Question

What does the view factor represent? When is the view factor from a surface to itself not zero?

Short answer

Answer: The conditions for a non-zero view factor from a surface to itself are: 1) The surface must be concave or bend inward, allowing the emitted radiation to be reflected within the surface itself, and 2) The surface may have a reflective coating, resulting in some of the emitted radiation bouncing back and reaching the emitting surface.

Step-by-step solution

Understand the view factor definition

The view factor (F) is a dimensionless quantity that represents the fraction of energy leaving one surface (A1) that directly reaches another surface (A2). It is denoted by F12, where "1" represents surface 1 (A1) and "2" represents surface 2 (A2). Mathematically, it can be expressed as: F12 = (radiation received by A2 from A1) / (radiation emitted by A1) The view factor helps to simplify and quantify the energy interaction between surfaces in radiation heat transfer calculations.

The reciprocity rule

The reciprocity rule is a principle that is used to find the view factors between surfaces. Given two surfaces A1 and A2, if you exchange their positions, the product of each area and its view factor remains constant, mathematically expressed as: A1 * F12 = A2 * F21 This rule helps to establish relationships between surfaces and simplifies the calculation of view factors in some cases.

Zero view factor and its exceptions

Generally, the view factor from a surface to itself is zero (F11 = 0). This is because a flat or convex surface cannot emit radiation that directly reaches itself. The radiation emitted by the surface reaches another surface or is absorbed by the surroundings. However, there are exceptions: - If the surface is concave or bend inward, like a hemisphere or a parabolic surface, the view factor from the surface to itself can be non-zero. This is because the emitted radiation can be reflected within the surface itself. - If the surface has a reflective coating, some of the emitted radiation can bounce back and reach the emitting surface, resulting in a non-zero view factor.

Conditions for non-zero self-view factor

From the above discussions, we can summarize the conditions for a non-zero view factor from a surface to itself as follows: 1. The surface must be concave or bend inward such that the radiation emitted can be reflected within the surface itself. 2. The surface may have a reflective coating, resulting in some of the emitted radiation bouncing back and reaching the emitting surface. In conclusion, the view factor quantifies the fraction of energy leaving one surface that directly reaches another surface. While it is generally zero when considering a surface's interaction with itself, certain cases such as concave surfaces and reflective coatings can result in a non-zero self-view factor.