READ EACH PROBLEM CAREFULLY. INCLUDE SKETCHES WHERE NECESSARY AND CLEARLY STATE

Question

READ EACH PROBLEM CAREFULLY. INCLUDE SKETCHES WHERE NECESSARY AND CLEARLY STATE ALL ASSUMPTIONS General Energy Balance A cubic transmission casing whose side length is 28cm receives an input from the engine at a rate of 175 hp. If the vehicle's velocity is such that the average heat transfer coefficient is 250 W/m2K and the efficiency of the transmission isn 95 (ie. the remainder is heat), calculate the surface temperature if the ambient temperature is 15°C. Assume that heat transfer only occurs on all but one of the cube faces. NOTE: 1hp 745 W

Explanation / Answer

SOLUTION:

Area of cube exposed to the surrounding air , A = 0.28x0.28 m2 = 0.0784 m2

Since only 5% of 175hp power is turned into heat,

So, Heat Transfer from the surface, Q = 175x745x 5/100 W = 6518.75W

Let the temperature of the transmission case surface be Ts , and outside air be at Tf =15oC= 288 K

As, from the Convective law heat transfer,

Q = hxAx(Ts-Tf)

So, Ts= Tf + Q/hA

Ts= 288 + 6518.75/(250x0.0784) K

Ts= 620.59 K = 347.59oC

Hence , the surface temperature of transmission case is 347.59oC.

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