Journal of Neuroscience Methods, 40 (199l) 49-62 © 1991 Elsevier Science Publishers B.V. All rights reserved 0165-0270/91/$03.50

49

NSM /)1293

Cooling/heating module for tissue chambers and solutions: theoretical considerations and practical design N . B . D a t y n e r a n d I.S. C o h e n Department of Physiology and Biophysics, Health Sciences Center, SUNY, Stony Brook, NY 11794-8661 (U.S.A.)

(Received 7 March 1991) (Revised version received 22 July 1991 ) (Accepted 23 July 1991)

Key words: Cooling; H e a t i n g ; H e a t pipe; Peltier; H e a t p u m p ; T e m p e r a t u r e c o n t r o l

We provide a theoretical framework for the estimation of the performance of a modular cooling/heating device for tissue baths. The framework can be adapted to other designs using Peltier elements for cooling and heating. The design employs a Peltier as a heat pump and a flat heat pipe to transport heat to or from a 'remote' site. In the cooling mode heat from the hot side of the Peltier is removed by a heat sink cooled by a fan. The small cross section of the heat pipe permits cooling/heating of tissue chambers on microscope stages or in locations where it would be impractical to mount a Peltier element. The faces of the heat pipe can be used to pre-cool/heat solutions using a simple capillary heat exchanger.

Introduction Systems using P e l t i e r e l e m e n t s for h e a t i n g a n d cooling e l e c t r o p h y s i o l o g i c a l c h a m b e r s a r e b o t h d e s c r i b e d in t h e l i t e r a t u r e ( C h a b a l a et al., 1985; C a n n e l l a n d L e d e r e r , 1986; F o r s y t h e a n d Coates, 1988; Lynch et al., 1988) a n d available c o m m e r cially ( M i d l a n d Ross Corp., C a m b r i d g e , M A 02140; M e d i c a l Systems Inc., G r e e n v a l e , N Y 11548). T h e s e systems g e n e r a l l y e m p l o y a w a t e r c o o l e d P e l t i e r e l e m e n t e m b e d d e d in or a d j a c e n t to an e l e c t r o p h y s i o l o g y c h a m b e r . T h e a d v a n t a g e of this a r r a n g e m e n t is t h a t the P e l t i e r e l e m e n t is efficiently c o u p l e d t h e r m a l l y to t h e c h a m b e r o r solutions. H o w e v e r , to b e i n c o r p o r a t e d in o r on t o p of t h e m i c r o s c o p e stage, P e l t i e r e l e m e n t s usually have to be small, r e q u i r e careful s h i e l d i n g

Correspondence: N.B. Datyner, Dept. of Physiology and Biophysics, Health Sciences Center, SUNY at Stony Brook, Stony Brook, NY 11794-8661, U.S.A. Tel.: (516)-444-3613; Fax: (516)-444-3432.

to m i n i m i z e e l e c t r i c a l i n t e r f e r e n c e a n d typically n e e d a fluid-filled j a c k e t a n d c i r c u l a t o r to m a i n tain the n o n - c h a m b e r side of the e l e m e n t n e a r room temperature. Furthermore, condensate forming around the Peltier element necessitates t h a t the e l e m e n t be carefully i n s u l a t e d f r o m the tissue c h a m b e r . D e s c r i b e d b e l o w is a c o o l i n g / h e a t i n g device (Fig. 1) which e l i m i n a t e s m a n y o f t h e s e p r o b l e m s . A l t h o u g h p r i m a r i l y i n t e n d e d for cooling, o u r device is also s u i t a b l e for h e a t i n g by r e v e r s i n g the p o l a r i t y of the v o l t a g e a p p l i e d to the P e l t i e r element. O u r e m p h a s i s on cooling reflects the fact t h a t P e l t i e r e l e m e n t s are u n i q u e l y s u i t e d to cooling a p p l i c a t i o n s . In o u r design the P e l t i e r elem e n t is not a d j a c e n t to the tissue c h a m b e r b u t is c o n n e c t e d to it via a h e a t pipe. T h e h e a t p i p e t r a n s p o r t s h e a t b e t w e e n the tissue c h a m b e r a n d P e l t i e r e l e m e n t . By l o c a t i n g the P e l t i e r e l e m e n t at a d i s t a n c e from t h e tissue c h a m b e r it is possible to use larger, m o r e efficient P e l t i e r e l e m e n t s a t t a c h e d to a i r - c o o l e d h e a t sinks. This e l i m i n a t e s the n e e d for c i r c u l a t i n g fluid a n d a s s o c i a t e d

50

pumps and plumbing. Furthermore, since the fan can be separated from the cooler assembly, problems caused by vibration are eliminated. For a simplest arrangement the tissue chamber can be placed on an aluminium or copper plate attached to the end of the heat pipe. For pre-cooling/ heating solutions a simple capillary heat exchanger is placed on the face of the heat pipe with the outlet positioned close to the inlet to the tissue bath. In the first part of the paper, the theoretical section, we consider and define the elements of a typical modular cooling/heating system. We then provide the equations necessary for a computer model of the system and test the model by comparing its predictions with the measured performance of the several c o o l e r / h e a t e r modules. The model not only allows one to verify the suitability of a particular Peltier element or elements for a particular c o o l e r / h e a t e r design but also allows an assessment of the relative importance of the components making up the design. We believe this rational approach to designs using Peltier elements can lead to the construction of individualized cooling/heating systems for electrophysiological needs with substantially improved performance.

~smt~

Fig. 1. Cooler module construction. Cross-section through cooler assembly illustrating the assembly of the fan, heat sink, Peltier element, heat pipe and insulation.

Theoretical estimates of performance

A. Determinants of cooler / heater performance and parameter measurements for computer model In this theoretical section we consider the elements making up the c o o l e r / h e a t e r module. Fig. 2 is a thermal schematic of the physical elements which make up the c o o l e r / h e a t e r module and the thermal resistances used in the analysis in section B. Cooling versus heating. Although the Peltier element is particularly suited for cooling, it is inherently a bidirectional heat pump. It is important to realize that in the c o o l e r / h e a t e r module the thermal resistances on either side of the Peltier element are quite different; On the heat sink side there is a low thermal resistance (typically < 0.5 ° C / W ) while on the heat pipe side the thermal resistance is typically an order of magnitude greater. For cooling, the input power to the Peltier element flows to the heat sink (via the hot side of the element), as does any heat extracted from the heat pipe. For heating, both the input power and additional heat extracted from the heat sink flow to the heat pipe. Thus it takes much less power to heat since the Peltier is always operating at more than 100% efficiency. When cooling, the efficiency is typically less than 30%. Because the c o o l e r / h e a t e r module design is more critical for cooling, the following section is primarily concerned with cooling. The Peltier element. The basic consideration for choosing one or several Peltier elements is the power that must be transported. However, convective cooling of the hot side of the Peltier element via a heat sink (rather than a water jacket) limits the maximum power that can be dissipated before degrading the performance of the Peltier. For example, a 10 ° C increase in the heat sink temperature will be reflected in an approximately 10 °C increase in Tc (the temperat u r e of the cold face of the Peltier element) as well as a similar increase in the temperature of the load. To avoid using an excessively large heat sink, Peltier element or elements with power transporting capabilities matching those required

51 should be selected rather than elements which are able to transport more power. If o n e r e s t r i c t s t h e r a n g e o f P e l t i e r e l e m e n t s t o t h o s e o p e r a t i n g a t a c o n v e n i e n t v o l t a g e (e.g., 12 V ) t h e n t h e c h o i c e is c o n f i n e d t o s e l e c t i n g t h e m a x i m u m P e l t i e r c u r r e n t (/max), t h e a r e a o f t h e element and the number of elements. Although t h e a m o u n t o f p o w e r t r a n s p o r t e d , Qc, i n c r e a s e s m o n o t o n i c a l l y w i t h Ip ( t h e P e l t i e r c u r r e n t ) , t h e

HeatsmkJfan

e f f i c i e n c y o f p o w e r t r a n s p o r t (Qc" l O 0 / V e ' I p " n) i n c r e a s e s a n d t h e n d e c l i n e s a t h i g h e r Ies ( a t f i x e d T h - T o , t y p i c a l l y 40 ° C). T h e r e f o r e , t o a c h i e v e both satisfactory efficiency and sufficient power t r a n s p o r t I e s h o u l d fall in t h e r a n g e o f 5 0 - 7 0 % o f lm, x. I n c r e a s i n g t h e a r e a o f t h e e l e m e n t reduces the thermal resistance of the contact region on either side of the Peltier element thereby yielding better performance. Whether to use a

Heatl~pe

P~er element

~,

Load

m

~'

,, " "

0hs-P ~p

~)P-h~

/~g~---.---

Th

Qc*VpIp

0exit011)~enl~ OhlP4oad 0k)adTamb

Tc Qc Ihp~0~-m

T~d Q~d

'lp F3 Pettier ekmmt 1 Qc2÷Vp2.1p2 ÷Vpl.Ip1 4--

,/

,. ,, IU ¢2,VP2.1P2j

PetUer element 2 OP1.P2 ,~ I~c2 ~--

ThtI "T',T ITcl Th2L~..Tc2 - VPl" IP1

VP2'tP2

C Q=

Tc -"' Th

L~V~p.Ip

Fig. 2. Thermal resistances for computer model. A: thermal resistances corresponding to the physical elements making up the cooler. The thermal resistances are shown below the physical device. The Peltier element removes heat Qc from the right-hand thermal circuit and passes Qc + Vp - Ip to the left-hand thermal circuit. The thermal resistances are defined in the Glossary. B: modification to accommodate Peltier elements cascaded thermally. The cascaded Peltier elements are substituted for the single element shown in panel A. Qc2 is transported by Peltier element 2 and passed along with Vpz. Ip2 through the thermal resistance between the 2 elements (6~p~_p2). Peltier element 1 passes power Qcz + VP2 IP2 + vel • Ipl to the left-hand thermal circuit. The computer model equations for Peltier element 2 are analogous to the case for a single Peltier element (Vp is replaced by Vp2, 1 by 12 and TdeI by Tdcl2= Th2 - Tc2). For Peltier element 1, the equation for Peltier voltage, Vp1, has the same form as Eqn. (1). In the case of cooling, the power produced by the Peltier element (i.e., Vpl. IP1) is added to Qc2 + Vpe'IP2. The temperatures Td and Th2 a r e related by Tc~ = Th2 + Vp2 • Ip2 " O P 1 - P 2 where O p l _ p 2 is the thermal resistance of the junction between the 2 elements. The thermal resistance of this junction is similar to those between the heat sink and Peltier element (6)h~_P) since the areas involved are the same. For heating the modifications to the equations are similar to the case of cooling. C: adaption for heating. Consider Peltier element physically repositioned with the cold face adjacent to the heat sink and the hot face adjacent to the heat pipe. In practice the voltage polarity applied to the Peltier element is reversed. This causes heat, Qc, to be pumped from the heat sink to the load. The thermal circuit section shown in this panel would be substituted for the Peltier element in panel A.

52 single or multiple elements depends on whether enough power can be transported with a single element. In general, if the input power is held constant, better performance will be achieved with a single element since two elements at reduced Ies will operate at a lower efficiency than a single element. In general improved performance with the increased contact area does not compensate for this reduced efficiency. The solution to the equations given in section B allows one to accurately compare the performance of different combinations of Peltier elements.

Model parameters Heat sink and fan (O)hs).

The measured thermal resistance range for Oh~ is 0.330 . 4 0 ° C / W (data Table III, Ohs = [ T h s - Tamb]/ [ V p ' l e + Qc]). Heat sink web (O~eb). The thermal resistance from the Peltier hot surface to the heat sink outer surface (Oweb + Ohs_p) ranged from 0.31 to 0.37 ° C / W (data Table III; /gweb + Ohs_ P = (T h - Th~)/(V P "Ip + Qc) for our design). Using the average value for Ohm_P (0.145 ° C / W ; see below), the thermal resistance of the web alone, /gweb, is approximately 0.165-0.225 ° C / W .

Junction heat sink-Peltier, Peltier-heat pipe (6)hs_ e and 6)e_hp). For the 12 V Peltier element (area 8.83 cm 2) manufacturer's data for thermal grease junctions (0.97-1.6 ° C / W for 1 cm 2) gives a value of 0,145° C / W for ~ge_h0 and @~-e (IERC data). Heat pipe entry/exit (~hpe = Oentry = ~)exi, )" Under conditions where 10 W was transported through the heat pipe, we measured the temperature difference across the heat p i p e / a l u m i n i u m spreader region. From these measurements Oh~ = 0.5 o C / W . Heat pipe (Ohp). With experimental conditions identical to those used to measure ~ghp~ we estimated 19hp = 0 . 3 ° C / W by measuring the temperature difference along the length of the heat pipe. Junction heat pipe-load (~ghp_loaa). The estimate ~ghp_load of 0.17 ° C / W used in the model was derived in the same manner as ~ghs_P using the contact area of 6 cmz between the heat pipe

and edge of the 6 cm × 6 cm aluminium plate used for testing the c o o l e r / h e a t e r module performance.

B. Computer model for predicting perJbrmance of cooler / heater A major difficulty developing c o o l e r / h e a t e r systems using Peltier elements is accurately predicting the performance of a completed system. Most manufacturers provide various performance plots for Peltier elements and usually describe simple procedures for deciding whether a given Peltier element or elements are able to transport the power required for a given cold side temperature. Some treatments describe the performance of the Peltier element in detail (CAMBION, 1972) but the integration of this information with the practical constraints involved in a given application is left to the investigator. Our computer model links the manufacturer's data for the performance of the Peltier element with the thermal circuit for our c o o l e r / h e a t e r module, thereby allowing us to predict the behavior of similar c o o l e r / h e a t e r modules using different heat sinks, numbers of Peltier elements, etc. With suitably characterized thermal circuits the same approach can be applied more generally. For our Peltier element model we converted the Universal Performance graphs for Peltier elements made by M E L C O R (MELCOR, 1985) into 2 equations (Eqns. 1 and 2 below). The equations assume that the Peltier element(s) are in parallel thermally. Fig. 2B and the legend describe the modifications for elements arranged in series thermally (i.e., cascaded).

Peltier element model equations V e = ( ( a l - I 2 + a 2 . I + a3)-Tae, + a 4 . I . Z A c ) . N

(1) where a~ = - 1.6 × 10 -7 a 2 = 5.48 × 10 -~ a 3 = 2.08 × 10 -4 a 4 = 0.00256 Vp= voltage across Peltier element

l = Ip/lma x • 50

53

I /max

le Tde I = T h

= normalized Peltier element current = max current for Peltier element = current through Peltier element

-L

= temperature across Peltier element = temperature of hot side of Peltier element = temperature of cold side of Peltier L element IAc = 1 + 0.06" ( T h - 50)/15 IAc = temperature dependence of voltage Td~l Th

VS. Tde 1

N

"12 + b 2

" I + b3)"

Sc

"(Td~ I + T~)

+(b4"Ia+bs'I+b6)'Ac)'G'N'n

Thermal load and heat sink equations To account for the thermal load and the heat sink on either side of the Peltier element there are 2 additional equations given below. On the load side:

= number of couples

Qc = ((b,

When the element is used for heating, the polarity of the voltage applied to the element is reversed. Alternatively, since the Peltier element is a symmetrical device, one could imagine that for heating the element is physically turned around and the polarity of the applied voltage is left unaltered. Thus for heating, the Peltier element would be as in Fig. 2C. Substituting this for the element in Fig. 2A leads to the equations for heating given below.

(2)

where

r c = ramb -- Qc "Oeff

(3A)

'load' line for cooling b I = 6.1 × 10 b 3 = - 0.0265 b 5 = 0.132

6

b 2 = -8.073 × b4=

10 - 4

0.00256

b6 = -0.05

Qc = heat removed by the cold face of Peltier element T~ = temperature error correction ( 1 0 ° C for cooling, 0 ° C for heating) Sc = 1 + 0.02. (T h - 50)/15 is the temperature dependence of amplitude of Q~

T h = Tam b +

Given a particular T h, TdeI and Vp Eqns. 1 and 2 can be solved to give an operating current I and Q~. We found it necessary when using the equations to describe cooling to add the correction term Te to obtain results for Q~ that were consistent with experimental data. Without this correction term the equations faithfully represent the manufacturer's data except at very small Peltier currents ( < 10% of /max)" The correction term is equivalent to the Peltier element transporting 15% less power at the maximum TaeI (approximately 70 ° C) than is represented by the Universal Performance data. Part of Te may be due to inaccuracies in our measurement of T h.

(3B)

' l o a d ' line for heating where Tamb= ambient temperature Ocff=effective thermal load attached Peltier Vp, I p , Q c , Th, Zc are defined above

to

Oeff = {~P-hp q- •hpe + O h p / 2 + Ohp-amb

(OhP/2 + Ohpe+ OhP-l°ad+ Ol°ad)

VS. Tde t

Ac = 1 + 0.08- (T h - 50)/15 is the temperature dependence of slope Qc vs. Td~1 G = geometry factor n = number of Peltier elements

(Q~ + V p ' l p ) ' O e f f

(3C)

O hp-amb @ O h p / 2 + Ohp ~ + O hp-load + (~)load

where thermal resistance of junction between the face of Peltier and heat pipe Ohp e = thermal resistance for heat enteri n g / exiting heat pipe thermal resistance along heat pipe (~hp = length hp amb = thermal resistance from heat pipe surface to ambient thermal resistance of junction be0 hp- load = tween heat pipe and load 0load = thermal resistance of load On the heat sink side: Op

hp

Th = Tamb + ( O h s + Oweb + O h s - P ) " ( Qc + Vp -Ip) for cooling (4A) rc = ramb -- (Ohs -I- Oweb q- Ohs e ) Q c for heating

(4B)

54

where Ohs

= thermal resistance of heat sink with fan 6~web = thermal resistance of heat sink web Ohs_p = thermal resistance of the junction from heat sink to Peltier Vp, Ip, Q~, Th, T~ are defined above Eqns. 3A, B describe the 'load' lines for cooling and heating (see Fig. 3B) for the effective thermal load (Eqn. 3C) attached to the Peltier element. This effective thermal load accounts for all the thermal resistances to the right of the Peltier element (Fig. 2A). Eqns. 4A,B describe the thermal path from the left side of the Peltier through the heat sink to the ambient for cooling and heating, respectively. All the thermal resistances were obtained experimentally or from manufacturer's data as described in section A. We used the program MATHCAD (Version 2.0) to solve Eqns. 1-4 to determine a unique operating point for a particular c o o l e r / h e a t e r

module-thermal load configuration given a Peltier voltage Vp. Below we use the model to examine the performance of a c o o l e r / h e a t e r module using different combinations of Peltier elements.

Three 2 V vs. single 12 V Peltier element: matched power transport In this case we compare the performance of several low-voltage/high-current Peltier elements with that of a single 12 V/low-current element. By using several lower voltage elements we increase the area through which power is passed to the heat sink. The reduced temperature gradient across the Peltier elements should yield an improvement in performance. To test any improvement in performance we constructed a c o o l e r / h e a t e r using three 2 V Peltier elements (Model 801-1007-01-00-00, Midland Ross Corp., Cambridge, MA 02140) in series electrically and

TABLE I C O M P A R I S O N O F TWO C O O L E R ASSEMBLIES An aluminium plate was attached to the heat pipe as described in the text. Two c o o l e r / h e a t e r modules were tested, one with the single 12-V Peltier element and a second with three 2-V elements connected electrically in series. The voltage Vp is across an individual Peltier element while Iv is the current through an element. Vp was varied in each case to cover the range of Iv from approximately 0.4/max to 0.8 /max and the power applied to the Peltier approximately matched for the two configurations (refer to column V p . I v . n). Tioad, the temperature of the load, was measured using a YSI-511 thermistor probe placed on the aluminium plate adjacent to where the heat pipe was clamped to the plate. Ths was measured by placing the thermistor probe on the web of the heat sink over the area above the Peltier element(s). T h and Qc are estimated from the model. Square brackets denote model estimates. The parameters for the model are: both configurations: O h s = 0 . 3 5 ° C / W / O e n t r y and O e x i t = 0 . 5 o C / W , Ohp_amb = 1 5 ° C / W , O h p = 0 . 3 5 ° C / W , 0 . 1 7 ° C / W , Oioad = 1 7 ° C / W , T¢ = 10°C, Tamb = 2 5 ° C single 12-V: Oweb + ~ghs-P = 0-34 ° C / W , ~gp-hp = 0.145 ° C / W , /max = 3.9A, G = 0.078, N = 127, n = 1 three 2-V in series: Oweb + ~ghs_P = 0.20 ° C / W , ~gp_hp = .084 ° C / W , Im~x = 9A, G = 0.18, N = 17, n = 3

Ohp_load =

The thermal resistance for the aluminium plate, Oio~a, was found using the method described in Fig. 3C. Ohp-amb was selected by comparing the temperature of the heat pipe predicted by the model (with ~load = 5000 ° C / W to simulate the absence of a load attached to the heat pipe) with experimental measurements made prior to the aluminium plate being attached to the heat pipe. For the experimental measurements Tamb = 24.6 ° C.

Single 12-V

Three 2-V in series

Vp (V)

1p (A)

lip. Ip .n (W)

7.24 10.5 13.2

1.6 [1.6] 2.3 [2.3] 2.9 [2.8]

11.6 24.2 38.3

0.96 1.35 1.74

4.0 [3.7] 6.0 [5.1] 7.5 [6.6]

11.5 24.3 39.2

Tload ( o C)

Th ( o C)

Ths ( o C)

Qc

[4.2] [1.5] [2.1]

[34.7] [43.4] [52.6]

29.0 [29.9] 33.6 [34.3] 39.2 [39.0]

[2.6] [3.0] [2.9]

1.7 [3.1] 0.0 [ - 0 . 5 ] < 0.0 [ - 1.3]

[32.3] [38.3] [45.9]

31.5 [29.7] 32.3 [33.5] 38.7 [38.3]

[2.8] [3.3] [3.4]

5,4 1,5 1,7

(W)

55 parallel thermally. The power transporting capabilities of the 3 elements matched that of the single e l e m e n t u s e d in t h e 12 V d e s i g n . E x p e r i m e n t a l d a t a for t h e t e m p e r a t u r e o f t h e c o o l e d p l a t e a l o n g w i t h t h e m o d e l p r e d i c t i o n s is g i v e n for 3 d i f f e r e n t p o w e r i n p u t s g i v e n in T a b l e I (Vp. I p . n was k e p t t h e s a m e for t h e 2 a s s e m blies). T h e p e r f o r m a n c e o f t h e t h r e e 2 V P e l t i e r e l e m e n t c o o l e r a s s e m b l y is s u p e r i o r to t h a t o f t h e s i n g l e 12 V e l e m e n t a s s e m b l y . T h e m o d e l r e s u l t s g i v e n in T a b l e I d e m o n s t r a t e t h a t this is expected. The model calculations suggest that there is a 2 . 4 - 6 . 7 ° C r e d u c t i o n in T h b r o u g h t a b o u t by the increased contact area of the 3 Peltier elements.

p o w e r t r a n s p o r t is d o u b l e d t h e r e d u c e d e f f i c i e n c y (column marked 'eft') of the pair of elements o p e r a t i n g at a l o w e r v o l t a g e n e g a t e s any b e n e f i t o f this i n c r e a s e d a r e a .

Single 12 V Peltier element vs. two 12 V Peltier elements

Construction

W h i l e in t h e e x a m p l e a b o v e t h e p e r f o r m a n c e o f m u l t i p l e l o w - v o l t a g e P e l t i e r e l e m e n t s is s u p e r i o r to t h a t o f a s i n g l e 12 V e l e m e n t , t h e m o d e l c a n b e u s e d to s h o w t h a t this will n o t b e t h e c a s e for a p a i r o f 12 V e l e m e n t s . T h e r e s u l t s in T a b l e II d e m o n s t r a t e t h a t t h o u g h t h e s u r f a c e a r e a for

The cooler/heater m o d u l e a s s e m b l y is c o m posed of 4 elements: the heat pipe (Model Q W 1 0 R - 0 9 5 M - 1 1 0 , N o r e n P r o d u c t s Inc., M e n l o P a r k , C A 94025), a 12 V P e l t i e r e l e m e n t ( M o d e l CP1.0-127-05L, Melcor Electronic Products C o r p . , T r e n t o n , N J 08648), h e a t sink ( M o d e l 421,

Natural convection T o e x a m i n e w h e t h e r o p e r a t i o n w i t h o u t a fan is p o s s i b l e w e u s e d t h e s a m e O~o~O a n d t h e m a n u f a c t u r e r ' s v a l u e o f Oh~ for n a t u r a l c o n v e c t i o n for t h e M o d e l 421 h e a t sink. T h e r e s u l t s s h o w n in T a b l e II ( f o r c e d c o n v e n t i o n , n = 1 vs. n a t u r a l c o n v e c t i o n , n = 1) i n d i c a t e that, u n l e s s o n l y limi t e d c o o l i n g is r e q u i r e d , n a t u r a l c o n v e c t i o n is i n a d e q u a t e for c o o l i n g t h e h e a t sink.

TABLE lI MODEL COMPARISON OF A SINGLE 12-V VERSUS TWO 12-V PELTIER ELEMENTS Comparison of temperature of the cold side of the Peltier, Tc for coolers using either one (n = 1) or two (n = 2) 12-V Peltier elements using forced convection (i.e., with fan). The total input power was kept the same for the comparisons. The efficiency (Qc/Vp.Ip. n) is shown in the column marked 'eft'. The parameters for the model are: for all cases: Ocm~y and [~exit = 0 " 5 ° C / / w , O hp . . . . b = 15 ° C / W , T¢ = 10 o C, Tdmb = 25.0 ° C, lma,, = 3.9 A, G = 0.078, N = 127

O hp =

0.35 o C/W,

O hp_load =

0.17 ° C/W, O io,d = 17°C/W,

forced convection: Oh~ = 0.35 ° C / W n = 1: ~)web -{- O h s - P = 0.34 ° C/W, ( ~ P - h p = 0.145 o C / W n = 2: Oweb + Ohs_ P = 0.17 ° C/W, Op_hp = 0.0725 o C / W natural convection: O h~ = 1.23 ° C/W, (EG & G Wakefield data) n = 1: Oweb+ Oh~-e = 0.34 ° C/W, Oe_hp = 0.145 ° C / W The natural convection columns demonstrate the significantly reduced performance of the cooler when the fan is not used. The Peltier voltages (Vp) are higher than for the forced convection case due to the substantial increase in T h. Vp ' I p • n

(W)

13.9 26.0 36.0

Forced convection n= 1

Natural convection n= 1

n=2

TLo.a ( ° c)

Vp (v)

eft (%)

Tlo.a ( ° c)

Vp (v)

eff (%)

Tioaa

Vp

eff

Th

( ° c)

(v)

(%)

( ° c)

3.2 1.5 2.0

8.0 11.0 13.0

20 12 8

6.2 3.5 3.1

5.71 7.86 9.31

17 11 8

10.7 13.0 16.5

8.3 11.6 13.9

13 5 2

49.7 67.8 82.6

56

A l R i l l mlmm

t

B lO 9 8

2' P'

7 8.

a-ta e ~ - e

./

5, 4. 3, 2

.,oT,:'L:...-.:

I. 0 -15

I -10

-5

5

o

1

I ¸'20 25

15

Tc(°C)

.-Io

C

Qto,d = Qc6)hp-~imb / ( 6), + Ohp .... h) Tk,.a = Z,m,b

25

Ql,,~d" 6) to~,d

where O~ = 6 ) h p / 2 + 6)¢mry + (")hp-lo,d + 6)lo,a (See Section B. Eqn. 3C for definition of terms.) For heating these equatkms are, respectively:

~Tplat,a,eplate)

eload

(°c,~)

cold face of the Peltier element, Tc, recorded (Table II1). The solid line is the regression line (T~ + 10.8 = 2.49-Q,.) for the 3 experimental points (filled circles). For experimental measurements T a m b = 2 3 ° C , V v = t/).52 V and t v = 2 . 3 A. The exact test voltage is not critical as the cooler performance is relatively insensitive to changes in Vp over the range 10.5- 13.5 V (see Table I), The dashed line is computed from the computer model (Section B) used to predict the cooler performance (parameters: T,amb = 2 3 ° C , Ohs = 0.35° C / W , Oh~ v + O)*~b = 0 . 3 4 ° C / W , 6)hp-amb = 5 0 0 0 ° C / W , (')J,,,,d = 5 0 0 0 ° C / W , 7~. = 1 0 ° C , Vp = 10.5 V, G = 0.(t78, N = 127). 6)hp-amb and 6)load w e r e set to large values to simulate the absence of the heat pipe and thermal load. 6)~,t,-y, 6)~xit, Ohp and 6)hp-Joad cab have any value. The dotted line is the 'load' line for 6)eff = 9 . 0 ' ~ C / W (see Eqns. 3A, 3C, Section B) the effective thermal resistance for the heat p i p e / p l a t e used to cool a 30-ram plastic culture dish. C: plot illustrating the temperature of the thermal load for cooling. T~,,,,d, for different thermal loads; 6)load, based on the data of panel B. The plot is derived by varying @toad over a range ( 0 . 5 ° C / W to 30 o C / W in this case) and solving the regression line in panel A (i.e., T¢ + 10.8,= 2.49.Qc) with the 'load' line T~ = ]~,mb Q~'6)eff (see Section B, Eqn. 3C; ¢3e0. is the effective thermal load attached to the Peltier element) for a set of operating points T~, Q~. Tload for each operating point is calculated from the following equations.

15 Qload = (Qc + V p ' l p ' n ) ' 6 ) p - a m b / ( 6 ) l + O h p . . . . b )

lo

TIo,d = T~n,t,+ Qloaci" 6)load

5. o

0

5

tO

15

~-0

Tload(°C)

Fig. 3. C o o l e r / h e a t e r module performance for cooling. A: the heat pipe and clamping apparatus were removed to expose the cold face of the Peltier element. A copper plate (0.9-mm thick) with a groove machined in it for a thermistor probe (YSI-511, Yellow Springs Instruments, Yellow Springs, O H 45387) was then ' b o n d e d ' to this cold face with thermal grease and finally a thin foil heater (Part: HK5303R9.9L12A Mince Products Inc., Minneapolis, M N 55432) held again with thermal grease attached to the copper plate. A block of styrofoam insulated the assembly. The groove in the copper plate permitted accurate m e a s u r e m e n t s of the temperature of the cold face of the Peltier element to be made. B: plot of heat transported, Q~, versus the cold face temperature of the Peltier element, T c. Power, Qc, was applied to the Peltier using the foil heater (see panel A) and the temperature of the

The point T01~te, 6)plate corresponds to the 6 cm x 6 cm a!uminium plate used tO cool the 30 m m plastic culture dish. In this case the thermal load 6)plate ( = t 7 ° C / W ) was determined experimentally as described below. In general, for thermal loads where the :internal temperature gradients are small, the load can be treated as a lumped system and the thermal resistance 6)~oad estimated by heating the load to a temperature T i and recording the temperature of the load as it cools to ambient temperature (T, mb). For a lumped load the temperature decay is exponential. Plotting - l n ( T - T a m h / (T i - T a m b) versus time gives a time constant ?lo~d- Since ~'~,,~d= 6)]o,a'P'C'V where p = density of load material, c = heat capacity of load material and V = volume of load, an estimate can be obtained for 6)~oad" In the case of the 6 em x 6 cm aluminium plate a foil heater (similar to that in Fig. 3A) was used to heat the plate to 53 ° C (T i) and the temperature recorded as it fell to room temperature (24.2 ° C). The plot of - l n ( T - Z , m b / ( T i - Tamb) yielded a time constant ~'pt,t~ = 244 s . p . c . V for the plate was 14.4 J t K - 1 hence 6)plat~., = 17 o C / W .

57

E G & G Wakefield Engineering, Wakefield, MA 01880) and fan (No. 3012, Circuit Specialists, Scottsdale, A Z 85271-3047). Fig. 1 illustrates details of the assembly. Prior to assembly the edge of the Peltier element should be sealed with a thin layer of silicon glue to prevent condensation forming between the faces of the element. A thermal spreader (in our case an aluminium plate 3 c m × 3 c m × 1 . 7 mm) should be glued with thermally conducting epoxy (Part 33HS001, Mouser Electronics, Mansfield, T X 76063) to the end of the heat pipe to be placed against the Peltier element. This reduces the thermal resistance between the heat pipe and Peltier element surface and maintains a constant temperature across the face of the element. If the heat pipe is in contact with only a fraction of the Peltier surface, heat is effectively transported across only the region of contact because the thermal conductivity of the ceramic surface of the Peltier is low (typically < 2% that of aluminium). Thin layers of thermal grease ( < 0.075 mm thick) should be applied between the Peltier element and heat sink as well as the element and thermal spreader. In our basic design the assembly is held together with a piece of 1-cm thick TABLE II1 P E R F O R M A N C E DATA FOR PELTIER WITH APPLIED T H E R M A L LOAD A foil heater was used to apply power, Qc to the cold side of the Peltier. The temperature of the cold side of the Peltier, T~ was recorded for two different power inputs. The temperature of the hot side of the Peltier, T h, and the temperature of the heat sink, Th~ can be used to estimate the thermal resistance of the web of the heat sink as well as that of t h e h e a t sink. T,~ was monitored using a YSI-511 thermistor probe held in place with a dot of thermal grease. The probe was located directly above the hot face of the Peltier element of the heat sink. T h was measured with a thermistor placed in the lower corner of a 0.5-cm diameter hole drilled through the heat sink. The thermistor was coated in each case with a layer of thermally conducting grease. The Peltier voltage Vp = 10.5 V and Current Ip = 2.3 A. Qc

Tc

Th

Ths

(W)

( o C)

( ° C)

( ° C)

(1 4.8 10.(1

- 10.1 - 0.3 14.4

41.8 43.0 45.6

32.9 33.4 34.9

plexiglass attached with bolts screwed into 4 holes tapped in the web of the heat sink. A layer of styrofoam, cut to fit snugly in the heat sink web, separates the heat pipe and plexiglass. When the 4 bolts are tightened, compression of the styrofoam around the heat pipe and spreader provides mechanical support. The edges of the Peltier element are insulated with thin pieces of styrofoam. The fan can be attached to the heat sink by 4 bolts slotted into grooves cut into the edge of the heat sink. Tape or thin pieces of plexiglass attached at the heat pipe end of the heat sink prevent warm air blowing onto the heat pipe. The exposed heat pipe can be insulated with styrofoam or bubble plastic to prevent condensation.

Results

I. Performance of Peltier element/heat sink for cooling To provide a fundamental measure of the Peltier e l e m e n t / h e a t sink combination, its performance was first defined at a voltage that yielded optimum power transport. To simulate a thermal load a foil heater was attached to the cold face of the Peltier element and power applied to the heater (Fig. 3A). Since the foil is ' b o n d e d ' to the cold side of the Peltier element with thermal grease and insulated with a layer of styrofoam on the air side, practically all the power produced by the foil heater is transported across the Peltier element (at T~. = - 10 ° C we estimate the heat gained from the air side to be < 0.25 W). We have therefore ignored heat gains from the air side of the foil heater and taken the power applied to the heater to be identical to the power transported by'the Peltier element, Qc. The relationship between the temperature of the cold side of the Peltier element, To, and the power transported by it at that temperature, Qc, is shown in Fig. 3B (complete experimental data is given in Table III). The relationship was found to be approximately linear. The solid line in Fig. 3B is the regression line for the 3 measurements. With a thermal load attached to the cold face of the Peltier element the element will operate at one of

58

the combinations of (Qc, T~) on this line. For a simple thermal load such as the heat p i p e / aluminium plate described below, the operating point is determined by the intersection of this line with the 'load' line for the thermal load (dotted line in Fig. 3B). The 'load' line expresses the relationship between power gained (or lost) by the thermal load and the increase (or decrease) in the temperature of the thermal load relative to ambient. In this case the 'load' line for the heat p i p e / a l u m i n i u m plate is simply a straight line with a slope of 9 ° C / W , its thermal resistance (the thermal resistance, fgeff, can be estimated using Eqn. 3C, section B above). The dashed line is the performance of the c o o l e r / heater module predicted by the theoretical model;

A

there is good agreement with the experimental data.

II. Applications of cooler/heater module (a) Cooling tissue chambers To cool a 30-mm plastic culture dish we mounted it onto a 6 cm × 6 cm plate of aluminium (1.7 mm thick) with a center hole 1.7 cm in diameter. The aluminium plate was clamped to the heat pipe along one edge with a thin layer of thermal grease in the joint. This simple arrangement could be used to cool solution in the culture dish to approximately 9 ° C . The average plate temperature in this case was approximately 3 °C while the heat pipe temperature was 0 o C. For plates or chambers with different thermal resistances to this particular plate, the plot in Fig. 3C can be used to estimate the temperature of the chamber or plate. The method for estimating thermal resistance (6)to~d) of a thermal load is described in the legend of Fig. 3C. The plot is

A

I0, 85-

r(°c)

420-2-

-6

1

2 rlo,,,.~t.,, (mV.~,~l

C

1.0

4-

•

•

0.9 0.8

3-

~

.

0

"

0.7 0.8

q 2-

I--g

0.5

q'/Qe

0.4

0-----0

0.3 t-

0.2 0.1

l

o,"

i

1

I

]

2 3 Flowrate (ml/min)

0.0

Fig. 4. Test of capillary heat exchanger with cooler/heater module. A: for the capillary heat exchanger a glass capillary was placed along the heat pipe and covered with an aluminium strip with a v-shaped groove machined in it (see inset). Contacting surfaces were coated with thermal grease. To regulate the outflow temperature a heater was attached to the outflow of the capillary using flexible silicon tubing. B: the temperature of solution at the outlet (Zoutlet; filled triangles) of the capillary was measured along with the temperature of the heat pipe (Thp: open triangles) at the point where the capillary emerged from the aluminium strip. Flow rates varied from 0.6 m l / m i n to 3.4 m l / m i n . Although ideally Thp would be measured at the midpoint of the heat pipe the temperature gradient along the heat pipe is small (for Q~ = 4 W the temperature difference between the ends is approximately 1.4 o C). C: the power removed from the inflowing solution (q) was estimated using q = f/60'4.2"(Toutlet- Tamb) where f = flow rate ( m l / m i n ) and Toutlet= temperature of solution leaving the capillary (Beek and Muttzall, 1975; Pitts and Sissom, 1977). The ratio of power removed by the flowing solution to power removed by the Peltier element ( q / Q c ) was estimated from the regression line in Fig. 3B, adjusted by 1 ° C to allow for a I ° C increase in ambient temperature (i.e., Q,, was estimated from the solution of Tc = Thp - Qc.((,0p_ho + ~ghpe + ~ghp/2) (see Fig. 2A) and T¢ + 9.8 = 2.49. Qc (cooler/heater module performance). For flow rates above 2 m l / m i n the solution flowing through the capillary extracts approximately 80% of the power removed by the Peltier element.

59

derived from the intersections between 'load' lines for a range of thermal loads (with the thermal resistances [~load) attached to the heat pipe, and, the relationship between Qc and Tc in Fig. 3B.

estimated power that the Peltier element could remove at each heat pipe temperature. This simple heat exchanger extracts about 80% of the available power at flow rates above 2 m l / m i n .

(b) Pre-cooling solutions

(c) Heating

For pre-cooling solutions a glass capillary was placed along the heat pipe and covered with an aluminium strip with a v-shaped groove machined in it (Fig. 4A). Prior to assembly the groove and contacting surfaces were coated with thermal grease. Passing water through the 12-cm length of glass capillary (O.D. 1.15 mm, I.D. 0.065 ram) at 0.6 m l / m i n dropped the t e m p e r a t u r e from 24.0 ° C to - 1 . 2 ° C at the outlet. At the highest flow rate tested, 3.4 m l / m i n , the outlet temperature was 8.5 ° C. The outflow t e m p e r a t u r e versus flow rate is shown in Fig. 4B. At flow rates above 2 m l / m i n the outlet t e m p e r a t u r e exceeds the heat pipe t e m p e r a t u r e by up to 4 ° C, indicating that for these flow rates a heat exchanger with a greater contact area would be necessary to achieve maximal heat transfer. Fig. 4C shows the power extracted from the water flowing through the capillary (q) and the ratio of this power to the

Since our primary interest was in cooling, we performed only simple heating tests to compare the experimental performance of the c o o l e r / heater module with the model predictions. In the first test we measured the heat pipe temperature with no thermal load attached to the heat pipe (Table IV). These measurements can be used to estimate the outflow temperature if a capillary heat exchanger like that above is used. In a second test intended to mimic a chamber with a substantial area we attached (using thermal grease) a heat sink (Model 680-125, E G & G Wakefield, thermal resistance 5 o C / W ; compare with 17 ° C / W for the 6 cm × 6 cm aluminium plate) to the heat pipe. Table IV illustrates that even for this substantial thermal load there is no difficulty in achieving temperatures in the physiological range with modest input power to the Peltier element.

T A B L E IV PERFORMANCE

OF THE COOLER/HEATER

MODULE

FOR HEATING

Two c o n f i g u r a t i o n s w e r e e x a m i n e d . T h e p e r f o r m a n c e of the c o o l e r / h e a t e r m o d u l e was m e a s u r e d with no t h e r m a l load a t t a c h e d to the heat pipe ( ' n o load' in Table). In the s e c o n d c o n f i g u r a t i o n a heat sink ( t h e r m a l r e s i s t a n c e 5 ° C / W ) was a t t a c h e d to the heat pipe using t h e r m a l grease. Tio,d, the t e m p e r a t u r e of the load, was m e a s u r e d using a YSI-511 t h e r m i s t o r p r o b e p l a c e d at the c e n t e r of the heat sink on the face away from the h e a t pipe. Th~ was m e a s u r e d at the j u n c t i o n b e t w e e n the fin closest to the web and the web surface (the a c t u a l location for this m e a s u r e m e n t is not critical since the t e m p e r a t u r e g r a d i e n t s in the heat sink in these tests are minimal). T h is e s t i m a t e d from the model. S q u a r e b r a c k e t s d e n o t e m o d e l e s t i m a t e s . Both c o n f i g u r a t i o n s : Ohs = 0.35 ° C / W , (~hpe =.0.5 o C / W , 0)hp_amb = 15 o C / W , 0)hp = 0.35 o C / W , (0hp_load ~ 0.17 o C / W , 0 o C, T~,m~, = 24 ° C, Ow~b + O h~-P = 0.34 o C / W , ~ p_ hp = 0.145 ° C / W , lm~,, = 3.9 A, G = 0.078, N = 127, n = 1. No load: O)lo~d = 5000 o C / W ; heat sink as load: Oioad = 5 ° C / W . For the e x p e r i m e n t a l m e a s u r e m e n t s Z~mh = 24.0 ° C. Vo (V)

Ip (A)

V e • Ip" n (W)

T]oad ( o C)

Th~ ( ° C)

No load

1.9 3.3 5.8

0.30 [0.31] 0.56 [0.58] 1.03 [0.93]

0.6 1.8 6.0

36.8 [38.8] 44.8 [50.2] 60.0 [71.4]

26.4 26.1 26.2

5 ° C / W load

1.9 3.2 5.9

0.34 [0.38] 0.60 [0.62] 1.02 [1.05]

0.6 1.9 6.0

33.1 [32.1] 38.3 [38.3] 47.8 [51.9]

25.0 25.0 25.3

"/'~ =

60

(d) Regulating temperature We have not considered the design of temperature controllers for the heater/cooler module since these are available commercially (e.g., Model 809-3030-01-00-00, Midland Ross Corp.) and have been described in the literature (e.g., Chabala et al., 1985). An alternative to controlling the Peltier element voltage is to operate the cooler/heater at a fixed voltage (e.g., 12 V) in the cooling mode and control temperature either by reheating the outflowing solution or, in the case of a chamber, reheating the plate on which the chamber is placed. For reheating solution flowing out of the capillary heat exchanger we constructed a simple heater by winding a piece of resistance wire (0.35 /2/cm, approx. 30 cm tong, Magnet Wire Inc., Corona, NY 11368) around a short length (2-3 cm) of glass capillary tubing and fixing it in place with 5-rain epoxy. By connecting this tube with the capillary emerging from the heat pipe with silicon tubing, the position of the heater can be adjusted so as not to interfere with apparatus on the microscope stage. For the 6 cm x 6 cm aluminium plate we reheated the plate with a foil heater (approx. 10 ,(2 resistance) attached to the underside of the plate.

Experimental application The cooler/heater module in conjuction with a capillary heat exchanger was used to pre-cool solutions in a study of the kinetics of calcium and barium currents at reduced temperatures in acutely dissodated canine cardiac Purkinje myocytes. Results are illustrated in Fig. 5. The input voltage to the Peltier element was adjusted so that Tyrode entering the experimental chamber (details of chamber in Datyner et al., 1985) was at 14.5°C. The flow rate was approximately 0.5 ml/min. Experimental details are provided in the figure legend.

Rates of cooling/heating To describe the rate at which the cooler/ heater module cools or heags, we measured the time constants for heating/'cooling with (1) only the heat pipe assembly attached to the module and (2) with the 6 cm × 6 cm aluminium plate described above attached to the heat pipe. With

Q

C

L_ d

i

,c"

A

-20C

-400

-'~A -60(

-4o

-2o

6

Ba12ram

20

4'0

60

V (mV)

Fig. 5. Experimental data. Current-voltage relationships ( l Vs) for calcium and barium currents recorded at 14.5 ° C in Tyrode solutions containing 12 m M Ca 2+ and 12 m M Ba 2÷, respectively. Current traces in 12 m M Ca 2+. A: in response to voltage clamp steps of - 2 5 , - 2 0 , ... - 5 inV. B: in response to voltage clamp steps of 0, + 5 . . . . + 50 mV. Current traces in 12 m M Ba 2+. C: in response to voltage clamp steps of - 15, - 10. . . . + 15 mV. D: in response to voltage clamp steps of +20, +25, ... + 6 5 mV. E: I - V s of peak current in the Ca 24 and Ba 2+ containing solutions. The data was not leak subtracted so the reversal potentials do not indicate the selectivity. Whole cell currents were recorded with an Axoelamp 2A clamp (Axon Instruments. Foster City, CA 94404) in the switched clamp mode (10 kHz switching frequency). Holding potential - 5 0 mV. Bathing solution contained in mM: CaCI 105, NaCI 35, KCt 6, N a H C O 3 12, N a H 2 P O 4 0.4, MgCI 2 1.6. 4-AP 0.5, glucose 10, taurine 25, beta-bydroxybutyric acid 5 and Na-pyruvate 5. p H 7.2-7.4. Pipette solution in raM: CsCI 105, KCI 35, MgCI 2 4, H E P E S 10, E G T A 5, A T P 2 and creatinine phosphate 3. p H 7.4. Scale bars: 80 ms, 100 pA.

61 TABLE V TIME CONSTANTS FOR COOLING/HEATING Time constants were measured with no thermal load attached to the heat pipe ('no load'). In the second configuration the 6 cmx6 cm aluminium plate was attached to the end of the heat pipe with thermal grease. Temperatures were probed at the end of the heat pipe for 'no load' and half way along the furthest edge of the 6 cmx 6 cm plate, perpendicular to the heat pipe. For cooling Vp = 10.5 V, 'no load' temperature approx. 0 ° C, 6 cm x 6 cm plate temperature 7 o C. For heating Vp = 3.3 V, 'no load' temperature approx. 47°C, 6 cmx6 cm plate temperature 44 ° C. For reheating and cooling to ambient Ve = 0 V. T~mb= 27 ° C. r (sec)

Cooling

Reheat to ambient

No load

37

55

6 cm X6 cm Plate

67

67 *

Heating

Cooling to ambient

55

76

104

135

* There was a second, slower component of decay with a time constant of approximately 400-600 s distinguishable in this test. This component made up about 30% of the total amplitude of the decay.

the h e a t p i p e a s s e m b l y the t i m e c o n s t a n t s for h e a t i n g a n d cooling r a n g e d from 37 to 76 s. T h e r e is an a d d i t i o n a l 10-s d e l a y for h e a t transp o r t along the h e a t pipe. W i t h t h e 6 cm × 6 cm p l a t e a t t a c h e d , time c o n s t a n t s w e r e longer, ranging from 67 to 135 s. T h e d a t a a r e s u m m a r i z e d in T a b l e V.

Discussion

W e have p r e s e n t e d a design for a m o d u l a r c o o l e r / h e a t e r for p r e - c o o l i n g / h e a t i n g s o l u t i o n s a n d / o r c o o l i n g / h e a t i n g tissue c h a m b e r s . In any design using a P e l t i e r e l e m e n t for cooling, p o w e r levels on t h e hot side of t h e P e l t i e r e l e m e n t a r e typically 4 - 1 0 t i m e s t h o s e o n the cold side, h e n c e the t h e r m a l p a t h w a y on t h e hot side of t h e P e l t i e r e l e m e n t m u s t be t r e a t e d carefully to m i n i m i z e its t h e r m a l resistance. O u r design p e r f o r m a n c e m i g h t b e i m p r o v e d if h e a t sinks with t h i c k e r or m o r e c o n d u c t i v e w e b s (e.g., c o p p e r ) a r e selected. W e did not use h e a t sinks with c o p p e r webs (e.g., M o d e l 505, E G & G W a k e f i e l d ) as t h e i r s t r u c t u r e

is not well m a t c h e d to o u r p a r t i c u l a r c o o l e r structure. W h i l e it is efficient to use a h e a t p i p e on the cold side of the P e l t i e r e l e m e n t (low p o w e r side) it is clearly i m p r a c t i c a l to use a h e a t p i p e to r e m o v e h e a t from the hot side o f the P e l t i e r e l e m e n t since t h e r e w o u l d be a s u b s t a n t i a l temp e r a t u r e rise along the h e a t p i p e ( a p p r o x i m a t e l y 10 ° C for 30 W p o w e r levels). T o i m p r o v e the p e r f o r m a n c e of the a l u m i n i u m p l a t e for cooling, insulation could be used a r o u n d the c u l t u r e dish a n d b e l o w t h e plate. In a p p l i c a tions w h e r e the 5 - 6 ° C t e m p e r a t u r e g r a d i e n t across the p l a t e is u n d e s i r a b l e , the p l a t e thickness s h o u l d b e i n c r e a s e d . T h e g r a d i e n t is a p p r o x i m a t e l y p r o p o r t i o n a l to the thickness of the plate; t h e r e f o r e , to r e d u c e the d i f f e r e n c e from 5 ° C (for a 1.7-mm thick p l a t e ) to I ° C w o u l d r e q u i r e a p l a t e 8.5-mm thick. T o r e d u c e the t h e r m a l resist a n c e of the j u n c t i o n b e t w e e n the h e a t p i p e a n d plate, a c h a n n e l could be m a c h i n e d t h r o u g h the p l a t e (or a r e m o v a b l e section used) to allow contact on b o t h sides of the h e a t pipe. A c h a m b e r suitable for i s o l a t e d cell studies similar to that d e s c r i b e d in D a t y n e r et al. (1985) could be fabric a t e d of a l u m i n i u m a n d e i t h e r a n o d i z e d or insul a t e d with a plastic coating. O n e d i s a d v a n t a g e of the c o o l e r / h e a t e r m o d ule is that for m o v e a b l e m i c r o s c o p e stages the e n t i r e m o d u l e a s s e m b l y n e e d s to be m o v e d if the h e a t p i p e is a t t a c h e d to a m e t a l c h a m b e r or m e t a l p l a t e b e n e a t h the c h a m b e r . A l t h o u g h the weight of a p p r o x i m a t e l y 500 g could be s u p p o r t e d by m o s t stages, it may be d e s i r a b l e to r e d u c e the w e i g h t c a r r i e d by the stage. O n e p o t e n t i a l solution to this p r o b l e m is to a t t a c h teflon p a d s or castors to the u n d e r s i d e of the h e a t sink. T h e h e a t sink can t h e n ride on a s e p a r a t e ' s h e l f ' m o u n t e d b e l o w the level o f the m i c r o s c o p e stage such that most of the weight is b o r n e by this shelf.

Acknowledgements

This w o r k was s u p p o r t e d by g r a n t s P P G HL20558, HL28958 a n d HL43731 from the NHLBI.

62

Glossary

Vp Ip Th

L Qc I max

G N il Toutlet

Z~mb Ths

Tdel TIoad Thp

Qlo+,d

(~)hp arab Voltage applied to Peltier element Current flowing through Peltier element Temperature of hot face of Peltier element Temperature of cold face of Peltier element Heat removed by the cold face of Peltier element Maximum current for Peltier element Geometry factor for Peltier element Number of couples Number of Peltier elements Temperature of fluid exiting capillary heat exchanger Ambient temperature Temperature of heat sink Temperature difference across Peltier element (T h - Tc) Temperature of thermal load Oioad Temperature at midpoint of heat pipe Heat removed from thermal load 69load

69hs 69hs -P

[~web 69 P-hp

69 hoe

Thermal resistance of heat sink Thermal resistance of junction between the Peltier element and heat sink Thermal resistance of web of heat sink Thermal resistance of junction between the Peltier element and heat pipe Thermal resistance for heat entering/exiting heat pipe (= 69entry =

Oexi,) 69hp

Thermal resistance along heat pipe length

Ohp_k,ad

O~o.d

Thermal resistance from heat pipe surface to ambient Thermal resistance of junction between heat pipe and load Thermal resistance of load

References Beek, W.J. and Muttzall, K.M.K. (1975) Transport Phenomena. John Wiley, London, pp. 145+223. CAMBION (1972) The Cambion Thermoelectric Handbook, Cambridge Thermionic Corporation, Cambridge, MA 02138, pp. 9-32. Cannell, M.B. and Lederer, W.J. (1986) A novel experimental chamber for single-cell voltage-clamp and patch-clamp applications with low electrical noise and excellent temperature and flow control. Pfliigers Arch., 406: 536-539. Chabala, L.D., Sheridan, R.E., Hodge, D.C., Power, J.N. and Walsh, M.P. (1985) A microscope stage temperature controller for the study of whole-cell or single-channel currents. Pfliigers Arch., 404: 374-377. Datyner, N.B., Gintant, G.A. and Cohen. 1.S. (1985)Versatile temperature controlled tissue bath for studies of isolated cells using an inverted microscope. Pfliigers Arch., 403: 318-323. EG&E Wakefield Engineering (1984) Heatsinks for thermal dissipation greater than 10 Watts. EG&G Wakefield Engineering, Wakefield, MA 01880. Forsythe, I.D. and Coates, R.T. (1988) A chamber for electrophysiological recording from cultured neurons allowing perfusion and temperature control. J. Neurosci, Methods, 25: 19-27. 1ERC (1984) IERC Thermal Management Guide. 1ERC. Bur+ bank, CA 91510-7704. Lynch, J.W., Barry, P.H. and Quartararo, N. (1988) A temperature and solution control system for measurement of single channel currents in excised membrane patches. Pfliigers Arch., 412: 322-327. MELCOR (1985) Thermoelectric Heat Pump Module Specifications. MELCOR, Trenton, NJ 08648. Pitts, D.R. and Sissom, L.E. (1977) Heat Transfer. McGraw Hill, New York.