S~ar Ent, vfy Vol. 25, pp. 471,.473 Pergamon Press Ltd., 19$0. Printed in Great Britain

TECHNICAL NOTE

Effect of combined tilt and end clearance upon natural convection in high LID rectangular honeycomb

P. S. Wut and D. K. EDWARDS School of Engineering and Applied Science, UCLA, Los Angeles, CA 90024, U.S.A.

(Received 2 October 1979; revision accepted 4 March 1980)

INTIODUCTION

Previously, experimental data for a rectangular honeycomb with L/D = 4 and W/L = 2 were reported for tilts up to 30 ° from the horizontal and various top and bottom gaps between the absorber plate and honeycomb core and between the coverglass and honeycomb core[l]. Figure I defines core thickness L, cell width W, and dimension D as well as showing the location of the top and bottom gaps. Tentative conclusions reached previously were that properly-sized honeycombs could be used to damp natural convection (as well as reradiation) heat losses through the coverglasses of solar collectors even when small gaps were present and even when tilted.

More extensive results have now been obtained for tilts up to 90 ° from the horizontal and for honeycombs with L/D =" 5, W/L - ! and L / D - 8, WIL - 0,5 and I. These new results make it possible to draw more general conclusions about the effect of tilt and end clearance on honeycomb performance.

I ~ T S

As before[l] silicone oil was employed as the test fluid in order to study convection in the absence of significant heat radiation. The honeycomb cores were made from polyurethane-varnished paperhoard approx. 0.4 mm thick, and the inside cell dimension D was approx. 5 mm. Exact inside dimensions were as follows:

L D w L/D W/D WlL

18.4 mm 4.7 mm 20.4 mm 4.71 4.34 1.1 ! 36.4 mm 4.6 mm 20.7 mm 7.91 4.50 0.57 36.8 mm 4.6 mm 41.8 mm 8.00 9.09 1.14

Figures 2-4 show the results as Nusselt number Nu vs Ray- leigh number Ra for various tilts ~. Both Nu and Ra are based

tPresently member of the technical staff, Hughes Aircraft Co., Canoga Park, Calif.

upon total length L + ~ + St. They are

_ qL,o,, ~ Z L ~ , Nu-~--~ Ra= av

where q is the average heat flux [W/m2], k is fluid conductivity, AT is temperature difference, g is gravitational acceleration, j9 volume expansion coefficient, a thermal diffusivity and v kine- matic viscosity.

Figure 2 shows the effect of a single gap for LID - 5. In the horizontal position r = 0 °, a 1.5-mm gap has little effect, whether at top or bottom. However, a 3.0-ram top gap caused a 40 per cent increase in convective heat transfer. In the vertical position at ~- = 90 o (recall W is horizontal, D is tilted), a small gap at the heated surface (still called "bottom") or a large gap at either surface permits approx. 30 per cent more convection. The t = 30 ° data are similar to the • = 0 = data, and the 60 ° data are similar to the ~" = 90" data.

The presence of a small gap at the heated surface might be expected to behave like a large gap at the cold surface in oil, because of the significant lowering of viscosity with temperature. Such would not he expected in air.

For the larger L/D cell, the data in Fig. 3 show that a large gap, particularly at the heated bottom plate, acts to damp the con- vection more strongly.

Comparisons of Figs. 2 and 4 for the same L/D cell shows that a gap at each surface leads to greater damping in the vertical position.

CONCLUSIONS

The previous tentative conclusions (1) that a small gap of up to 1.5 mm is not significant, (2) that a single bottom gap is less damaging than a single top gap, and (3) that two gaps (of the sizes considered) are better than one remain in force for mild tilts (~<30°). At ~=90 °, however, a single large gap was found to increase the convection and thus be undesirable. If, for a verti-

Toe V, EW " , Y l l

SIDE VIEW l~ Fig. I, Rectangular honeycomb cell dimensions.

471

472 Technical Note

a

3 - I I I I I I I 1 1 1 1

Nu - - ?-= 0 o

- - 0 GAP " ~Po3 o 1.5 mm TOP

A 1.5 mm BOT. 1

Nu

2

No

2

1

Nu

2

_ 7_-3o o ,~o ~ o

- - A[](~ [] ~ o - - L I D : 4 . 7

W / D : 4 . 3 0 W/L : 1.1

Z [] _ 7"= 600 A q o

-- A o

ZXnO a _ A Oo

o Q

7% 900 A

~A O - A

-

° I° I Ir~l I I I l l l I 10 4 2 4 6 8 10 5

Ra

b I i I I I I l l ] ~ I I - ' T'= 0 o ' Eh~ o( - -

D A o O D Q A A O

o A[]Ao o ONOGAP [] A o o 3.0 mmTOP "~' o A3.0mmBOT. I

nf: b - T : 0o[] - -

A 0 o~ 0 L / D : 4 . 7 --

0 W / D : 4 . 3 0 W / L : 1.1

o

7"= 600

[]

D A

O Q

? ~ - [ ] O - - O~ 0

DA o [3,,,, o A 0

0

m A - T = 900 c A --

__ E ]L~ C

u~ ~ ~oq~O o,> °° - A ~ O 0 0

° ~ t I I I [ I l l l I 10 4 2 4 6 8 10 5

Ra

Fig. 2. Effect of a single small or large gap, L/D = 4.7,

3 - - I I

- - T = 0 ° 2 - -

Nu

,

2

Nu

- - T = 300

_c~ ~ oNO GAP "~ O3 mm TOP

A 3 mm BOT.

a b I n I _ _ I I 7--T--:

- - 7-= 0 o

_ o oc o

o

o O D d S ' A t " -

r-1

[] o NO GAP - n 3 mm TOP A3 mm BOT.

- - T= 600

2 - -

N u ~

1

4

I I

6

o []

0 0 E ~ A A O0~l n

o n A

o°~ A COl A

L / D --7.9 W / D -"4.5 W / L =0.6

^o%S -

• I

- - T = 300

- - _ (

0 %

0 %

- T = 6 0 °

10 5 2 4 6 4

Ra

^oOQ ~ A

o~o,, " L / D = 8 .0

W / D = 9 . 1 W / L - 1.1

o J O Q - -

I ol ° ' ~ z ~ I I

6 10 5 2 4

R a

Fig. 3. Effect of a single large gap, L I D = 8.

Technical Note 473

3

2

Nu

1

2

Nu

1

2

Nu

1

2

Nu

1

a b _ I I I I I 1 I l i k J I _ _ I I' I I I I I I I . L , O l _ - ¢__0 o ~ ~:oo ~ ) z ~ c ~ _ _ o ..,.~_~ ONO GAP

o~r~ ~- o l . 6 m m O3A ONO GAP - - [] o 6 ~ TOP & BOT . . . . o A 3.0 mm r,~o A O 1.5 mm TOP-

[] cc~ ~ 3.0 mm BOT o o~, TOP & BOT. c [ ~ A 3.0 mm TOP

- - ^0. :3 1..~.m m SOl__ - - T--30° ~ T=30° ^ o ° - i -

_ o o _ . , , _ _ , , , , , , - . - 0 0 ~ A W / D =4 .3 W / D : 4 . 3

0 0 A W / L : !.1 A W/L : 1.1 Q [] O

T= 600 o - - C - -

- o %'~ _ oO~ d~

o

T : 900 ~_

0 0 ~ AOAOAA'-

O o 'oAOA A.

o p i o i ~ I I I I I I I

10 4 2 4 6 105 Ra

_ T= 60 o o _ (

.1

e,,o t, ° oa

_ ' r: 9 0 0 _~

o O ~ o 0 -

o o o o [] ~ D ~

o i' ,O,o,o lp i 10 4 2 4 6 105

Ra Fig. 4. Effect of two gaps.

cal.wall winter collector, a gap at one surface is required for thermal expansion or convenience in fabrication, one should attempt to provide a second gap at the other surface.

Acknowledgement--The work reported here was supported by a grant from the National Science Foundation.

REFERENCES !. D. K. Edwards, J. N. Arnold and I. Carton, End clearance

effects on rectangular-honeycomb solar collectors. Solar Energy 18, 253-257 (1976).