CHE151 Introduction to Heat TransferFall Semester, 2019Homework Assignment #9Due Thursday November 14, 2019 at the start of classInIntroduction to Heat Transfer 6thand 7thEditionNOTE: Problem numbers have changed between editions; the problem numberare given for the 6thand 7theditions. I am also providing the first few words tohelp find the correct problem if you have the 8thedition. Also note that this inIntroductionto Heat TransfernotFundamentalsof Heat TransferProblem 7.66 begins with “An aluminum transmission line with diameter of 20mm…”Problem 7.84 begins with “Tissue engineering involves the development…”Problem 8.4 begins with “An engine oil coller consists of a bundle…”Problem 8.12 begins with “Water enters a tube at 27°C with a flow rate…”Problem 8.30 begins with “Air atp=1 atm enters a thin-walled (D=5-mmdiameter)…Problem 8.49 begins with “Colling water flows through the 25.4-mm…”

PROBLEM 7.66KNOWN:Aluminum transmission line with a diameter of 20 mm having an electrical resistance ofR′= 2.636×10-4ohm/m carrying a current of 700 A subjected to severe cross winds.To reducepotential fire hazard when adjacent lines make contact and spark, insulation is to be applied.FIND:(a) The bare conductor temperature when the air temperature is 20°C and the line is subjectedto cross flow with a velocity of 10 m/s; (b) The conductor temperature for the same conditions, butwith an insulation covering of 2 mm thickness and thermal conductivity of 0.15 W/m⋅K; and (c) Plotthe conductor temperatures of the bare and insulated conductors for wind velocities in the range of 2 to20 m/s.Comment on the features of the curves and the effect that wind velocity has on the conductoroperating temperatures.SCHEMATIC:ASSUMPTIONS:(1) Steady-state conditions, (2) Uniform surface temperatures, (3) Negligible solarirradiation and radiation exchange, and (4) Constant properties.PROPERTIES:Table A-4, Air (Tf= (Ts+ T∞)/2, 1 atm):evaluated using theIHT Propertieslibrarywith aCorrelationfunction; see Comment 2.ANALYSIS:(a)For thebareconductor the energy balance per unit length isinoutgenEEE0′′′−+=&&&cvc0qq A0′−+=&(1)where the cross-sectional area of the conductor is Ac=πD2/4 and the generation rate is()()(2224ecqIR / A700A2.63610/ m0.020m/ 4π−′==××Ω&(2)53q4.111 10W / m=×&The convection rate equation can be expressed as()()cvc,barettDqTT/ RR1/ hDπ∞′′′=−=×(3,4)and the convection coefficient is estimated using the Churchill-Bernstein correlation, Eq. 7.46, withReD= VD/ν,()L4/51/ 21/35/8DDD1/ 42/30.62 RePrhDReNu0.31k282,00010.4/ Pr⎡⎤⎛⎞⎢⎥==++⎜⎟⎢⎥⎝⎠⎡⎤⎣⎦+⎢⎥⎣⎦(4)(b) For the conductorwith insulationthickness t = 2 mm, the energy balance per unit length isinoutgenEEE0′′′−+=&&&()2c,instec0TT/ RI R/ A0∞′′−−+=(5)Continued …

PROBLEM 7.66 (Cont.)wheretR′is the sum of the insulation conduction and convection process thermal resistances,()()()tD2tRnD2t / D / 2 k1/ hD2t+′⎡⎤⎡⎤=+++⎣⎦⎣⎦lππ

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