assignchap12extra-29-52

assignchap12extra-29-52 - PROBLEM 12.29 KNOWN: Spectral...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PROBLEM 12.29 KNOWN: Spectral emissivity. dimensions and initial temperature of a tungsten filament. FIND: (a) Total hemispherical emissivity. 8. when filament temperature is T. = 2900 K; (b) Initial rate of cooling. defdt. assuming the surroundings are at Tm = 300 K when the current is switched off: (c) Compute and plot E as a function of T. for the range 1300 S '[‘s E 2900 K; and (d) Time required for the filament to cool from 2900 to 1300 K. SCHEMATIC: qrad Evacuated Tungsten 045 mm filament. ‘ D = 0.8 mm. 5A L = 20 mm, T8 = 2900 K. 0.10 Tf= 1300 K 7t 0 2 4 (m) ASSUMPTIONS: (l) Filament temperature is uniform at any time (lumped capacitance). (2) Negligible heat loss by conduction through the support posts. (3} Surroundings large compared to the filament, {4) Spectral emissivity. density and specific heat constant over the temperature range, (5) Negligible convection. PROPERTIES: ’I‘ableA-J. Tungsten (2900 K}; p = 19, 300 lag/m3. er, a 135 J/kg~K. ANALYSIS: (a) The total emissivity at Ts = 2900 K follows from Eq. 12.38 using Table 12.1 for the band emission factors. 5 : IO EAELbUs )d’l' : ElfiOHEttm) T 52“ "FOHme) (1) e = 0.45 x 0.72 + 0,1t1~ 0.72) : 0.352 < where Fwazlum) = 0.72 at RT = ZumXZQOOK = 5800 MIH‘K. (b) Perform an energy balance on the filament at the instant of time at which the current is switched off. ;_ - CITS hill _Eout : Mcp dl AS (ethur —E): A.) (GUT: —£oTS4) : Mep de/dt and find the change in temperature with time where A. = rtDL. M : p0, and ‘v’ : (TIDE/4H“ cl’l‘S a‘DLcrteT: #a’lfilr) 7 40 t' C“ p (2119/4)ch Dept) (5T: 0T3” ) 7 t' ' 0T. 7 4x507x10 Swat-"mg-K4(0.352x29004—0.l><3004)K4 dt 19. 300 kg; m2 x 185 ig'kg - K X00008m (c) Using the [HT Tool, Radiation, Band Emission Factor. and liq. (l), a model was developed to calculate and plot 8 as a function of T5. See plot below. = 1977 K/s < PROBLEM 12.29 (Cont.) (d) Using the [HT Lumde Capacitance Model along with the IHT workspace for part (C) to determine E as a function of 1;, a model was developed to pl'edlCt 11 as a function ol'cooling time. The results are shown below for the variable emissivity case (2 vs. 'l‘S as per the plot below left) and the ease where the emissivity is fixed at 50900 K): 0352. For the variable and fixed emissivity eases. the times to reach T‘. = 1300 K are Iv\'.|r = S [lth i S < 0.4 0.3 7 E a 3 CD 0.2 - I _ 0 2 4 6 8 10 0-1 I r . - - a Elapsed time, 1(5) 1000 1500 2000 2500 3000 ‘ ‘ I I . — Variable emisswity Filament temperature, Ts (K) _+ Fixed emissivity, eps = 0.35 COMMENTS: (l)From the E vs. Tq plot, note that E increases as T5 increases. Could you have surmised as much by looking at the spectral emissivity distribution, at vs. It? (2) How do you explain the result that t“.Ir > tax? PROBLEM 12.52 KNOWN: Pewer dissipation temperature and distribution of spectral emissivity for a tungsten filament. Distribution of spectral absorptivity for glass bulb. Temperature of ambient air and sun'oundings. Bulb diameter. FIND: Bulb temperature. SCHEMATIC: Glass bulb, T5 iris. 1 D = 75 mm. at, I ‘11 ‘13 Tungsten filament 0.7L T = 3000 K, sf 052 if} ./ 0" Tm = 25°C Clitionv Pelee = 75 W D 0-4 2-0 101m) ASSUMPTIONS: (l) Steady—state. (2) Uniform glass temperature- TS‘ and uniform irradiation of inner surface. (3] Surface of glass is diffuse, (4) Negligible absorption of radiation by filament due to emission from inner surface of bulb, (5) Net radiation trtmsferfrem outer surface of bulb is due to exchange with large surroundings, (6) Bulb temperature is sufficiently low to provide negligible emission at it < 2am. (7) Ambient air is quiescent. PROPERTIES: Table M. air (assume rf : 323 K): v = 1.82 x 10'5 mils. o: = 2.59 x 105 mzlth = 0028 WhirK. a: 0.0031 K‘l, Pr = 0.704. ANALYSIS: From an energy balance on the glass buib‘ a If a 1 r 4 _ 71 qrad.i : Qradm +Clconv : J-L'b‘3"(r.s ’Tsur)+ h _ loo) (.1) where Eb : £l>2wn 2 a;_>2lum : l and h is obtained from Eq. {9.35) _ 0.589 Ralj‘l ED NU Z 2 + : (2) D 9/10 4’9 k [1+ (0.416911%) ] with Ran : g ('1‘s —'l1,¢, )D3 Iva. Radiation absorption at the inner surface of the bulb may be expressed as I 2 Clrad.i : CCG : O5 (Pelee HID ) [3) where. from Eq. (12.46)‘ or :aIJ‘gA (Gil IONA +052J‘2'0 0'4 (G;_/G)dl+a3j: (GA/omit The irradiation is due to emission from the filament, in which ease {GA/G} ~ (E;_ll£)f: (Er-,aLEg‘b/EfEb). Hence. a = (“i “'1‘ lily-45:12. (EQUb’JEb )d/L +012 lFr )LiffrJ. (ELIHEI; )‘M '-’ ((13 l 1‘1 (Fit: " Eta)” (4) where. from the spectral distribution ofProblem 12.25. 8ij E 81 = 0.45 for 2. < 2pm and EM 2 £3 = 0.10 for l “2 211m. From Eq. (12.38) Er =l:5r,1 (E/lJflfibliUL = 51 F(0—>2,um) +52 (1 —F(n—>2pm)) With AT,‘ : 2ymx3000 K 26000 hm-K. F(0..)2#m) = 0.738 from Table 12.1. Hence. ff 2 0.45x0.738 + 0.1(1 —0.738) = 0.358 Equation (4) may now be expressed as (I :(alLEI-)ElF(0—>0.411I11)+(02}£I')El(WU—Emu)_F(0-—>0.4um))+(a315f)52(1_F(0—)3t1m)) where. with AT = 041th 3000 K = 1200 me. F(0_,0_4#m) : 0.0021. Hence. a (1m.358)0.45 X00021 + (0.110.358)0.45><(0.738 — 0.0021) + (110.358)0.1 (i 70.738) 0.168 Substituting Eqs. (2) and {3) into liq. (l). as well as values of £1, : l and 06 : 0.168, an iterative solution yields TS 2348.1K < COMMEN'l‘S: For the prescribed conditions, (lgildyi = 713 mez. qf—adfl = 385.5 \Vi’mz and qgom, = 327.5 Win12. ...
View Full Document

This note was uploaded on 08/08/2008 for the course ME 364 taught by Professor Rothamer during the Fall '08 term at Wisconsin.

Page1 / 4

assignchap12extra-29-52 - PROBLEM 12.29 KNOWN: Spectral...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online