Question

A cylinder, 6 mm in diameter, has a length of 24 mm. One end of the cylinder is open while all other surfaces have external insulation. The inside of the cylinder is diffuse and gray having an emissivity of 0.8 and a uniform temperature of 1000 K. (a) Draw a sketch and state your assumptions (b) Determine the radiant power leaving the open end of the cylinder. (c) Calculate the effective emissivity of the cylinder (see note below). (d) The length of the cylinder is decreased to 6mm, what is the effective emissivity of the cylinder? (e) If the length of the cylinder is decreased further, do you expect an increase or decrease in the effective emissivity? NOTE: The effective emissivity of any cavity is defined as the ratio of the radiant power leaving the cavity to that from a blackbody having the area of the opening and a temperature of the inner surfaces of the cavity.

Answer 1

(A)

Assumptions For Analysis of cylinder

1.The cross section of cylinder should be Prismatic

2.Heat transfer by convection and conduction should be negligible

3.all external surface should be well insluated except one open end

(B)

Calculation for radiant power leaving the open surface:-

view factor for Az A1 s Are II 2 Ty 6² = 28.27 mm 11 - TTDH+ D? 0 ЧИt Ф Sput valves 6 0.05882 Ux24 + 6 q- Fat Azot = 0.05882 you 8 x 28.21x30 43.678164.10009 a = 0.0755

(c) &(d)

& emissivity of cylinder fedtestive emissivity] e-1 & black bady] عطعوط effective emissivity Exetud Foto A2+ 4 0.05882X 0.8 te = 0.047056 @ when decrease the length of cylinder the effective e par emissinity of cylinder is changes because it does not depends on cross. Section nat

(e)

when we increase or decrease the length of cylinder there is no change in the effectie emissivity because the effective emissivity is indepentent on length