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chap1assign - PROBLEM 1.11 KNOWN Dimensions and thermal...

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Unformatted text preview: PROBLEM 1.11 KNOWN: Dimensions and thermal conductivity of a chip. Power dissipated on one surface. FIND: Temperature drop across the chip. SCHEMATIC: ,k—mSLtbsfra re Chip, k=150W/M°K ASSUMPTIONS: (1) Steady-state conditions, (2) Constant properties, (3) Uniform heat dissipation, (4) Negligible heat loss from back and sides, (5) One-dimensional conduction in chip. ANALYSIS: All of the electrical power dissipated at the back surface of the chip is transferred by conduction through the chip. Hence, from Fourier’s law, mm a 01' AT: t~P2 : 0.001mx4w 2 kW 150 W/m-K(0.005 m) AT 3 1.1“ C. < COMMENTS: For fixed P, the temperatme drop across the chip decreases with increasing k and W, as well as with decreasing t. PROBLEM 1.23 KNOWN: Width, input p0wer and efficiency of a transmission. Temperature and convection coefficient associated with air flow over the casing. FIND: Surface temperature of casing. SCHEMATIC: a, = 30°C h; = 200 W/mZ-K q -‘-—"'-l> Po = “Pi T ______, P5150 “P w=o.3m ASSUMPTIONS: (I) Steady state, (2) Uniform convection coefficient and surface temperatme, (3) Negligible radiation. ANALYSIS: From Newton’s law of cooling, q : 11As (Ts ‘11»): 6hW2 (Ts ‘10) Where the output power is n P,- and the heat rate is q = 1"} “”Po = P; (1—17): lSthX746W /th0.07 = 7833 W Hence, q = 30°c+————7§§§W—-W =102.5°C < 6 law2 6x200 W/mZ-KX(0.3m)2 Tssz+ COMMENTS: There will, in fact, be considerable variability of the local convection coefficient over the transmission case and the prescribed value represents an average over the surface. PROBLEM 1.44 KNOWN: Radial distribution of heat dissipation in a cylindrical container of radioactive wastes. Surface convection conditions. q FIND: Total energy generation rate and surface temperature. SCHEMATIC: ASSUMPTIONS: (l) Steady—state conditions, (2) Negligible temperature drop across thin container wall. ANALYSIS: The rate of energy generation is - . _ I 2 Eg = Jqu=q0 00 [l—(r/ro) ]27rrLdr Eg = 27:qu (r3 Iz—rg 14) or per unit length, - 2 Efflqor‘). < 2 Performing an energy balance for a control surface about the container yields, at an instant, E’—E’ =0 g out and substituting for the convection heat rate per unit length, . 2 ”gr" = h(27rr0)(TS 40°) TS = Tm + q°r° ‘ < 4h COMMENTS: The temperature within the radioactive wastes increases with decreasing r from TS at r0 to a maximum value at the centerline. ...
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chap1assign - PROBLEM 1.11 KNOWN Dimensions and thermal...

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