Question

This is a heat transfer question, please explain each step draw a clear diagram and show a nice and clean explanation. I want to make sure I understand this clearly. Thank you so much in advance!

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

24 is bu dy God 6 2 D - fiz AZ TD D+ YL fiz ales 18 80 we know the forreta cof Shape factor jey FIzA - f2. Az [seciprocity theored] "f21=1 [Because the radiation from atmosphes to the cylinder 0.006 3 AI -D²+2TRL 0.086+ 410.024) R. cef Surface D = ID?ta D2 Asea 0.05881 = 4.802810"m? ssphore. Put the value of fir in the equation smatic 't is SE E = 567x108 [lood)(Tata) 1-08 I 4.802 X109x0.8 0.0588x 4.802x1094 sessed As the atmospheric terip! is not given 80 we neglect the Tary. on scelning aboue Equation we will gest, This the total Radiative E = 1.5.78 Watt power from surface to surface og for calculating the effective Emissivity, which is the ratio o E E = Eb 5.678x10°[loody - 2.779X10 4 al 1.578 E - 1.578 56780

Step SOLUTION :- As in the given problem the diameter of cylinder is GMM 8 length is 24mm, one side of cylinder is open & other sides are closed & assured to be a grey Body 80 according to the question the diagram shown below! 80 L form Shan is 7 CFO L=240414 GEO-8 Talovok > 6MM assure put As a open let us as a Body ② is cylinderical Surfaces and 2 surface ie., consider as a Atrasphere The assumptions for a grey body is the monochromatic Emissinity "&" is independent of wavelength"&" or it is assure to be constant. E = constant W 812 he on 1-6 + 80, to calculate Radiant power E, which is expressei Ao o (T" - T24 where, А fizat is the fractional A,E FILA part of Radiation Energy from surfaces to Surface for Temperature of the surface, E = It is the Grissinity of grey Body Stefan Boltzman constant ley 5.67810 A It is the total surface Area of the cylinder 2 ro T €

ANSWERS: DIE = 1.578 Watt E = 2.779 105 (d) t = 2.685 X 105 on decreasing the length of the Cylinder the Effective INCREASES 11 Emissinity 35392.1329