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Apr 3, 2024
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ME 309 HW 2 (Chapter 2) Question 1 of 5 Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity k = 50 W/m-K and a thickness L = 0.4 m, with no internal heat generation. Determine the heat flux, in kW/mZ2, and the unknown quantity for each case. Case Ty (°C) 50 -30 70 T,(°C) -20 -10 20/20 134 40 30 dT/dx (K/m) q; (kW/m?) -175 8.75 50 -2.5 160 -8 -80 4 200 -10 1— 2= = B support
ME 309 HW 2 (Chapter 2) Question 2 of 5 < > 20/20 i= Show Attempt History Consider a plane wall 140 mm thick and of thermal conductivity 120 W/m-K. Steady-state conditions are known to exist with T; = 500K and T, = 700 K. Determine the heat flux g7, in kW/mZ, and the temperature gradient dT/dx, in K/m, for the coordinate systems shown. T(x) T(x) T(x) » X X X (a) (b) (c) Part A @ v Your answer is correct. ’ B support
VNP BT Question 2 of 5 < > 20/20 = Part A ‘ v Your answer is correct. Determine the heat flux g7 ,in kW/mZ2, and the temperature gradient dT/dx, in K/m, for the coordinate system shown. T(x) (a1), = -171.4284 KW/m? dT @ ( — ) = 142857 K/m dx i
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ME 309 HW 2 (Chapter 2) Question 2 of 5 < > 20/20 = Part B ‘ v Your answer is correct. ’ Determine the heat flux g/ , in kW/m?, and the temperature gradient dT/dx, in K/m, for the coordinate system shown. T(x) T, (¢2), = 171.4284 KW/m? R support =) = _ K j (dx )b 1428.57 /m
VNP B Question 2 of 5 < > 20/20 i= Part C ‘ v Your answer is correct. ’ Determine the heat flux g¥ ,in kW/m?2, and the temperature gradient dT/dx, in K/m, for the coordinate system shown. T(x) (a7), = -171.4284 kW/m? dT @ (—) = 1428.57 K/m dx /, B support
ME 309 HW 2 (Chapter 2) Question 3 of 5 < > 20/20 i= Consider a 310 mm x 310 mm window in an aircraft. For a temperature difference of 80°C from the inner to the outer surface of the window, calculate the heat loss through L = 10-mm-thick polycarbonate, soda lime glass, and aerogel windows, respectively. The thermal conductivities of the aerogel and polycarbonate are k,, = 0.014 W/m-Kand k,. = 0.21W/m-K, respectively. Evaluate the thermal conductivity of the soda lime glass at 300 K. If the aircraft has 120 windows and the cost to heat the cabin air is $1/kW-h, compare the costs associated with the heat loss through the windows for an 8-hour intercontinental flight. The thermal conductivity of the soda lime glass, in W/m-K: kgl = 14 W/m-K The heat loss through the soda lime glass, in W: Grg = | 107632 W The heat loss through the polycarbonate, in W: Gy = | 161448 W The heat loss through the aerogel windows, in W: Geq = | 1076 w The costs associated with the heat loss for glass windows, in $: B support Cy = $ | 103327 @ The costs associated with the heat loss for polycarbonate windows, in $:
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ME 309 HW 2 (Chapter 2) Question3of 5 < > 20/20 = = The heat loss through the soda lime glass, in W: Grg = | 107632 W The heat loss through the polycarbonate, in W: Gy = | 161448 W The heat loss through the aerogel windows, in W: Geq = | 1076 W The costs associated with the heat loss for glass windows, in $: Cy = $ | 103327 The costs associated with the heat loss for polycarbonate windows, in $: C, = $ | 15499 The costs associated with the heat loss for aerogel windows, in $: C,=9%] 1033 Physical Properties Mathematical Functions @ eTextbook and Media
ME 309 HW 2 (Chapter 2) Question 4 of 5 < View Policies Show Attempt History 20/20 = Uniform internal heat generationat ¢ = 2.00 x 107 W/m?3is occurring in a cylindrical nuclear reactor fuel rod of 50-mm diameter, and under steady-state conditions the temperature distribution is of the form T' () = a + br?, where T'is in degrees Celsius and r is inmeters, whilea = 800°Cand b = -1.667 x 10°°C/m?2 The fuel rod propertiesare k = 30 W/m-K,p = 1100 kg/m® andc, = 800 J/kg-K. Physical Properties Mathematical Functions Step 1 ‘ v Your answer is correct. Find the steady state temperature gradient at the outer surface of the rod, in °C/m. or = 8335 ar r=r, - - °C/m Attempts: unlimited
VNP BT Question 4 of 5 Step 2 20/20 = v Your answer is correct. What is the steady state rate of heat transfer at the outer surface, in W/m? q (ro) = Step 3 39277.76 W/m Attempts: unlimited v Your answer is correct. What is the steady state rate of heat transfer at the centerline, in W/m? q (0) = W/m Attempts: unlimited
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VNP BT Question 4 of 5 < > 20/20 = Step 4 v Your answer is correct. If the reactor power level is suddenly increased to g, = 1x 108 W/m3 (att = 0 sec),immediately after that what is the temperature at the centerline, in °C? T(0) = | 800 °C Attempts: unlimited Step 5 v Your answer is correct. ’ Immediately after the sudden increase in reactor power level to g, = 1x 108 W/m3(att = 0 sec), what is the time rate of temperature change at the centerline, in °C/s? oT = = 90.9 °C/s ot B support
ME 309 HW 2 (Chapter 2) Question 5 of 5 < 20/20 i= The steady-state temperature distribution in a one-dimensional wall of thermal conductivity 50 W/m-K and thickness 140 mm is observed to be T’ (OC) = a+ bx?,wherea = 200°C,b = -2000 C/m2, and x is in meters. (1) What is the heat generation rate g in the wall? (2) Determine the heat fluxes at the two wall faces. Physical Properties Mathematical Functions Step 1 ‘ v Your answer is correct. What is the temperature gradient evaluated at x = L,in°C/m? dT — = -560 °C/m dx x=L Attempts: unlimited
VNP B Question Step 2 50f 5 < 20/20 = ‘ v Your answer is correct. What is the second derivative of temperature with respect to x evaluated at x = L,in°C/m?%? Step 3 -4000 °C/m? Attempts: unlimited v Your answer is correct. What is the heat generation rate in the wall, in W/m3? q: 200000 W/m?3 Attempts: unlimited R support
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VNP B Question 5 of 5 Step 4 < 20/20 = ‘ v Your answer is correct. What is the heat flux at x = 0, in W/m2? q" (0) = Step 5 W/m? Attempts: unlimited v Your answer is correct. What is the heat flux at x = L,in W/m?? q " X(L) = eTextbook and Media 28000 W/m?2 Attempts: unlimited R support
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