10335d91-313c-4b45-9b7b-2e9521c63d3f 28 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:

D.1 50 mm * :

k 15 W m K * / * :

q' 20 kW m 3^/ * :

T.2 773 K * :

T.2 °C 499.85

Stefan Boltzmann constant:

σ 5.670400 108 -^* W m 2^K 4^* / * :

F.12 1 :

1 f x a b Bisection k 1 MAXITERS range c a b + 2 / : c f 0 ≡ break a f c f * 0 > a c : b c : if if 21 line for c 21 line :

A.1 π D.1 * : 0.157 m *

D.2 A.2 π D.2 * :

T 300 K * :

T ε D.2 eq 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 / (* - :

ε D.2 fT T ε D.2 eq 800 K * FindRoot :

MAXITERS 50 :

One value:

ε .1 :

D.2 60 mm * :

ε D.2 fT 811.748 K *

Range for ε

ε 0.1 1 0.11 range :

ε ε D.2 fT vectorize augment

Vectorize usually get confused when are two matrices involved, like in

Range for ε & D.2

D.2 0.06 m * (1 m * (0.1 m * range :

TD k 1 D.2 rows range D2 D.2 k el : TD k el ε ε D2 fT vectorize augment eval : 21 line for TD mat2sys.1 21 line :

ε ε D.2 k el fT vectorize augment

D2 and eval seems to avoid that.