[Nft^-ftm-^'^i^o/ RM E53J07 ■. I. J -ra^a^ fjl'. :;x»7'?rv rtt.,.-,nS®^:,.--«<^ )i'S^.<^mr~.:. „■. ~ .■ -.■i-- :■ ".^'^•''- NACA RESEARCH MEMORANDUM MEASUREMENT OF HEAT-TRANSFER AND FRICTION COEFFICIENTS FOR FLOW OF AIR IN NONCIRCULAR DUCTS AT HIGH SURFACE TEMPERATURES By Warren H. Lowdermilk, Walter F. Weiland, Jr., and John N. B. Livingood Lewis Flight Propulsion Laboratory- Cleveland, Ohio . UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 1 20 MARSTON SCIENCE UBRARY P.O. BOX 117011 GAINESVILLE. FL 3261 1 -701 1 USA ;^- N.VIIO-..^i. NATIONAL ADVISORY COMlvilfTEE FOR AERONAUTICS WASHINGTON January 25, 1954 15- % y^'^ ^^' ^'^o%io 'MCk RM E53J07 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS RESEARCH MEMORANDUM MEASUREMENT OF HEAT-TRANSFER AND FRICTION COEFFICIENTS FOR FLOW OF AIR IN NONCIRCULAR DUCTS AT HIGH SURFACE TEMPERATURES By Warren H. Lowdermllk, Walter F. Weiland, Jr., and John N. B. Livingood SUMMARY Measurements of average heat-transfer and friction coefficients were obtained with air flowing through electrically heated ducts having square, rectangular (aspect ratio, 5), ajid triangular cross sections for a range of surface temperature from 540° to 1780° R and Reynolds number from 1000 to 330,000. The results indicate that the effect of heat flux on correlations of the average heat-transfer and friction coefficients is similar to that obtained for circular tubes in a previous investigation and was nearly eliminated by evaluating the physical properties and density of the air at a film temperature halfway between the average surface and fluid bulk temperatures. With the Nusselt and Reynolds nxombers based on the hydraulic diameter of the ducts, the data for the non- circular ducts could be represented by the same equations obtained in the previous investigation for circular tubes. Correlation of the average difference between the surface corner and midwall temperatures for the square duct was in agreement with predicted values from a previous analysis. However, for the rectangu- lar and triangular ducts, the measured comer temperature was greater by approximately 20 ajid 35 percent, respectively, than the values pre- dicted by analysis. INTRODUCTION An experimental investigation was instituted at the NACA Lewis laboratory to obtain heat-transfer and related pressure-drop informa- tion for air flowing in tubes at high surface and fluid temperatures. The effects of such variables as surface temperature, inlet-air NACA RM E53J07 temperature, length-to-diameter ratio, and tube-entrance configuration on heat transfer and pressxire drop in smooth round tubes are summarized in reference 1. The scope of the general investigation is extended herein to in- clude the effect of flow-passage shape on heat-transfer and friction coefficients for air flowing through electrically heated square, tri- angular, and rectangular tubes at high heat-flxix conditions. Data were obtained for a range of Reynolds number from 1000 to 330,000 and surface temperature from 540° to 1780° R, and the results axe compared with those of reference 1 for circular tubes. APPARATUS AND PROCEDURE Arrangement of Apparatus A schematic diagram of the heater tubes and associated equipment is shown in figure 1. The experimental setup is the same as described in reference 1. Compressed air is supplied through a pressure- regulating valve, a cleaner, and a surge tank to a second pressure- regulating valve where the flow rate is controlled. From this valve, the air flows through a bank of rotameters into a three-pass mixing tank, through the test section, and into a second mixing tank from which it is discharged to the atmosphere. Electric power is supplied to the heater tube from a 208-volt, 60- cycle supply line through an autotransformer and a 14:1 power trans- former. The low-voltage leads of the power transformer are connected to the heater- tube flanges by copper cables. The capacity of the elec- tric equipment is 15 kllovolt-amperes. Test Sections Three different 24-inch-long cross-sectional shapes, as shown in figure 2 - squaxe, equilateral trieingle, and rectangle - were investi- gated, the inner dimensions of which were as follows: Shape Perimeter, Hydraulic Length to hydraulic- in. diam. , in. diam. ratio Square 1.80 0.45 53 Equilateral 2.31 .45 53 triangle Rectangle 3.0 .42 57 MCA RM E53J07 The test sections were fabricated from Inconel sheet stock with a thickness of 0.031 inch. The test-section sides were cut to the desired dimensions and clamped on ground- steel forms; each corner was welded with a heliarc welder. The excess weld material was ground off so that the comer wall thickness did not exceed l/32 inch. The inner corners of the test sections were sharp and even along the entire length of the test section. Steel flanges welded to the test sections at each end provided electric contact with the transformer leads from the power supply. Channels were milled in the outer faces of the flanges to minimize end heat losses, and the test sections were thermally insulated. Outside-wall temperatures were measured at 13 stations along the length of the test sections (fig. 2) with chromel-aJ-umel thermocouples and a self -balancing indicating potentiometer. At each station, ther- mocouples were located at the center of each side, except for the rec- tangular test section, where the thermocouples were omitted on the short sides. Thermocouples were also located at each corner at the three sta- tions located 3, 12, and 21 inches from the entrance. Static-pressure taps were located l/8 inch from the entrance and exit of each test section, and each section was fitted with a long- radius nozzle the throat dimensions of which matched the cross-sectional dimensions of the test section. Range of Conditions Heat-transfer and associated pressure-drop data were obtained with the square, the equilateral triangular, and the rectangular test sec- tions with rounded entrances over a range of Reynolds niamber from 1000 to 330,000, average outside-wall temperatures from 540° to 1780° R, and heat-flux densities up to 120,000 Btu per hour per square foot of heat- transfer area. SYMBOLS The following symbols are used in this report: A cross-sectional area, sq ft Cp specific heat, Btu/(lb)(°F) 4A D inside hydraiilic diameter, r^ — : — r — , ft E voltage drop across test section, v NACA RM E53J07 f average friction coefficient ff modified film friction coefficient G mass velocity, lb/(lir)(sq ft) g acceleration due to gravity, 4.17x10 ft/hr h average heat-transfer coefficient, Btu/(hr)(sq ft)(°F) I current flow through test section, amp k thermal conductivity, Btu/(hr)(sq ft)('^/ft) k* ratio of thermal conductivity of wall material to coolant L length of test section, ft Nu Nusselt number, hO/k Pr Prandtl number, Cpii./k p static pressure, Ib/sq ft abs Z^ over-all static-presstire drop across test section, Ib/sq ft Q7 heat loss from test section to surroiondings , Btu/hr R gas constant, 53.35 ft-lb/(lb) (°R) Re Reynolds number, pVD/ia S heat-transfer area of test section, sq ft s* ratio of wall thickness to hydraulic diameter T total temperature, °R T-|_ + T2 T]3 average fluid bulk tempera t\ire, ^ , °R Tg + T^ Tf average fluid film temperature, ^ , °R T - T c m Ts average surface temperature, Tm + ^ , °R NACA RM E53J07 I t static temperature, OR V velocity, ft/hr W flow rate, Ib/hr X ratio of specific heats [i absolute viscosity, lb/(lir)(ft) p density, Ib/cu ft Subscripts: av average b buli (when applied to properties, indicates evaluation at average buUi temperature, T5) c peripheral location at corner of test section f film (when applied to properties, indicates evaluation at average film temperature, If) fr friction m peripheral location midway between corners of test section s surface (when applied to properties, indicates evaluation at average surface temperature, Tg) 1 test-section entrance 2 test-section exit RESULTS AMD DISCUSSION Heat Balances Heat balances for each test section are shown in figure b, where the electric heat input minus the heat loss determined for condition of no air flow through the test section is plotted against the rate of heat transferred to the air as determined by air-flow rate and temperature measurements. The heat balances obtained at low heat in- puts and correspondingly low flow rates were very poor. In this re- gion the air temperature at the exit of the test section could not NACA RM E53J07 be measured accurately, because the very lov velocities in the outlet temperature mixing tank prevented the attainment of equilibrium condi- tions in the mixing tajik. The heat balances improved rapidly with increase in flow rate, and for values corresponding to turbulent flow in the test sections the data are in agreement with the match line (solid). The heat-transfer coefficients presented in reference 1 for round tubes, with which the present data are compared, were calciilated from the flow rate and tem- perature rise of the air measurements j hence, for consistency the pre- sent data are calculated in a similar manner for flow rates correspond- ing to Reynolds numbers of 10,000 or greater. For lower flow rates, the electric heat-input and heat-loss measxirements were believed to be more accurate than the measured outlet-air temperatiire . Therefore, the heat-transfer coefficients for Reynolds -numberB less than 10,000 are calculated from the electric heat-input and heat-loss measurements. Correlation of Heat-Transfer Coefficients The average heat-transfer coefficient h was computed from the experimental data by the relation Wcp b(T2 - Ti) ^ - S(T3 - T^) ^^^ where T2 = T-L + (3.415EI - Q^) for Reynolds numbers less than 10,000. The bulk temperatiire of the air T^-| was taken as the arithmetic mean of the temperatures at the entrance Tq^ and the exit Tg of the test sections. The average surface tem- perature Tg was taken as the arithmetic mean of the average outside comer temperature and the average outside midwall temperatiire. The temperature drop through the wall was neglected. The physical properties of air used in calculating the Nusselt, Reynolds, and Prandtl numbers are the same as those used in reference 1, wherein the viscosity and specific heat were based on values reported in reference 2, and the thermal conductivity was assumed to vary as the square root of temperature. The results presented in reference 1 for turbulent flow in circular tubes indicate that the average Nusselt number decreases progressively NACA RM E53J07 as the ratio of surface to fluid bulk temperature increases when the fluid properties are evaluated at the fluid bu lk temperature. The effect of the ratio of surface to bulk temperature was eliminated by evaluating the properties of the air, including the density term in the Reynolds number at the film temperature, defined as the arithmetic average of the surface and bulk temperatures. The data for Reynolds numbers gf eater than 10,000 were well represented by the following relation: . = 0.03.(-^)-(f^)-(r-^ which, for values of L/D between 53 and 57, becomes ^ = 0.023 kf i^-^r (:-^r <^> The average heat-transfer coefficients obtained herein for square, rectajigular, and triangular ducts for a range of Reynolds niimber from 1000 to 200,000 and ratios of surface to bvilk temperature from 1.2 to 2.3 are correlated accordingly in figure 4. A solid line representing data obtained in reference 1 with a circular test section having a length-to-diameter ratio of 60 for similar conditions is included for comparison. For Reynolds numbers greater than 10,000, the reference line represents equation (2)j for smaller Reynolds numbers the refer- ence line represents the data of reference 1 recomputed on the basis of the electric heat-input and heat-loss measurements for purposes of comparison. The data for the square tube (fig. 4(a)) agree well with the reference line for all surface to bulk temperature ratios and Reynolds numbers. For the rectangular duct having an aspect ratio of 5, the data (fig. 4(b)) are considerably higher than the reference line for Reynolds numbers from 1000 to 10,000 and are represented by equa- tion (2) for Reynolds numbers above 2500. The higher values are in agreement with data obtained for noncircular ducts at lower heat fluxes by other investigators. These data indicate that use of the hydraulic diameter does not result in correlation of data for various passage shapes in the laminar and transition flow regions. For Reynolds n\im- bers above 40,000 the data faJ.1 slightly below the reference line. In figure 4(c), the average heat-transfer coefficients for the triangular duct vary similarly to those obtained for the square duct. For Reynolds niombers above 10,000 the data were lower than the reference line by 5 to 15 percent and cotild best be represented by a line having a slope of 0.78 rather than 0.8. This difference in slope is also noticeable in figure 4(b) for the data of the rectangular duct for high Reynolds nvunbers. This variation in slope could be eliminated NACA RM E53J07 by defining the average surface temperature as the mldwall temperature instead of as the arithmetic average of the corner and midwall tempera- tures. For example (as is shown in fig. 7), the difference betveen the average surface and the average midwall temperatures for the triangular tube is 3 percent of the difference between the average midwall tempera- ture and the fluid bulk temperature for a Reynolds number of 10,000, and 11 percent for a Reynolds nimber of 100,000. Evaluating the average heat-transfer coefficient on the basis of the difference between the midwall and fluid bulk temperatures would result in a corresponding increase in the average heat-transfer coefficient axid, hence, would bring the data into agreement with the reference line for circular tubes. Measurements of the variation in rate of heat transfer around the periphery of noncircular ducts are required in order to define the average surface temperature for evaluating the average heat-transfer coefficient. Correlation of Friction Coefficients The method of calculating the average friction coefficient is es- sentially the same as described in reference 1, wherein ^ fr L PfV D 2g (3) where Apf-p = (Pi - Pg) Pf = (^ ® and t = - rg (r-i)H (§y rg (T-i)R & + 2T rg Cr-i)R {^' The subscripts 1 and 2 refer to positions within the ducts, located l/8 inch from the entrance and exit ends of the ducts, respectively. For Reynolds numbers less than 10,000 the exit static temperature tg is based on the value of the exit total temperature Tg determined from the electric heat-input and heat-loss measurements, as was men- tioned in the preceding section. MCA RM E53J07 The average friction coefficients as calculated above are shown in figure 5 correlated by the method summarized in reference 1 for high heat-flux conditions. Included for comparison is the line representing the K^rmAn-Nikuradse relation for turbulent flow in pipes modified for the effect of heat flux on the friction coefficient, which is 2 loeio (^^ '^M)- °-'^ <*' In figure 5(a), the average friction coefficients for the square duct for Reynolds numbers above 10,000 to 20,000 agree reasonably well with the reference line for circular tubes, although the friction coef- ficient increases with an increase in heat flux or surface to fluid bulk temperature ratio. In the transition region for low Reynolds num- bers, the friction coefficient varies considerably with heat flux. Similar variations were obtained in reference 1 for circular tubes. The data for the rectangular and triangular ducts (figs. 5(b) and (c), respectively) indicate that the friction coefficient increases more with increasing heat flux than in the square duct (fig. 5(a)), which may possibly be caused by the development of secondary flows in the rectangular and triangular ducts. Correlation of Peripheral Temperature Variations Corner surface temperatures were measured at three stations along the length of each test section (3, 12, and 21 in. from entrance). The average differences between the comer and midwall temperat\ires are plotted against the mass velocity in figure 6. The average difference plotted herein was taken as the arithmetic average of the differences between the local average comer and midwall temperatures at each sta- tion. In general, the local average peripheral temperature difference increased along the length of the test section; however, in several instances the local values near the exit were less than those measured at the center station, which indicates the possibility of locally de- veloped secondary flow near the comers. The average peripheral tem- perature differences increased at a decreasing rate with increases in mass velocity and heat flux. Maximiim values of 35°, 127°, and 110° R were obtained for the square, the rectangular, and the triangular ducts, respectively. In reference 3, a method was developed for predicting peripheral wall -temperature variations for flow in none ircular- tube heat exchangers with internal heat generation in the tube walls based on shear-stress 10 NACA RM E53J07 distributions measured by Nikuradse for flow in noncircular ducts. The average peripheral temperatiire differences are correlated accordingly in figure 1 , where the ratio of the difference between the corner and xhe midwall temperatirres to the difference between the surface (which was taken as the average midwall temperature) and fluid bulk tempera- tures is plotted against the dimensionless parameter, Nusselt number divided by the ratio of wall thickness to hydraulic diameter of the flow passage and the ratio of thermal conductivity of the wall mate- rial to the fluid (wherein the average heat-transfer coefficient is based on the difference between the average midwall and fluid bulk temperature). Included for comparison are the reference lines cal- culated for turbulent flow in the ducts from reference 3 for the case of no flow over the outer siirface of the duct; hence for the heat- transfer coefficient for the outer surface equal to zero. The data for the square duct agree fairly well with the predicted values in the turbulent-flow range. The measured values for the rectangular ajid triangular ducts were greater on the average by about 20 and 35 per- cent, respectively, than the predicted values. This difference in measured and predicted values results in part from the assumption of similarity between variation of rate of heat-transfer and sheax- stress distribution around the periphery of a noncircular duct and in part from the uncertainty in estimating the shear-stress distribution for a duct with aspect ratio of 5 from measurements obtained for a duct with aspect ratio of 3.5. Similar results are indicated for the tri- angular duct. Maximum values of the ratio of the average difference between the comer and midwall temperatures to the difference between the average sxirface and bulk temperatures obtained were 0.05, 0.25, and 0.20 for the square, the rectangular, and the triangular ducts, respectively. SUMMARY OF RESULTS The results of this investigation of heat transfer and pressure drop for air flowing through noncircular ducts having square, rectan- gular (aspect ratio, 5), and equilateral triangular cross sections for a range of surface temperatxu"e from 540° to 1780° R, corresponding surface to bulk temperature ratio from 1.2 to 2.3, and Reynolds num- bers from 1000 to 330,000 may be summarized as follows: 1. The effect of the ratio of surface to bulk temperature on cor- relations of the average heat-transfer axid friction coefficients was the same as that obtained in a previous investigation for similar rsjiges of conditions for flow in circiilar tubes and was nearly elim- inated by evaluating the physical properties and density of the air at a film temperature halfway between the bulk and surface temperatures. MCA RM E53J07 11 2. Correlations of the average heat-transfer and friction coeffi- cients were in reasonable agreement with the results obtained for the circular tubes with the Nusselt number and Reynolds nvimber based on the hydraulic diameter of the duct. 3. Correlation of the average peripheral temperature difference for the square duct was in agreement with values predicted by a pre- vious analysis. However, the measiired values for the rectangular and triangular ducts were greater by approximately 20 and 35 percent, respectively, than the predicted values. 4. Maximum values of the ratio of the average difference between the comer and midwall temperatures to the difference between the average s\irface and bulk temperatures obtained were 0.05, 0.25, and 0.20 for the square, the rectangular, and the triangular ducts, respectively. Lewis Flight Propulsion Laboratory National Advisory Committee for Aeronautics Cleveland, Ohio, October 9, 1953 REFERENCES 1. Humble, Leroy V., Lowdermilk, Warren H., and Desmon, Leland G. : Measurements of Average Heat-Transfer and Friction Coefficients for Subsonic Flow of Air in Smooth Tubes at High Surface and Fluid Temperatures. NACA Rep. 1020, 1951. (Supersedes NACA RM's E7L31, E8L03, E50E23, and E50H23. ) 2. Keenan, Joseph H., and Kaye, Joseph: Thermodynamic Properties of Air. John Wiley & Sons, Inc., 1945. 3. Eckert, E. R. G., and Low, George M. : Temperature Distribution in Internally Heated Walls of Heat Exchangers Composed of Noncircular Flow Passages, NACA RM E50J25, 1950. 12 NACA EM E53J07 o a Pi X Kl I © 0) P. bO I. eg bO c a NACA EM E53J07 13 a) I I ' §■ +> u 3 § o J3 B -H o CO 14 NACA EM E53J07 10X10 8 6 .06 .02 .01 Average surface Ratio of surface temperature, to "bulk fluid Tg, temperature, °R Tg/Tt A 680 1.2 V 890 1.5 O 1325 1.9 a 1780 2.3 / / r / / y y / / ^ t / / ■^ ^ / P^ < ^ J / rrl y /, ■f , < 9' -/ y T / •^ / <, y. f A <^ / ^A^ / y y/ '/ ^^^ f -4 ^ > ^ J .006 .01 .02 .04 .06 .08 .1 .2 .4 .6 .8 1 Rate of heat transferred to air, Wc (Tg - T-j^), Btu/hr (a) Square duct. Figure 3. - Heat balance. 4 6 8 10X10'* MCA EM E53J07 15 .6 .08 .06 .04 .02 -L\J i / ,/ f -B A ? > ^. -6 ,( ;^ r ^ S .4 .id ^ ^ '^ k leat Input - he -J / IT. -> .r^ ^ * -^ X > ' < / .08 ■*> ^ ■ ^^ .06 ^0 ii> ■^ /, 7 X y ^ /^J ^x m ^ ^' // .006 .01 .02 .04 .06 .08 .1 .2 .4 .6 .8 1 2 Rate of heat transferred to air, WCp(T2 - T-,^), Btu/hr (c) Triangular duct. 8 10X10* Figure 3. - Concluded. Heat balance. NACA EM E53J07 17 a o a; o 0. 600 400 200 100 80 60 40 20 10 /\ / ^ t. < / y ^ / lA <^ / A yL ^ ^A 0.8p^0.4- rdf ^Nusselt numter, Nu = 0.023Re /OIX \, ^^ f \ /^ Average surface Ratio of surface temperature, to bulk fluid Tg, temperature, °R Tg/T^ A 680 1.2 /, ^ \ \ f r i 7 o n 890 1.5 1325 1.9 1780 2.3 Circular duct (ref. l) / V t. n O n ^ .1 .6 .8 1 2 Reynolds number. Re, 4 6 PfVfcD 8 10 20 40X10^ (a) Square duct. Figure 4. - Correlation of heat-transfer coefficients for air flow in ducts with variable heat flux. Bellmouth entrance; inlet temperature, 535° R; properties of air evaluated at film temperature. 18 MCA EM E53J07 S S P. o 3 c Hi 600 400 200 100 80 ^Husselt number, Hu = 0.023Re ' Pr ' Average surface temperature , °R 670 890 1320 1710 Circular duct (ref . l) Ratio of surface to ■bulk fluid temperature, 1.2 1.4 1.8 2.1 .6 .8 1 2 Reynolds number. Re, 4 6 8 10 ^^f 20 40X10^ (b) Rectangular duct. Figure 4. - Continued. Correlation of heat-transfer coefficients for air flow In ducts with variable heat flux. Bellmouth entrance; inlet temperature, 535° R; properties of air evaluated at film temperature. NACA EM E53J07 19 3. 600 400 200 100 80 60 40 20 10 y / / / V y 4 yi^ 6^ ii A y \r y^A - Nusselt number, Nu = 0.023Re Pr ^\ A 6u 6 ^ » 1 / V p V O a 870 1.4 1175 1.9 1740 2.3 Circular duct (ref. l) ^ O^ O .,° A Q V D .08 .6 .8 1 2 Reynolds number. Re, 4 6 8 10 20 40X10' (c) Triangular duct. Figure 4. - Concluded. Correlation of heat-transfer coefficients for air flow in ducts with variable heat flux. Bellmouth entrance; inlet temperature, 535° R; properties of air evaluated at film temperature. 20 NACA EM E53J07 « o aj Id *^ 0 0) iH r-l Id Pi u W 0) (U >: +* < o< >on u -s 10 •P o t3 «3 d ■p Id u 0) 0) O -H to -P -P 0) c 4) tS •H 0) OS (U ■p ■P to o d •H Q) O 05 c t>» O -P •H tH 4J to a o rH o dj CO h > o o I >^ 1/3 Vi (U •H -S- ':).usTOfj;jaoD uoxq.Dfj;j NACA EM E53J07 21 (D U Oj Tj "s +^ <; o<] >Od o t3 cd o 0) K CO ■P tj • d (U C -p •rH aJ ^ U Is (U -P o >-. -P •H CO 0) o tJ CM H CO to o o C) o o u o o — 'q.usxD"pjjaoo uox^oxjj; ^J 22 NACA EM E53J07 ID U a ij -N tH -H 0) >H a fn =3 .-1 d to (h ■P P (d Eh O N •^ en tn ^3 (U 10 rH H H H l^a d B -p < O < >On # M C-) P H U • y a 0) o c -P •H al ^^ > (U o p. o M e CVl -p a) ^ •H o () t^^ +^ r-l cd to -p 13 •H eiJ <0 o d n -H rH ^ >« a! > Vi • Ch > » *v T) P 0) C -H K ^H O to o! •H C *s I-l P (U u d O Tj > to p tS ^ — ^ -H rH U O to O ^_^ •H O i-l & -P O a! to (D r-l -H 03 K o • !£> ^ 1) 4J •r) a) d 4) rH ^ O C 0) O H W 1 -H in > CO u a 0) ■H O -P h in <4-( 3 CV] -P Cf" OJ • CO (i to 01 i) '5 -p t^ u (D -P -i -P ClJ o^^ Td 1 ^c O fi H 0) CM H m H ft u S s -\ crt > OJ o d -P c* i-l ■s CO a! H >> h H O -P ^ — s 01 cd LO tH cd M > rH O V ■ ft o •H 0) ^^ %. bO (U 0) OS > ft u 0) (0 tp > O tfl O Oj O 05 r-l 2 C to O 3 ^ o ■P -H o > +? Ln gure 6. - velocity a pt, Ho '™I - ^i '3 3U3j;SJJTp 24 NACA EM E53J07 3 d ft Oh 130 120 110 100 90 80 70 60 50 40 30 20 10 y o / / / i / / / / / / / / h r / 1 / Average surface Ratio of surface temperature, to bulk fluid Tg, temperature, °R Tg/T^ A 670 1.2 V 990 1.4 <> 1320 1.8 n I'^IO 2.1 ^ / 1 / 1 p p / / ^^ / / P^ J X' If ^ y J /^ X 'i / i ] / 1 1 / i r / ____^ -— — ^ 1 / .^ n ^ J ^ ff ^ t^ %^ / ^ 50 100 150 200 250 Mass velocity, G, lb/(hr)(sq ft) 300 350X10-^ (b) Rectangular duct. Figure 6. - Continued. Variation of peripheral wall-temperature dif- ference with mass velocity at various average wall temperatures . NACA EM E53J07 25 120 110 100 100 150 200 250 Mass velocity, G, Yb/{bT){sq ft) (c) Triangular duct. Figure 6. - Concluded. 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