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The power delivered to the wheels of a vehicle (w) as afunction 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 andvelocity in mph. The amount of heat rejected from the engine block(qb) is approximately equal to the amount of power delivered to thewheel (the rest of the energy from the fuel leaves with the exhaustgas). The heat is removed from the engine by pumping water throughthe engine block with a mass flow rate of m = 0.80 kg/s. Thethermal communication between the engine block and the coolingwater is very good, therefore you may assume that the water willexit the engine block at the engine block temperature (Tb). For thepurpose of this problem, you may model the water as having constantproperties that are consistent with liquid water at 70oC. The heatis rejected from the water to the surrounding air using a radiator,as shown in the figure. When the car is moving, air is forcedthrough the radiator due to the dynamic pressure associated withthe relative motion of the car with respect to the air. That is,the air is forced through the radiator by a pressure differencethat is equal to ?V 2/2, where ? is the density of air. Assume thatthe temperature of ambient air is T? = 35oC and model the air inthe radiator assuming that it has constant properties consistentwith this temperature. The radiator has a plate-fin geometry. Thereare a series of tubes installed in closely spaced metal plates thatserve as fins. The fin pitch is pf = 1.2mm and there are W/pfplates available for heat transfer. The heat transfer core hasoverall width W = 50 cm, height H = 30 cm (into the page), andlength (in the flow direction) of L = 10 cm. For the purpose ofmodeling the air side of the core, you may assume that the air flowis consistent with an internal flow through rectangular ducts withdimension H x pf. Assume that the fins are 100% efficient andneglect convection from the external surfaces of the tubes as wellas the reduction in the area of the plates associated with thepresence of the tubes. Using the information above, develop a modelthat will allow you to predict the engine block temperature as afunction of vehicle velocity. Prepare a plot showing Tb vs V . Ifnecessary, 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 ofvehicle speeds are allowed? You should see both a minimum and amaximum limit.

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