ME 353 Heat Transfer 1

M.M. Yovanovich

VIEW2.MWS

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View Factors for Two-Dimensional Geometries.

The view factors F12 are presented in Table 13.1

of Incropera and DeWitt, 4th Edition, 1996.

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1) Parallel Plates w1 and w2 with Midlines

Connected by Perpendicular L.

2) Inclined Parallel Plates of Equal Width W,

Common Edge and Subtended Angle alpha.

3) Perpendicular Plates W1 and W2 with Common Edge.

4) Three-Sided Enclosure with Sides w1, w2 and w3.

5) Parallel Cylinders of radii r1 and r2, and Separation s.

6) Cylinder and Parallel Rectangle.

7) Infinite Plane and Row of Cylinders of Diameter D

and Spacing s.

Examples are presented at the end of the worksheet.

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> restart:

Parallel Plates W1 and W2 with Midlines Connected

by Perpendicular L.

> #W2 => W1, W1 = width1/perpendicular,
#W2 = width2/perpendicular.

> F12_ParallelPlates:=
(((W1 + W2)^2 + 4)^(1/2) -
((W2 - W1)^2 + 4)^(1/2))/(2*W1);

> W1:= w1/L; W2:= w2/L;

Inclined Parallel Plates of Equal Width W, Common Edge

and Subtended Angle alpha.

> #Plates are of equal width;
#alpha is the subtended angle in degrees.

> F12_InclinedPlates:= 1 - sin((alpha/2)*(Pi/180));

Perpendicular Plates w1 and w2 with Common Edge.

> F12_PerpendicularPlates:=
(1 + w2/w1 - sqrt(1 + (w2/w1)^2))/2;

Three-Sided Enclosure with Sides w1, w2 and w3.

> #The lengths of the three sides
#must form a triangle.

> F12_ThreeSidedEnclosure:=
(w1 + w2 - w3)/(2*w1);

Parallel Cylinders of Radii r1 and r2, and Separation s.

> F12_ParallelCylinders:=
1/(2*Pi)*(Pi + sqrt(C^2 - (R + 1)^2) -
sqrt(C^2 - (R - 1)^2) +
(R - 1)*arccos((R/C) - 1/C) -
(R + 1)*arccos((R/C) + 1/C));

> R:= r2/r1; S:= s/r1; C:= 1 + R + S;

Cylinder of Radius r and Parallel Rectangle.

> F12_CylinderParallelRectangle:=
r/(s1 - s2)*(arctan(s1/L) - arctan(s2/L));

>

Infinite Plane and Row of Cylinders of Diameter D and Spacing s.

> #Spacing S => D

> F12_InfinitePlaneRowCylinders:=
1 - sqrt(1 - (D/s)^2) +
(D/s)*arctan(sqrt((s^2 - D^2)/D^2));

Examples of the applications of the above view factors.

> example1:=
(w1 = 1, w2 = 3, L = 1/2);

> F12_ex1:=
evalf(subs(example1, F12_ParallelPlates), 4);

> example2:=
(alpha = 30); #alpha = 30 degrees;

> F12_ex2:=
evalf(subs(example2, F12_InclinedPlates), 4);

> example3:=
(w1 = 1, w2 = 4);

> F12_ex3:=
evalf(
subs(example3, F12_PerpendicularPlates), 4);

> example4:=
(w1 = 1, w2 = 1, w3 = sqrt(2));
#This is a right triangle.

> #The length of the sides must form a triangle.

> F12_ex4:=
evalf(
subs(example4, F12_ThreeSidedEnclosure), 4);

> example5:=
(r1 = 1, r2 = 2, s = 0.25);

> F12_ex5:=
evalf(
subs(example5, F12_ParallelCylinders), 4);

> example6:=
(s1 = 3, s2 = 2, r = 0.5, L = 0.3);
#s1 > s2.

> F12_ex6:=
evalf(
subs(example6, F12_CylinderParallelRectangle), 4);

> example7:=
(D = 0.2, s = 0.3);

> F12_ex7:=
evalf(
subs(example7, F12_InfinitePlaneRowCylinders), 4);

>