Exam1_Spring2013.pdf - ‘ gr#fi—lliE314ExamnoJ ‘7 S...

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Unformatted text preview: ‘ gr #fi—lliE314ExamnoJ _ ‘7 S 7/07) (115 pts., 1 hr. 15 mins. — Open Book ) (1. Make assumptions as necessary and list these clearly. 2. Show all intermediate steps in calculations and units clearly. 3. Clear sketches are needed for all problems. 4. Use of calculators permitted. 5. The total points below come to 115. You may choose not to attempt 10 pts. 1. A turbine blade is the critical part of the turbine engine which directly determines the turbine working temperature, power and efficiency. Blades are mounted on a rotating disc and are exposed to a hot gas stream with temperature Ts=1200 °C and convection coefficient of h=250 Wlm2 -K over the blade. These blades (made from Inconel, k =20 Wlm - K) have a length of L=50 mm. The blade has a uniform cross- sectional area of 140:6)(104 m2 and a perimeter of P=110 mm. The proposed cooling scheme (which involves routing air through the supporting disc) is able to maintain the base of each blade at a temperature of Tb=300 °C. (a) (10) is the proposed cooling scheme satisfactory if the maximum allowable blade temperature is 1050 °C and the tip may be assumed to be adiabatic? (b) (10)For the proposed cooling scheme, what is the rate at which heat is transferred from each blade to the coolant? Cajvwvv Turbine blade. k= 20w! 5 1e4m2. W . a: 0.11::K' A“: x - M K“) i —" b|MW§ACMaA Heed ivW—b‘i—V m (is) (MM (7%?” We ”lo dwelt 4M WW)! “Wolds. mm- - “m I if" .E/Wg D *— . :filviojm W “Hmalbgoc (PM Q51?) by lo- TL»? 7102) + gel/ILVV‘L) c ‘2 DOC 4" CoshLmL-Q :_ [100 LS~31\&”W%E'& 5‘; M, -\ \p Aer/vocfilm Jr». "3 (its? @ February 25, 2013: two 2. The base plate of a$fl W household Iron with a thickness L: 0. 6 fl base area of A=160 cm2 and thermal conductivity k: 20 Wlm- °C. The" Inner surface of the base plate Is subjected uniform heat flux generated by the resistance heater inside. When steady state operating conditions are reached, the outer surface temperature of the plate Is measured to be 85 °C. Ignore any heat loss through the upper part of the iron, (A) (10) Express the differential equation and the boundary conditions for the steady state, one dimensional heat conduction through the plate. (3) (10) Obtain a relation for the variation of temperature within the base plate by solving the differential equations. (C) (10) Determine the temperature at the inner surface (i. e. X: 0—). Wdl£ Wm ' 7K ‘ L-D in) gang Elicia wwwi emPLyfi" {CU} @1200 'W A=160 cm‘ February 25, 2013: 3. A 1.2 m high and 2.0 m wide double-pane window consisting of two 3.0 mm thick layer of glass (k = 0.78 Wlm - K) separated by a 12.0 mm wide stagnant air space (k = 0.026 Wlm - K). The temperature inside the room is maintained at 21 °C while the temperature of the outdoor is -5°C. The convection heat transfer coefficients on the inner and outer surfaces of the window are m = 10 Wlm2 -°C and h2 = 25 W/m2 -°C, respectively. Disregard the effect of radiation. (A) (5) Draw the thermal circuit for the heat transfer from the indoor to the outdoor. (D) (10) Calculate each thermal resistance and the total thermal resistance. (E) (10)Determine the steady rate of heat transfer through this double pane window. (F) (10)Find the outer surface temperature of the window. February 25, 2013: 4. Chickens with average mass of 1.7 Kg (k =0.45 Wlm - °C and d=0.13x10'6 mzls ) initially at a uniform temperature of 15 °C are to be chilled in agitated brine at —10 °C. The average heat transfer coefficient between the chicken and brine is determined experimentally to be 440 Wlm2 - °C_ Assuming the average density of the chicken to be 0.95 glcm3 and treating the chicken as a spherical object, (A) (15) Determine the temperature of the center of the chicken when it has been chilled for 2.0 h. (B) ( 15) Determine the temperature of the outer surface of the chicken when it has been chilled for 2. 0h. ...
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