IGNOU MRW 2 2026 - Derive the expression for shape factor for radiation emitting from a s

Question

Derive the expression for shape factor for radiation emitting from a surface 'i' and reaching the surface 'j'.

23 Apr 2026

Answer :

Word Count : 387

In radiative heat transfer, the shape factor, also known as the view factor or configuration factor, represents the fraction of radiation leaving one surface that directly reaches another surface. It depends only on the geometry and relative orientation of the surfaces, not on their temperatures or properties. Consider two differential surface elements (dA_i) and (dA_j), separated by a distance (r), with angles (\theta_i) and (\theta_j) between the line joining them and their respective surface normals. The radiation leaving surface element (dA_i) in the direction of (dA_j) is proportional to the intensity of emission and the projected area. The energy leaving (dA_i) and reaching (dA_j) can be expressed using the concept of diffuse emission, where radiation is uniformly distributed in all directions. The fraction of energy leaving (dA_i) that reaches (dA_j) is determined by geometric considerations involving solid angle. The solid angle subtended by

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