Is the view factor dimensionless?

Is the view factor dimensionless?

• A. Yes, it is a dimensionless geometric factor
• B. It has units of W/m^2
• C. It has units of meters
• D. It has units of kelvin

Answer: (A)

View factor is a dimensionless geometric quantity that describes what fraction of the radiation leaving one surface is intercepted by another. It depends only on the relative orientation, shapes, and separation of the surfaces, not on temperatures or emissivities. The standard definition is F_ij = (1/A_i) ∬_{A_j} (cos θ_i cos θ_j)/(π r^2) dA_j. In this expression, cos θ terms are dimensionless, r has units of length, and dA_j has units of area, so (cos θ_i cos θ_j)/(π r^2) dA_j is dimensionless. The outer 1/A_i factor scales the integral, but the integral itself contributes an area, leaving the overall result dimensionless. Since it represents a fraction of emitted energy, it has no units. For a closed surface, the sum of view factors to all other surfaces equals 1.

View factor is a dimensionless geometric quantity that describes what fraction of the radiation leaving one surface is intercepted by another. It depends only on the relative orientation, shapes, and separation of the surfaces, not on temperatures or emissivities. The standard definition is F_ij = (1/A_i) ∬_{A_j} (cos θ_i cos θ_j)/(π r^2) dA_j. In this expression, cos θ terms are dimensionless, r has units of length, and dA_j has units of area, so (cos θ_i cos θ_j)/(π r^2) dA_j is dimensionless. The outer 1/A_i factor scales the integral, but the integral itself contributes an area, leaving the overall result dimensionless. Since it represents a fraction of emitted energy, it has no units. For a closed surface, the sum of view factors to all other surfaces equals 1.