10335d91-313c-4b45-9b7b-2e9521c63d3f 19 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 499.85

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 * :

T 300 K * :

D2 60 mm * 100 mm * 1 m * 13 mat :

j 13 range i 110 range ε i el i 10 / : T i j el q' π D.1 2^* 4 / (* 1 ε i el - ε i el A.1 * / 1 F.12 A.1 * / + 1 ε i el - ε i el π * D2 j el * / (+ (* σ / T.2 4^+ 4 nthroot : 21 line for 11 line for

ε 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1101 mat

T °C 538.5984 532.3446 523.6638 519.0116 516.0385 511.9708 512.1478 510.3716 507.9544 508.6474 507.4915 505.9228 506.5243 505.7479 504.6962 505.0992 504.5791 503.8752 504.0765 503.7409 503.2872 503.3068 503.1105 502.8453 502.7065 502.6191 502.501 502.2253 502.2253 502.2253 103 mat

T1 ε T 1 col augment :

T2 ε T 2 col augment :

T3 ε T 3 col augment :

T1 T2 T3 3 1 sys