ME 353 Heat Transfer 1

M.M. Yovanovich

VIEW5.MS

View factors for enclosure formed by two coaxial disks and sides.

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The circular disks have radii r1 and r2 where r1 < r2. The distance

between the centroids is denoted as d.

Find the view factors F12, F21, F13, F23 and F33 for the case

r1 = 50 mm, r2 = 100 mm and d = 100 mm.

The view factor for two coaxial disks is known from Table 13.2

of the 4th edition of the text by Incropera and DeWitt.

> restart:

> syspar:= (r1 = 50/1000, r2 = 100/1000, d = 100/1000);

> areas:=
[A1 = Pi*r1^2, A2 = Pi*r2^2,
A3 = Pi*(r1 + r2)*sqrt(d^2 + (r2 - r1)^2)];

Computation of the values of the three areas.

> areavals:= evalf(subs(syspar, areas), 5);

View factor between two coaxial disks. From Table 13.2 of Incropera

and DeWitt.

> Fdiskdisk:= 1/2*(S - sqrt(S^2 - 4*(r2/r1)^2));
S:= 1 + (1 + R2^2)/R1^2;
R1:= r1/d; R2:= r2/d;

View factor algebra for three surface enclosure.

> eq1:= F11 + F12 + F13 = 1;
eq2:= F21 + F22 + F23 = 1;
eq3:= F31 + F32 + F33 = 1;

> F11:= 0; F22:= 0; #View factors for both disks

> #Reciprocity relations

> F21:= A1/A2*F12; F32:= A2/A3*F23; F31:= A1/A3*F13;

Computation of view factors.

> F12:= evalf(subs(syspar, Fdiskdisk), 5);

> F21:= evalf(subs(syspar, areavals, F21), 5);

> F13:= evalf(solve(eq1, F13), 5);

> F23:= evalf(solve(eq2, F23), 5);

> F33:= evalf(subs(areavals, solve(eq3, F33)), 5);

>