Name: ________________________ Student I. D. No. ________________ Heat Transfer CHEMICAL ENGINEERING 6453-001 THIRD AND FINAL EXAMINATION, 8 May 2002 Prof. Geof Silcox Department of Chemical and Fuels Engineering University of Utah Write all work on this exam paper. Open books, homework, and notes. 1) Please read each problem carefully and completely before attempting to solve it. 2) To receive full credit for a solution, you must state all equations that you use and you must state all values substituted in those equations. You must show all of your work to receive credit for a solution. 3) If you use values from a table, state which table you use. Exam Grade Summary Problem 1.0 _________/ 40 points Problem 2.0 _________/ 40 points Problem 3.0 _________/ 40 points Problem 4.0 _________/ 40 points Problem 5.0 _________/ 40 points Total _________/200 points2 2Problem 1.0 In Lesson 28 we noted that human skin can sustain a heat flux of 4.7 kW/m2 for 1 to 2 minutes without damage. Suppose a person's skin is exposed to the time-varying flux sketched below. 10q, kW/m25050 100150200time, s Estimate the temperature at the surface of the skin at 200 s. Assume that the skin and nearby tissue have an initial uniform temperature of 307 K and the following properties. ρ = 1000 kg/m3 c = 4180 J/(kg K) k = 0.37 W/(m K) Problem 2.0 The skin of a spacecraft, sketched in cross-section below, is being used as a radiating fin. The thickness of the radiating skin or plate is b and its width is w. It is backed by insulation. There is no convection to the surroundings. The temperature gradients in the plate, in the y-direction, are negligible. The plate is large enough that edge effects are negligible. Considering a fluid temperature Tf, a surface emissivity ε, a surrounding temperature Tsur, and a base temperature (at x = L) Tf, obtain the governing equation and boundary conditions for the steady state formulation of this problem. You need not solve the equations.3 3Tfinsulationbε2LxTsurbase T = Tf Problem 3.0 A 4.0-m diameter spherical enclosure is filled with an adsorbing and emitting gas at 1400ºC with an adsorption coefficient ka = 0.25 m-1. The wall is maintained at 450ºC. Find the net radiative flux (W/m2) leaving the wall when (a) the wall is black and (b) when the wall is gray with ε = 0.60. Problem 4.0 A chamber for heat-curing large steel sheets, painted black (ε2 = ε2' = 0.95) on both sides, operates by passing the sheets vertically between heated plates (ε1 = ε3 = 0.80). Plate 1 is maintained at T1 = 600 K and the other, exposed to the surroundings, is at T3 = 300 K. (a) When equilibrium has been reached, what is the net rate of heat transfer from plate 1 to 3 and what is the temperature (T2 = T2') of the painted sheet? You may neglect convection. (b) If the steel sheet is 1.00 mm thick with ρ = 7854 kg/m3, c = 434 J/(kg K), k = 60.5 W/(m K), roughly estimate the time required to reach equilibrium if the initial, uniform value of T2 = T2' = 300K. T1T3T2T2’4 4 Problem 5.0 In Problem 2 of Assignment 8 you developed a model for the rate of ice formation on the surface of a lake. (a) Extend that model to include radiation to the surroundings with Tsur = -100ºC where the emissivity of the ice is εi = 0.95. Estimate whether the radiative heat transfer is important. (b) State an algorithm for solving the resulting equations. Be sure to include all necessary initial