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GATE 2016 ME (ME2) – Question 26

Heat Transfer · Radiative heat transfer: laws, view factors, radiation network · 1 mark · Multiple choice

Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is 𝑅o and that of the inner cylinder is 𝑅i. The radiation view factor of the outer cylinder onto itself is

  1. $1-\sqrt{R_i/R_o}$
  2. $\sqrt{1-R_i/R_o}$
  3. $1-(R_i/R_o)^{1/3}$
  4. $1-R_i/R_o$

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Correct answer: (D) $1-R_i/R_o$

Explanation

The convex inner cylinder cannot see itself, so Fi,o=1. Reciprocity gives AoFo,i=AiFi,o, hence Fo,i=Ri/Ro for equal lengths. Closure for the outer surface gives **Fo,o=1−Ri/Ro, D**. End effects are neglected for very long cylinders.