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# hw4 - ME 114 Homework Set 4 Fall 2008 S hown have The fin...

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Unformatted text preview: ME 114 Homework Set 4 Fall 2008 S- hown have; The fin array ofProbiem‘STl‘Heis commonly found in compact heat exchangers, whose function is to provide a large surface area per unit volume in transferring heat from one ﬂuid to another. In such applications, it is desirable to minimize the thermal resistance Rh 0 of the ﬁn array. Consider a unit heat exchanger core that is 1 m long in the direction of air flow and l m wide in a direction normal to both the air ﬂow and the fin surfaces. The length of the fin passages between adjoining parallel plates is L = 8 mm. while the fin thermal conductivity and convection coefficient are k = 200 W/m ' K (alu- minum) and h = 150 W/rn2 - K, respectively. If the fin thickness and pitch are‘t = 1 mm and S = 4 mm, respectively, what is the value of RM? Hint: There is a We of ' Sgt/magi”) wrath-5a +h€ V Carri—Bf, S‘o UPLJL an”) Flirt-Ci. +0 camaloﬁe » “1. the geometry What {5 the bow/robin) _ . . . p Caﬂcitil‘am 51+ at [ME 0‘! Slams/mtﬁ‘jr A as Steel balls 12 mm in diameter are annealed by heating to 1150 K and then slowly cooling to 400 K in an air environment for which T3, = 325 K and h = 20 W/m2 - K. Assuming the properties of the steel to be k = 40 W/m - K. p = 7800 kg/m3, and c = 600 J/kg ' K, estimate the time required for the cooling process. Mtg 6+ V21 (1 {Gigi/1‘ . After a long, hard week on the books, you and your friend are ready to relax. You take a steak 50 mm thick from the freezer. How long do you have to let the good times roll before the steak has thawed? Assume that the steak is initially at —6°C, that it thaws when the midplane temperature reaches 4°C, and that the room temperature is 23°C with a con- vection heat transfer coefficient of 10 W/m2 - K. Treat the steak as a slab having the properties of liquid water at 0°C. Neglect the heat of fusion as- sociated with the melting phase change. Assam/16 Convection CM be?“ Due October 2 et'clgg‘ ' Cylindrical steel rods (A131 1010). 50 mm in diam- eter, are heat treated by drawing them through an oven 5 m long in which air is maintained at 750°C. The rods enter at 50°C and achieve a centerline . temperature of 600°C before leaving. For a con- vection coefficient of 125 W/m2 - K, estimate the speed at which the rods must be drawn through the oven. A row of 3—ft-long and Lin—diameter used uranium D. (I) 6 ﬂ 8 (D an L7 2 n—x m E- O 8 ﬂ 4 (D P: ('D g (D D. s. :5 6" (D 3 O I: .‘3 D. "U f? . a each other w1th a center-to-center distance of 8 in at a 15 ft from the ground surface at a location where tribunal conductivityof the soil is 0.6 Btu/h - ft - °F. If the “Ge temperature of the rods and the ground are 350“F and spectively, determine the rate of heat transfer from the _'OdS to the atmosphere through the soil. The soil temperature in the upper layers of the earth varies with the variations in the atmospheric conditions. Before a cold front moves in, the earth at a location is initially at a uni- form temperature of 10°C. Then the area is subjected to a tem- perature of - 10°C and high winds that resulted in a convection heat transfer coefﬁcient of 40 W/m2 ‘ °C on the earth’s surface for a period of 10 h. Taking the properties of the soil at that lo- cation to be k = 0.9 W/m - °C and a = 1.6 X 10'5 mils, deter- mine the soil temperature at distances 0, 10, 20, and 50 cm from the earth’s surface at the end of this 10-h period. Winds, ~10°C ...
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