Shown in Figure Q.2 is a two-dimensional equilateral triangular geometry whose surfaces are numbered 1, 2...

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Shown in Figure Q.2 is a two-dimensional equilateral triangular geometry whose surfaces are numbered 1, 2 and 3 as shown. All sides are 1 m in length. Blackbody emissive power of surfaces 1, 2 and 3 are E, E and E3 respectively. For an enclosure with n number of grey surfaces, the radiosity of the ith surface is linked to other radiosities via the equation: J - (1-6,;) FqJ, = 6, Ebi ] a) If all three surfaces (1, 2 and 3) of the triangular geometry are grey with emissivities , & and & respectively, show how you apply the above radiosity equation to write 3 equations that could be solved to obtain radiosities J, J, and J3. b) For a triangular geometry with surface areas 4, 4 and 43, the configuration factor F2 is given by F2 = (A + A A)/2A. Using this formula and other relevant configuration factor properties, calculate all necessary configuration factors required for the equations obtained in (a) and simplify the set of equations. Leave the blackbody emissive powers in their symbolic form. c) For a special case where the surface 3 of the above geometry is a re-radiating surface (p3 =1) and emissivity values of the other two surfaces are equal to 0.5, simplify the equations obtained in (b) and write a set of equations to obtain radiosities in terms of blackbody emissive powers. d) Use simple elimination to solve the equations obtained in (c) and write an expression for radiosity J, (in terms of blackbody emissive powers of surfaces 1 and 2). e) Use the expression obtained in (d) for J, to write an expression for heat transfer at surface 1. f) Draw an equivalent electrical circuit for the case described in (c) and obtain an expression for heat transfer at surface 1 to verify your result obtained in (e). 1 m 2 1 Figure Q.2 3 Shown in Figure Q.2 is a two-dimensional equilateral triangular geometry whose surfaces are numbered 1, 2 and 3 as shown. All sides are 1 m in length. Blackbody emissive power of surfaces 1, 2 and 3 are E, E and E3 respectively. For an enclosure with n number of grey surfaces, the radiosity of the ith surface is linked to other radiosities via the equation: J - (1-6,;) FqJ, = 6, Ebi ] a) If all three surfaces (1, 2 and 3) of the triangular geometry are grey with emissivities , & and & respectively, show how you apply the above radiosity equation to write 3 equations that could be solved to obtain radiosities J, J, and J3. b) For a triangular geometry with surface areas 4, 4 and 43, the configuration factor F2 is given by F2 = (A + A A)/2A. Using this formula and other relevant configuration factor properties, calculate all necessary configuration factors required for the equations obtained in (a) and simplify the set of equations. Leave the blackbody emissive powers in their symbolic form. c) For a special case where the surface 3 of the above geometry is a re-radiating surface (p3 =1) and emissivity values of the other two surfaces are equal to 0.5, simplify the equations obtained in (b) and write a set of equations to obtain radiosities in terms of blackbody emissive powers. d) Use simple elimination to solve the equations obtained in (c) and write an expression for radiosity J, (in terms of blackbody emissive powers of surfaces 1 and 2). e) Use the expression obtained in (d) for J, to write an expression for heat transfer at surface 1. f) Draw an equivalent electrical circuit for the case described in (c) and obtain an expression for heat transfer at surface 1 to verify your result obtained in (e). 1 m 2 1 Figure Q.2 3