Radiation: What is Shape Factor?

Shape Factor Definition

Shape Factor is defined as the fraction of radiative energy that is diffused from one surface element and strikes the other surface element directly with no intervening reflections.

• It is a function of geometry only.
• It is also called view factor or surface factor or configuration factor.

F_1-2 = Q_1-2/Q₁

Where,

F_1-2 = fraction of energy leaving surface 1 and reaching surface 2.

Q₁ = Rate of total energy radiated by surface element ‘1’.

Q_1-2 = Fraction of the rate of energy leaving surface element ‘1’ and reaching surface element ‘2’.

Read More- Surface Tension & Capillary Action

Reciprocity Theorem

• A₁F_1-2 = A₂F_2-1
• It indicates that the net radiant interchange may be evaluated by computing a one-way configuration factor from either surface to the other.

Shape Factor of Some Important Surfaces

• Plane Surface = 0 (F_11­ = 0)
• Convex Surface = 0 (F_11­ = 0)
• Concave Surface ≠ 0 (F₁₁ ≠ 0)

Important Points to Remember

• Shape Factor depends only on the geometry of a body.
• 0 ≤ F_m-n ≤ 1
• When one body is completely enclosed inside the other body, then the shape factor of the inner body to the outer body is equal to 1.
• A₁F_1-2 = A₃F_3-2 + A₄F_4-2 ; if radiating surface A₁ is sub-divided into A₃ and A₄.
• A₁F_1-2 = A₁F_1-3 + A₁F_1-4 ; if receiving surface A₂ is sub-divided into A₃ and A₄.

Read More- Heat and Mass Transfer: Objective Questions with Answers