Sample

10335d91-313c-4b45-9b7b-2e9521c63d3f 17 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

A long uniform rod of 50-mm diameter with a thermal conductivity of 15 W/m-K is heated internally by volumetric energy generation of 20 kW/m3. The rod is positioned coaxially within a larger circular tube of 60-mm diameter whose surface is maintained at 500 degC. The annular region between the rod and the tube is evacuated, and their surfaces are diffuse and gray with an emissivity of 0.2. a) Determine the center and surface temperatures of the rod. b) Determine the center and surface temperatures of the rod if atmospheric air occupies the annular space. c) For tube diameters of 60, 100, and 1000 mm and for both the evacuated and atmospheric conditions, compute and plot the center and surface temperatures as a function of equivalent surface emissivities in the range from 0.1 to 1.0.

Given:

k 15 W m K * / * :

q' 20 kW m 3^/ * :

D.1 50 mm * :

T.2 773 K * :

T.2 °C 500

Stefan Boltzmann constant:

σ 5.670400 108 -^* W m 2^K 4^* / * :

F.12 1 :

A.1 π D.1 * : 0.157 m *

D.2 A.2 π D.2 * :

L σ T 4^T.2 4^- (* 1 ε - ε A.1 * / 1 F.12 A.1 * / + 1 ε - ε D.2 A.2 * / (+ / q' π D.1 2^* 4 / (* ≡ T Solve (: T i K * 209715204 nthroot * 8 D.2 * 11977157673652500 ε * 47077374176771 π * + (* 59159173145617 m * 1 ε - (* + D.2 ε * / 4 nthroot * 56280207133024 nthroot / ≡ T K 209715204 nthroot * 8 D.2 * 11977157673652500 ε * 47077374176771 π * + (* 59159173145617 m * 1 ε - (* + D.2 ε * / 4 nthroot * 56280207133024 nthroot / - ≡ T i K * 209715204 nthroot * 8 D.2 * 11977157673652500 ε * 47077374176771 π * + (* 59159173145617 m * 1 ε - (* + D.2 ε * / 4 nthroot * 56280207133024 nthroot / - ≡ T K 209715204 nthroot * 8 D.2 * 11977157673652500 ε * 47077374176771 π * + (* 59159173145617 m * 1 ε - (* + D.2 ε * / 4 nthroot * 56280207133024 nthroot / ≡ 41 sys

L 4 el Assign (K 209715204 nthroot * 8 D.2 * 11977157673652500 ε * 47077374176771 π * + (* 59159173145617 m * 1 ε - (* + D.2 ε * / 4 nthroot * 56280207133024 nthroot /

T ε 0.1 ≡ D.2 60 mm * ≡ 21 sys at 811.7 K *

T ε x ≡ D.2 60 mm * ≡ 2 1 sys at T ε x ≡ D.2 100 mm * ≡ 2 1 sys at T ε x ≡ D.2 1 m * ≡ 2 1 sys at 3 1 sys 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 terminal=pngcairo file_name="C:/FHB/Software/SMath/SMath 98.6598/extensions/plugins/44011c1e-5d0d-4533-8e68-e32b5badce41/GnuPlot/df4ul4yf" dimensions=[250,250] font="Arial" font_size=8 xu_grid=40 yv_grid=40 xlabel="ε " ylabel="T in K" zlabel="z" xrange=[0,1] zrange=[-5,5] "set term pngcairo font ',8' enhanced size 250, 250" "set encoding utf8" "set grid xtics mxtics" "set grid ytics mytics" plot2D SAMPLE PLOT Sample Disable Disable 4095 8 Disable Arial Disable 5 Disable [blue,red,green] 40 40 Custom 250 250 Interactive C:/FHB/Software/SMath/SMath 98.6598/extensions/plugins/44011c1e-5d0d-4533-8e68-e32b5badce41/GnuPlot/df4ul4yf png Disable ε T in K z Enable Enable Default 0 1 -5 5 -5 5 Custom Disable Interactive Enable Enable Disable Disable Disable Disable 10 10 10 60 60 1 1 Interactive Disable MouseX1 MouseY1 MouseW1 Disable Azimuth1 Zenith1 Disable MinX1 MaxX1 Disable MinY1 MaxY1 Disable MinZ1 MaxZ1 T ε x ≡ D.2 60 mm * ≡ 2 1 sys at x 0.1 1 explicit color red ≡ T ε x ≡ D.2 100 mm * ≡ 2 1 sys at x 0.1 1 explicit color forest_green ≡ T ε x ≡ D.2 1 m * ≡ 2 1 sys at x 0.1 1 explicit 5 1 sys