Question

(a) Calculate the shape factor F22 for radiation exchange between two black bodies arranged in the following configuration: AAN D2- Assume surface 1 is a disc and surface 2 is a hemisphere with a diameter of D. The surface area of a hemisphere is nt.D2/2. (b) If it is hypothetically assumed that the Pyramid of Khafre is hollow, determine the values for all the radiation shape factors from the base of the pyramid to each of its four sides. Assume the base is a square and the four remaining surfaces as isosceles triangles.

Answer 1

a) Given's A = area of disc Az = Surface area of Hemisphere An= *p? 2 A = 7 (-2) ? No? 16 surface 2 Surfaces surface 3 As = 7 [D² (23] = 7 x 7 8 = 37 3T Surf Apply E, , = 0 (Flat ; Fiz=0 ; F31=0 F33=oL and Summation rules - For 1 For 3 Fi + F2+ F3 = 1 Ezi + Fzz + F33 = 1 o + Fizto 0 + F3z +0=1 1 Fir=1 F32=1 Apply reciprocity rule -- Alfia = A2 F21 A x1 = Az F1 F2 = AL TD² Az 16 11 ol- CS Scanned with AD2 CamScanner

similarly! Az Foz = A₂ F2 3 3px1 = 7 px Fing F23 = 3 8 Now Apply summation rule for Surface 2,- Fait F22+ F23=1 ² + F22 + 38 = 1 1 F22 =2=0.5 F22=0.5 (le) Given - Let us say base = surface (1) Four sides of surface (2) Base 17 1 (5) (4) Solen - From summitry we can say Fiz=Fizz Fiq=fis and Fizo [flat surface Apply summation rule for surface (1):- Fil+ F12 + F 13 + Fiat Fis=1 0+4 (Fiz) = 1 > Fiz=1/4 = 0.25 CS Scanned with 12 = F13 = F14- FIS = 0.25 CamScanner