ME 353 Heat Transfer 1

M.M. Yovanovich

VIEW1.MWS

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View Factors

1) Aligned Parallel Rectangles,

2) Coaxial Parallel Disks,

3) Perpendicular Rectangles with a Common Edge.

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> restart:

> #Aligned parallel rectangles.
#See Table 13.2 and Fig. 13.4.

> #X = SideX/Separation, Y = SideY/Separation.

> F12AlignedParallelRectangles:=
2/(Pi*X*Y)*(ln(((1 + X^2)*(1 + Y^2)/
(1 + X^2 + Y^2))^(1/2))
+ X*(1 + Y^2)^(1/2)*arctan(X/sqrt(1 + Y^2))
+ Y*(1 + X^2)^(1/2)*arctan(Y/sqrt(1 + X^2))
- X*arctan(X) - Y*arctan(Y));

> #Check the above expression for X = Y = 1.

> evalf(
subs(
X = 1, Y = 1,
F12AlignedParallelRectangles), 4);

Coaxial Parallel Circular Disks.

> restart:

> #Coaxial Parallel Circular Disks.
#See Table 13.2 and Figure 13.5.

> #R1 = Disk1Radius/Separation,
#R2 = Disk2Radius/Separation.

> F12CoaxialParallelDisks:=

> 1/2*(S - sqrt(S^2 - 4*(R2/R1)^2));

> S:= 1 + (1 + R2^2)/R1^2;

> #Check the above expression for R1 = R2 = 1.

> evalf(
subs(
R1 = 1, R2 = 1, F12CoaxialParallelDisks), 4);

Perpendicular Rectangles with a Common Edge.

> restart:

> #Perpendicular Rectangles with Common Side,
#See Table 13.2 and Figure 13.6.

> #H = Height/CommonSide,
#W = Depth/CommonSide.

> F12PerpendRectangleCommonEdge:= (
1/(Pi*W)*(W*arctan(1/W) + H*arctan(1/H)
- sqrt(H^2 + W^2)*arctan(1/sqrt(H^2 + W^2)) +
(1/4)*ln(((1 + W^2)*(1 + H^2))/(1 + W^2 + H^2)*
((W^2*(1 + W^2 + H^2)/
((1 + W^2)*(W^2 + H^2)))^(W^2)*
((H^2*(1 + H^2 + W^2)/
((1 + H^2)*(H^2 + W^2)))^(H^2))))));

> #Check the above expression for H = W = 1.

> evalf(
subs(H = 1, W = 1,
F12PerpendRectangleCommonEdge), 4);

>