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Engineering

Thermal Engineering

Radiation View Factor

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Parallel Disks of Equal Diameter

F_{1-2} = \frac{1}{2} \left(1 - \frac{1}{\sqrt{1 + \left(\frac{2z}{D}\right)^2}}\right)

Brief Explanation: This formula calculates the view factor between two parallel disks of equal diameter when they're separated by a distance

z

. The view factor quantifies the fraction of radiation leaving the first disk that directly strikes the second disk.

Opposed Rectangles with a Common Edge

F_{1-2} = \frac{1}{2\pi} \ln\left(\frac{\left(X_1+X_2+Z\right)\left(Y_1+Y_2+Z\right)}{Z\sqrt{\left(X_1+X_2\right)^2+Z^2}\sqrt{\left(Y_1+Y_2\right)^2+Z^2}}\right)

Brief Explanation: This formula calculates the view factor between two rectangles with a common edge, but are opposed to each other.

X_1, Y_1

and

X_2, Y_2

are the lengths of the sides for the respective rectangles and

Z

is the distance between the rectangles along the common edge.

Two Perpendicular Rectangles with a Common Edge

F_{1-2} = \frac{1}{\pi} \ln\left(\frac{\left(1+\frac{A_1}{X_1}+\frac{A_1}{Y_1}+\frac{A_1}{X_1Y_1}\right)^{1/2}}{\left(1+\frac{A_2}{X_2}+\frac{A_2}{Y_2}+\frac{A_2}{X_2Y_2}\right)^{1/2}}\right)

Brief Explanation: This formula gives the view factor between two perpendicular rectangles sharing a common edge.

A_1

and

A_2

are the areas of the rectangles, and

X

and

Y

are the dimensions of the sides of the rectangles making up the areas.

Perpendicular Planes

F_{1-2} = \frac{1}{\pi} \arctan\left(\frac{A_1}{L^2}\right)

Brief Explanation: This formula is for calculating the view factor from a small area (

A_1

) on one plane to a very large (assumed infinite) perpendicular plane at a distance

L

Disk and Infinite Plane

F_{1-2} = \frac{1}{2} \left(1 - \frac{z}{\sqrt{z^2 + R^2}}\right)

Brief Explanation: This formula calculates the view factor between a circular disk and an infinite plane when the center of the disk is perpendicular to the plane at a distance

z

R

is the radius of the disk.

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