V 2 + 0.6300[hp/mph]V - 0.3937[hp] where power is in horsepower and velocity in mph. The amount of heat rejected from the engine block (qb) is approximately equal to the amount of power delivered to the wheel (the rest of the energy from the fuel leaves with the exhaust gas). The heat is removed from the engine by pumping water through the engine block with a mass flow rate of m = 0.80 kg/s. The thermal communication between the engine block and the cooling water is very good, therefore you may assume that the water will exit the engine block at the engine block temperature (Tb). For the purpose of this problem, you may model the water as having constant properties that are consistent with liquid water at 70oC. The heat is rejected from the water to the surrounding air using a radiator, as shown in the figure. When the car is moving, air is forced through the radiator due to the dynamic pressure associated with the relative motion of the car with respect to the air. That is, the air is forced through the radiator by a pressure difference that is equal to ?V 2/2, where ? is the density of air. Assume that the temperature of ambient air is T? = 35oC and model the air in the radiator assuming that it has constant properties consistent with this temperature. The radiator has a plate-fin geometry. There are a series of tubes installed in closely spaced metal plates that serve as fins. The fin pitch is pf = 1.2mm and there are W/pf plates available for heat transfer. The heat transfer core has overall width W = 50 cm, height H = 30 cm (into the page), and length (in the flow direction) of L = 10 cm. For the purpose of modeling the air side of the core, you may assume that the air flow is consistent with an internal flow through rectangular ducts with dimension H x pf. Assume that the fins are 100% efficient and neglect convection from the external surfaces of the tubes as well as the reduction in the area of the plates associated with the presence of the tubes. Using the information above, develop a model that will allow you to predict the engine block temperature as a function of vehicle velocity. Prepare a plot showing Tb vs V . If necessary, produce additional plots to help with your explanation. If the maximum allowable temperature for the engine block is 100oC (in order to prevent vaporization of the water) then what range of vehicle speeds are allowed? You should see both a minimum and a maximum limit.

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Answer 1

e engine block (qb) is approximately equal to the amount of power delivered to the wheel (the rest of the energy from the fuel leaves with the exhaust gas). The heat is removed from the engine by pumping water through the engine block with a mass flow rate of m = 0.80 kg/s. The thermal communication between the engine block and the cooling water is very good, therefore you may assume that the water will exit the engine block at the engine block temperature (Tb). For the purpose of this problem, you may model the water as having constant properties that are consistent with liquid water at 70oC. The heat is rejected from the water to the surrounding air using a radiator, as shown in the fig