Sādhanā Vol. 34, Part 2, April 2009, pp. 243 254. Printed in India Heat transer studies or a crystal in a synchrotron radiation beamline A K SINHA Synchrotron Utilisation and Materials Research Division, Raja Ramanna Center or Advanced Technology, Indore 452 013 e-mail: anil@rrcat.gov.in MS received 14 August 2007; revised 11 November 2008 Abstract. Heat load studies have been perormed or the irst crystal o a double crystal monochromator to be installed in a beamline o the 2 5 GeV synchrotron radiation source Indus-2. Finite element analysis (FEA) has been used to calculate the temperature distribution and the mechanical distortions on these crystals. Several cases o cooling schemes and heat loads have been studied. Based on these FEA results, the analytical relationships available in the literature have been modiied. It is shown that modiied analytical results compare well with the empirical results obtained rom FEA. The optimisation o the cooling conditions can be achieved by doing FEA calculations or only one case. All other cases can then be calculated by using analytical relations proposed here. The proposed analytical equations are generic in nature and can be applied or any source crystal combination and thereore would be useul or perormance prediction o any new monochromator on a new synchrotron source without taking recourse to time consuming, computation-intensive FEA. Keywords. crystal. Synchrotron radiation; heat load; inite element analysis; silicon 1. Introduction The 2 5 GeV, 300 ma Indian synchrotron radiation (SR) source Indus-2 (Raja Rao 1998) is operational at Raja Ramanna Center or Advanced Technology, Indore. Some initial experiments using SR is under way. Indus 2 has been designed to emit continuous SR in the hard X-ray regime rom its bending magnets, as well as the insertion devices (wavelength shiter, wigglers) installed in the straight sections o the storage ring. The high lux and high brightness o the synchrotron source can be utilised i the high brightness is transerred to the experimental station with minimal loss in the brightness. One source o degradation is thermo-mechanical distortion in the optical elements because o the large heat load. For instance, the perormance o a crystal monochromator installed in the beamline degrades because o the distortion induced by thermal irradiation by synchrotron radiation. To minimize this degradation, it is customary to cool the crystal. A number o 243
244 A K Sinha Table 1. Indus-2 synchrotron radiation source characteristics. Indus-2 Electron energy 2 5 GeV Max. electron current 300 ma Bending magnet Wavelength shiter Magnetic ield 1 5T 5 0T Critical wavelength 2 0 Å 0 6 Å Power radiated 28 W 90 W per mrad o horizontal acceptance cooling schemes are reported in literature. For intermediate heat loads, an indirect cooling scheme is ollowed (Jensen et al 1995, Michaud 1986), in which crystals are kept on a water-cooled copper base. The scheme oten uses some material between base plate and crystal to improve the thermal contact. A direct cooling scheme, by making channels in the crystal, is adopted or high heat loads (Mochizuki et al 1995, Oversluizen et al 1989, Arthur et al 1992). There are variations to these cooling schemes. For ultra high heat loads (radiation rom insertion devices) cooling is direct and the coolant is liquid gallium (Smither et al 1989). In addition, some improvised methods like use o thin crystals (Freund et al 1992), Si crystals at cryogenic temperatures (Knapp et al 1995, Kuzay 1992, Wang et al 1995), jet cooling (Berman & Hart 1992) etc. are also used. Finite element (FE) analysis is done or optimisation o the cooling geometry as well as the cooling parameters or individual beamlines. In addition, the mechanical distortion results are used in the raytracing program to estimate the realistic perormance o a beamline. In spite o numerous FE calculations, very little guideline exists or perormance prediction o a new monochromator on a new synchrotron source. Analytical ormulae (Smither et al 1989), based on simple physical arguments, have limited applicability in predicting the perormance o crystals. In this paper, analytical relations have been worked out or maximum temperature rise in the crystal as a unction o Bragg angle and these are compared with the empirical relations obtained rom rigorous FE calculations using inite element sotware Ansys (Ansys 1998). Also various components o the crystal distortion have been calculated using analytical relations and empirical results obtained using FE calculations. Two cooling geometries, viz. the indirect cooling and the direct cooling o the crystals are studied here. 2. Calculation details Indus-2 characteristics are given in table 1. The total power radiated by the wavelength shiter is 90 W or 1 mrad o horizontal acceptance, which is large enough to necessitate convection cooling o the irst optical elements o the beamline. In the beamlines proposed on Indus-2, crystal monochromator can be either the irst optical element (OE), immediately ater the rontend, or it can be the second OE, preceded by a mirror. Both these cases have been considered or FE calculations. In the second case the absorbed heat load is about 3 5 times less than the irst case because o the absorption in the preceding mirror. In addition or each location o the crystal, two convection ilm coeicients have been taken or FE calculations. Also, two cooling geometries have been considered. These are indirect (igure 1a) and direct
Heat transer studies or a crystal in a synchrotron radiation beamline 245 Figure 1. Cooling geometries o indirect cooled crystal (igure 1a) and direct cooled crystal (igure 1b). The dimensions o the crystals are 80 mm 60 mm 2 mm (igure 1a) and 80 mm 60 mm 40 mm (igure 1b). For the case o direct cooling, the dimensions o the cooling channels are 5 mm 1 mm and the separation between the channels is 1 mm. The channels are made 0 5 mm below the surace o the crystal. There are 30 channels in all. (igure 1b) cooling. Table 2 gives the parameters or indirect cooling or the various cases considered. All the symbols used in this paper are deined in List o symbols at the end (beore reerences). Table 2. Various cases and corresponding input parameters or indirect cooling o the crystal. Distance o the crystal rom the source point has been taken to be 22 m. h Power absorbed Power density Case Crystal position [W/cm 2 / C] [W] [W/mm 2 ] Case I 1 st optical element 0 45 81 0 6 Case II 1 st optical element 0 60 81 0 6 Case III 2 nd Optical Element 0 45 22 5 0 17 Case IV 2 nd Optical Element 0 60 22 5 0 17 For 1 mrad o horizontal acceptance crystal normal to the incident radiation
246 A K Sinha 2.1 Finite element analysis The radiation emitted by a synchrotron source is anisotropic and moreover the cooling geometry o the crystal is also generally complicated. Thereore, it is diicult to estimate the temperature distribution, and hence the mechanical distortion, analytically. Finite element (FE) analysis is commonly used to study the problem. In this paper, we have done FE calculations or two cooling geometries or obtaining temperature distribution in the crystal using FE sotware Ansys. Figure 1 shows the two cooling geometries o the crystal along with dimensions. The crystals are cooled by lowing water at 25 C (RT). For indirect (igure 1a) cooling, a 2 mm thick Si(111) crystal is kept on water cooled copper base. To improve thermal contact, In Ga alloy paste is painted in between Si and copper suraces. For direct cooling, on the other hand, 30 rectangular channels are made in the crystal itsel. Cooling luid (water) is lown through these channels. The channel dimensions are similar to that in the paper by Assouid et al (1995). The lux o cooling luid in the case o direct cooling is approximately 14 l/m that is equivalent to a luid velocity o 100 cm/s, which is within the streamline range. The average ilm coeicient is calculated using Baker and Tessier equation (Rohsenow & Choi 1961): h = A 1K d + A 2k 0 6 Cv 0 4 Va 0 8 (1) d 0 2 ν 0 8 and ound to be 0 6 W/cm 2 / C. Constants A 1 and A 2 are empirically determined to be approximately 1. Turbulent low gives more eective cooling but the mechanical vibrations degrade the monochromator perormance. For comparison and to evaluate the cooling dependence on water low rate, we have done FE calculations or h = 1 2 W/cm 2 / C as well, which also alls in the streamline low region. Similarly or direct cooling, low rate o 10 l/m gives a ilm coeicient o 1 2 W/cm 2 / C. We have also done calculations or h = 0 6 W/cm 2 / C or the same geometry. This means decreasing the velocity by approximately 3 times compared to the case o h = 1 2 W/cm 2 / C. Heat load is approximately Gaussian in the vertical plane and uniorm in the horizontal plane. Temperature distribution has been calculated using thermal element solid 87 in ANSYS 5 7. The elements have 10 nodes and are tetragonal in shape. These elements are recommended or the case that is to be transormed to structural problem. The thermal strain has been calculated by transorming thermal element to structural element (element solid 92). Since the temperature rises are small, the physical properties o Si and Cu were taken to be constant (RT value), independent o temperature. 3. Results and discussions Using FE analysis, we have estimated the temperature distribution and distortion in the irst crystal o a double crystal monochromator (DCM) or indirect as well as direct cooling o the crystal, or the our cases given in table 2. Various Bragg angle settings o the crystal corresponding to photon energies o 5 to 25 kev have been considered. Section 3 1 gives the temperature distribution results or indirect cooling. In this section, we irst obtain temperature distribution in the crystal using rigorous FE analysis. It is seen that there is a large discrepancy between the values o maximum temperature rise in the crystal calculated analytically using existing ormulae and the FEM results (Smither et al 1989). We, considering some realistic assumptions, have modiied analytical ormulae. The results based on these analytical ormulae are ound to be matching quite well with the empirical relations obtained by itting FEM
Heat transer studies or a crystal in a synchrotron radiation beamline 247 Figure 2. Typical temperature distribution on the crystal as obtained rom the inite element analysis or indirect (igure 2a) and direct (igure 2b) cooled crystals. Shown contours are or 81 W (or 1 mrad horizontal acceptance) and Bragg angle o 23 3. The ilm coeicient values are 0.6 W/cm 2 / C or indirect cooled crystals and 0.6 W/cm 2 / C or direct cooled crystals. Figure 2a shows the ull crystal, whereas, igure 2b shows hal o the crystal. data. In section 3 2, temperature results or direct cooling are similarly derived and discussed. The crystal distortion results have been obtained by FEM as well as analytically in section 3 3. 3.1 Temperature results or indirect cooling For indirect cooling, igure 2a shows a representative temperature distribution as obtained by FE analysis. This contour plot is or crystal as the irst optical element (absorbed power = 81 W or 1mrad o horizontal acceptance). The Bragg angle is 23 3 and h = 0 6 W/cm 2 / C. The igure shows that the maximum temperature reached on the crystal surace is 44 8 C. Similar calculations have been done or all Bragg angles. Figure 3a shows T max T 3 plotted as a unction o photon energy relected by the crystal, or the our cases given in
248 A K Sinha h 1/2 Figure 3. Dierence ( T max T 3 = T 1 T 3 ) between maximum temperature on the surace o the crystal (T 1 ) and average temperature o the out lowing water (T 3 ) is plotted as a unction o photon energy, which is being relected by the crystal, or the case o indirect cooling (igure 3a) and direct cooling (igure 3b). Scattered points are the results o inite element analysis and the curves are empirical it to the data using Eq. (2a) or igure 3a and Eq. (8) or igure 3b. Various curves are or dierent values o power absorbed by the crystal and the convection ilm coeicients. table 1. The scattered points are the FE results and the lines show empirical it to them using the relation: T max T 3 = K 1 P max + K 2PmaxP 1/2 1/2 abs. (2a) Where K 1 and K 2 are the itting constants. Values o the constants ound rom the empirical it are 0 22 and 0 27 respectively. We ind rom the igure that the its are quite good. Next, we will compare these results with the analytical results. For discussion, we irst take the case o the crystal being the irst OE, h = 0.45 W/cm 2 / C and Bragg angle o 23 3 (set to relect 5 kev photons). The FE calculation or this case gives maximum temperature increase ( T max ) on the surace o the crystal 23 C (see igure 2a). Analytically, T max can be written as sum o temperatures o various parts o the crystal as
Heat transer studies or a crystal in a synchrotron radiation beamline 249 below T max = T 12 + T 23 + T 3. (2b) Using simple physical arguments, various components in Eq. (2b) are given as Re. (Smither 1989) T 12 = DP max K T 23 = P max h (3a) (3b) T 3 = P absn. (3c) mc v Calculating the temperature values using the above equations, we get T 12 = 2 9 C, T 3 = 0.5 C and T 23 = 32 C. So, T 23 obtained using the analytical relation (32 C) is much larger than that obtained using FEM ( 20 C, see igure 2a). This discrepancy comes rom the act that while Eq. 3b assumes that T 2 is the temperature throughout the cooling channel cross section whereas in reality there is a large variation in the temperature across the cross section. Equation 3b in the same orm can be used i h is replaced by an eective ilm coeicient, h w. To calculate h w we assume that the lowest temperature o the copper block is T. The temperature o the copper water interace decreases linearly rom T 2 to T 3 or the top plate o the cooling channel and rom T 3 to T or the bottom plate o the cooling channel. Thereore, total heat taken out by the our walls o the copper cooling channel is (h /2){A 1 T 23 + A 1 T 3 + 2A 2 ( T 23 + T 3 )/2}. Since the average temperature o the cooling liquid is T 3, the total heat convection in terms o the eective ilm coeicient is h w 2(A 1 + A 2 ) T 3. Equating the two, we get h w = (h /2){A 1 T 23 + A 1 T 3 + 2A 2 ( T 23 + T 3 )/2}. (4) 2(A 1 + A 2 ) T 3 Since T 3 T 23, Eq. 4 reduces to h w = h T 23 4 T 3. (5) Replacing h in Eq. 3b by h w,weget T 23 = (4N/mC v) 1/2 P 1/2 From Eqs. 2, 3 and 6, we get h 1/2 maxp 1/2 abs T max T 3 = K 1 P max + K 2P 1/2. (6) maxp 1/2 abs h 1/2, (7) where K 1 = D/K e = 0 2 and K 2 = (4 N/mC v ) 1/2 = 0 16 or the case under discussion. It is seen that the above equation is the same as Eq. 2a, obtained rom empirical itting o FEM results. The values o constants or the empirical its were K 1 = 0 22 and K 2 = 0 27.
250 A K Sinha It is seen that the unctional dependence have been correctly predicted by the analytical calculations. In addition, there is an excellent agreement between K 1 obtained empirically rom FEM (0 22) and that obtained analytically (0.2). However, the two values o K 2 are o by a actor o 1 5. This is not unexpected as only approximate temperature values were taken in the derivation o Eq. (5). The discrepancy also indicates that it is not straightorward to estimate the value o the constant K 2, without going into details o the cooling geometry and the heat loading. However, the constants K 1 and K 2 need to be obtained only once or a particular geometry and these values then give good estimates or dierent heat loads and dierent h. This shows that the constants are independent o heat load levels and value o h. Thereore, the optimisation o the cooling geometry as well as convection ilm coeicient etc. can be done by perorming FEM calculations or one value o these parameters and the values or other cases can then be derived using Eq. 2a. Thus, the unctional dependence o the temperature distribution on input parameters can be correctly predicted analytically using the modiied ormula. 3.2 Temperature results or direct cooling Temperature distribution, derived rom FE calculations, or a directly cooled crystal is given in igure 2b. This plot is or absorbed power o 81 W (or 1mrad o horizontal acceptance), Bragg angle o 23 3 and h = 0 45 W/cm 2 / C. Similar FE calculations have been done or other cases. Figure 3b shows ( T max T 3 ) plotted as a unction o photon energy or cooling geometry shown in igure 1b. FE results are shown by the scattered points along with the it to the point using the empirical equation: T max T 3 = C 1P max h 1/2 + C 2P 1/2 maxp 1/2 abs h 1/2. (8) The values o C 1 and C 2 are ound to be 0 3 and 0 11 respectively. Again the it between the FEM calculations and the empirical data are good or all cases o heat load, ilm coeicient and Bragg angle. This shows the validity o unctional dependence o Eq. 8. In this geometry it is not straightorward to calculate eective D and K analytically because there is heat low along both the horizontal and the vertical directions. However, the only dierence between the unctional dependence or this case and the case o indirect cooling is the dependence o the two terms on h 1/2. Dependence o the irst term on h is explained by arguing that larger the h larger will be the heat low along horizontal direction (on x-y plane); and eective D will be smaller giving smaller T 12. This explains why T 12 depends inversely upon h. Similarly, T 23 will have a slower dependence on h. This is also observed in the empirical relation (Eq. 8). 3.3 Crystal distortion results The three components o the crystal distortion (Lenardi 1993) are bowing, bump and increase in Darwin width because o the change in d value o the crystal. These distortions are caused due to the non-uniorm temperature distribution in the crystal. Bowing (bending) is caused by the thermal expansion o the crystal in the direction parallel to the surace; due to the thermal variation along the depth o the crystal. Bump, on the other hand, is caused by the expansion o the crystal in the direction perpendicular to the surace due to the thermal variation along the direction parallel to crystal surace. For Indus-2 heat load, the angular errors due to irst two eects are comparable and the third eect is negligible. Thereore, we consider only the irst two components.
Heat transer studies or a crystal in a synchrotron radiation beamline 251 Figure 4. Maximum thermal slope error on the crystal calculated using inite element structural analysis (scattered points) and using analytical relations (continuous curves), or the case o indirect cooling. Various curves are or dierent values o power absorbed by the crystal and the convection ilm coeicients. 3.3a Bump: The Bump height (H) is calculated using the ollowing equation (Lenardi 1993): H = α e D e ( T 12 /2 + T 23 + T 3 ). (9) And, the maximum slope error is θ max (rad) =±1 43 H/FWHM, where FWHM is the ull width at hal maximum o the Gaussian heat load. α e D e in the case o indirect cooling is calculated using the equations: and α Si D Si T 1I + α Cu D Cu T I2 = α e D e T 12 T 1I + T I2 = T 12 K Si T 1I D Si + K Cu T I2 D Cu = K e T 12 D e, and ound to be 1 13 10 6 cm/ C. Here T 1I is the temperature dierence between the surace o the crystal and Si-Cu interace. Similarly T I2 is the temperature dierence between the interace and the bottom o Cu. Above equations represent respectively the thermal strain and conduction equations across the interace. Since, everything in Eq. 9 is known, we can estimate H, and hence θ max, analytically. Also, to see the correctness o this analytically derived bump height, it has also been calculated rom rigorous FE structural analysis. FEM results or θ max are plotted in igure 4 (scattered points) along with θ max obtained analytically (continuous line) or the our cases o heat absorption and cooling conditions (table 2). The igure shows that the agreement between the two is good. This shows that or indirect cooling geometry, crystal deormation can be estimated analytically i temperature values are known. Figure 4 shows that the maximum slope error is 47μrad or P abs = 81 W/mrad o horizontal acceptance and h = 0 45 W/cm 2 / C, when the crystal is set to relect 5 kev photons (Bragg angle = 23 3 ). This slope error is less than the Darwin Width (60 μrad) o Si (111) or 5 kev photons. Thereore the cooling design is acceptable, even or maximum heat load and lower cooling.
252 A K Sinha Figure 5. Maximum bowing distortion per unit length calculated using analytical relations (continuous curves), or the case o indirect cooling. Various curves are or dierent values o power absorbed by the crystal and the convection ilm coeicients. In the case o direct cooling, Eq. 9 is used to calculate the bump. In this case, taking D e to be the thickness above the cooling channel (0 05 cm) o the crystal does not provide a good it. We have taken the value o D e to be 0 55 cm, which is the distance rom the surace o the crystal to the bottom o cooling channel to get a good it. Maximum slope error calculated analytically is compared with those obtained rom structural FE analysis (igure 4). The agreement between the two is ound to be reasonable. Maximum slope error obtained using FEM or the worst case o heat load and lower value o ilm coeicient is less than 15 μrad, which is well within acceptable limits. 3.3b Bowing: Bowing Radius (R) = D/(α T 12 ) (Lenardi 1993) and bowing distortion per unit length θ b = 1/R radian/cm have been calculated by estimating T 12 using the empirical relations T 12 = T max T 3 0 27 (P max P abs /h 1/2 or indirect cooling and T 12 = C 1 P max /h 1/2 or direct cooling. In igure 5, θ b (μ rad/cm) as a unction o photon energy has been plotted or the our cases (table 2) or indirect cooling. From the igure we ind that the maximum bowing is 50 μrad/cm. For the case o direct cooling, the maximum bowing is 20 μrad/cm, which is much less than the case o indirect cooling. These results are expected and in agreement with the literature (Michaud 1986, Oversluizen et al 1989, Assouid et al 1995). We ind that, in general, there is a good agreement between the temperature as well as crystal deormation results calculated using thermal and structural FE analysis respectively with the analytical ormulae. In the case o indirect cooling, which is rather simple cooling geometry, we are able to explain all the components o the empirical temperature rise ormula satisactorily. Also in this case, the crystal deormation results are well accounted or. However, in the case o direct cooling, the geometry o cooling is complicated and hence cooling phenomena is complex. So some o the terms in the empirical temperature rise ormula is only partially explained. However, the it between FEM values and the values obtained using empirical ormula or various values o P max and h is satisactory. Also, or explaining crystal distortion results, we have taken the value o D e rather arbitrarily to be the distance between the surace o the crystal and bottom o the cooling channel, which needs explana-
Heat transer studies or a crystal in a synchrotron radiation beamline 253 tion. Thereore, more theoretical work is required to be done to explain empirical results in the case o direct cooling o crystals. 4. Conclusions For wavelength shiter insertion device source on Indus-2 synchrotron ring (2 5 GeV, 300 ma), temperature distribution and thermal distortion have been studied by Finite Element Analysis; or the irst crystal o a double crystal monochromator. Calculations have been done or two cases namely one in which the crystal is the 1 st optical element (OE) and second in which crystal is the 2 nd OE, preceded by a mirror. In the irst case when the crystal is the irst OE, the total incident heat load is 81 W per mrad o horizontal acceptance, whereas when the crystal is second optical element the incident heat load is 22 5 W or 1 mrad o horizontal acceptance. Also, two geometries o cooling have been discussed. In indirect cooling, thin crystal (2 mm) is kept on a water-cooled Cu plate. In direct cooling, rectangular channels are drilled in the crystal and water lows through them. As expected, the temperature rise is the maximum or the case when the crystal is the irst OE and is set to relect the lowest energy photons (5 kev). The temperature rise is 23 C. Corresponding slope error as well as bowing distortion have been calculated and ound to be 47 μrad and 50 μrad/cm respectively. These are within 100% o the Darwin width (Assouid et al 1995). This shows that indirect cooling, which is less eicient but easier to achieve is acceptable or Indus-2 heat load, even i the crystal is the irst optical component. Empirical relations or calculation o maximum temperature rise in the crystal have been worked out rom FEM results or both cooling geometries. Existing analytical ormulae have been modiied. It is shown that the unctional dependences o the maximum temperature rise on absorbed power; the modiied analytical relations proposed by us correctly predict convection ilm coeicient and Bragg angle. This is very handy, because the optimisation o the cooling conditions can be achieved by doing FEM calculation or only one case. All other cases can then be calculated by using analytical relations proposed here. List o symbols T 1 = Maximum temperature o the surace o the crystal T 2 = Temperature o the copper water interace T 3 = Mean temperature o out lowing water T = Temperature o in lowing water T I = Temperature o silicon copper interace or indirect cooling case T max = T 1 T T ij = T i T j h = Convection ilm coeicient P abs = Absorbed power or 1 mrad horizontal an P max = Maximum power density N = Number o milirad absorbed K = Thermal conductivity m = Mass o water lowing per second C v = Speciic heat o water D = Thickness o the crystal above the cooling channel
254 A K Sinha D e = Eective thickness o the crystal θ = Bragg angle σ = Vertical divergence o the source A = Area o cross section o the cooling channel (igure 1 or details) θ max = Maximum slope error H = Bump height V a = Fluid low velocity d = Equivalent diameter o the cooling channel ν = Kinematic viscosity o water α = Coeicient o thermal expansion Reerences ANSYS-5.7 1998 Engineering analysis systems (Houston, PA: Swanson Analysis Systems Inc) 15342 Arthur J, Tompkins W H, Troxel Jr C, Contolini R J, Schmitt E, Bilderback D H, Henderson C, White J, Settersten T 1992 Rev. Sci. Instrum. 63: 433 Assouid L, Lee W, Mills D M 1995 Rev. Sci. Instrum. 66: 2713 Berman L E, Hart H 1992 Rev. Sci. Instrum. 63: 437 Freund A K, Marot G, Kawata H, Joksch S, Ziegler E, Berman L E, Hastings J B 1992 Rev. Sci. Instrum. 63: 442 Jensen B N, Mancini D C, Nyholm R 1995 Rev. Sci. Instrum. 66: 2129 Knapp G S, Rogers C S, Beno M A, Wiley C L, Jennings G, Cowan P L 1995 Rev. Sci. Instrum. 66: 2139 Kuzay T M 1992 Rev. Sci. Instrum. 63: 468 Lenardi C 1993 Lecture notes, Second School on the Use o Synchrotron Radiation in Science and Technology (Unpublished) Michaud F D 1986 Nucl. Instrum. Methods in Phys. Res. A246: 444 Mochizuki T, Zhang X, Sugiyama H, Zhao J, Ando M, Yoda Y 1995 Rev. Sci. Instrum. 66: 2167 Oversluizen T, Matsushita T, Ishikawa T, Stean P M, Sharma S, Mikuni A 1989 Rev. Sci. Instrum. 60: 1493 Raja Rao A S 1998 Indus-2 project report Center or Advanced Technology, Indore Rohsenow W M, Choi H Y 1961 Heat, Mass and Momentum Transer (NJ: Prentice Hall Englewood Cli), Chap 5 11: Chapman A J 1974 Heat Transer (New York: Macmillan), Chap 5 13 Smither R K, Forster G A, Bilderback D H, Bedzyk M, Finkelstein K, Henderson C, White J, Berman L E, Stean P, Oversluizen T 1989 Rev. Sci. Instrum. 60: 1486 Wang Z, Yun W, Kuzay T M, Knapp G, Rogers S 1995 Rev. Sci. Instrum. 66: 2267