Johnson, J. R., Choksi, N. M., Eubank, P. T., IND.ENG. CHEM.PROCESS DES. DEVELOP. 7, 34 (1968). Kays, W. M., in Knudsen, J. G., Katz, D. L., “Fluid Dynamics and Heat Transfer,” p 376, McGraw Hill, New York, 1958. O’Connor, T. J., Comfort, E. H., Cass, L. A., A I A A J . 4, 2026 (1966). Penner, S.S., “Chemistry Problems in Jet Propulsion,” Pergamon Press, New York, 1957. Priem, R. J., Heidman, M. F., ”Propellant Vaporization as a Design Criterion for Rocket Engine Combustion Chambers,” NASA TR R-67, 1960.
Ranz, W. E., Marshall, W. R., Chern. Eng. Prog. 48 (3), 141 (1952). Schlichting, H., “Boundary Layer Theory,” McGraw-Hill, New York, 1960. Skrivan, J. F., Von Jaskowsky, W., IND. ENG. CHEM. PROCESS DES. DEVELOP. 4, 371 (1965). Vasiliu, J., J . Aerosp. Sci. 29, 19 (1962).
RECEIVED for review April 13,1970 ACCEPTED July 27,1970
Average Heat Transfer Coefficients from Plasma Gases to an Internally-Finned Tube Engineering Correlations Richard J. Henry’ Aerospace Engineering Department, University of Connecticut, Storrs, Conn. 06268 An empirical correlation for average Nusselt numbers was determined for argon and nitrogen gases in a high-temperature or plasma state flowing through a water-cooled calorimeter with internal, longitudinal fins. Average Reynolds numbers, based on a gas-side hydraulic diameter of 0.0366 foot, ranged from 86 to 372, and the entrance gas temperature ranged from 1060” to 10,600”R.To evaluate the average fin heat transfer coefficients, an iteration calculation procedure together with a fin root effectiveness expression were used. Nusselt number values were correlated as a function of the Peclet number-geometry factor product and a viscosity correction ratio.
N u m e r o u s investigations have been published describing theoretical and experimental heat transfer studies using plasma gases, such as those of Emmons (1963), Skrivan and Jaskowsky (19651, and Johnson et al. (1968). The latter two have provided experimental data correlations on local heat transfer coefficients for the entrance sections of tubular elements. Results reported in this work extend the above-mentioned studies including the effect of internal fins on the average heat transfer process. This empirical correlation for laminar, plasma flow heat transfer has possible application for the scale-up design of finned heat exchangers used in chemical synthesis programs and plasma studies-e.g. calorimetric enthalpy balance for local or total energy. Apparatus and Measurements
The plasma generator, calorimeter, and associated instrumentation used in this experimental study were discussed in considerable detail by Henry (1970). Briefly, the generator system with head, ballasting resistor, and power supply was capable of continuously covering the range from 0.5 to 10.0 kW. Gas flow was measured by Present address, Deutsche Forschungs-und Versuchsanstalt fur Luft-und Raumfahrt, 7 Stuttgart-Vaihingen, Germany.
122
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a calibrated rotameter system having an accuracy of &2% of full scale. Steady, nonswirl gas flow was achieved through micrometer adjustments of the gas flow over the cathode electrode of the generator. A schematic diagram of the calorimeter is shown in Figure 1. Plasma efflux diameter from the generator was approximately equal to the inside diameter of the calorimeter. Hence, smooth flow transition resulted, with no abrupt area changes disturbing the flow pattern. Orientation of both generator and calorimeter was horizontal. Water coolant flow to the calorimeter was measured by a flowmeter whose accuracy was calibrated a t &2% of full scale. Temperature rise through the calorimeter was measured by means of a copper-constantan, A T thermocouple. Hence, the temperature rise was evaluated directly which eliminated errors accumulated by individually determining both inlet and exit coolant temperatures and then calculating the difference. Gas flow exiting from the calorimeter was restricted by an orifice. A single iron-constantan thermocouple located at the exit measured the gas temperature. When this thermocouple was traversed across the orifice diameter for all input power conditions, no significant temperature variation was noted. Temperature measurements from
WATER OUT
Figure 1 . Water-cooled calorimeter design with internal fins
FINS 14in
L
-
18in __
I
----
thermocouples located on the exterior of the calorimeter insulation indicated negligible heat loss to the environment.
and unfinned surfaces. Fin coefficients resulted from the heat balance condition
Correlation Method and Analysis
where evaluation of the fin coefficient required an iteration process using the fin root effectiveness expression given by Equations 6 and 7 . The total heat transfer, Q, was evaluated from the heat removed by the coolant flow, u',, and the temperature rise, A T < . The summation of gas-side surface areas, ZA, is given by
Heat Transfer Model. Convective heat transfer from the hot gas core to the water-coolant was limited by the energy flux through the gas boundary layer. Thus, heat transfer was controlled by the magnitude of gasside heat transfer coefficients. Temperature of the copper tube wall was essentially constant and assumed equal to that of the coolant. Forced convection contributed all the heat transfer, since radiation and conduction processes were neglected. Radiation calculations made using expressions determined by Barzelay (1966) and subsequently verified by Johnson et al. (19681, indicated that radiative contributions never exceeded 3% with maximum plasma temperatures in the heat transfer chamber of approximately 6500" K for argon and nitrogen gases. Correlation Procedure. The dimensionless variables selected in this analysis are related to the Graetz entrance heat transfer problem and are discussed by Bird et al. (1960). The average Nusselt number, NU, was assumed to be a function of the average Peclet number-geometry product, Pe & , L , and a viscosity correction term, F/ F ~ .Inclusion of the latter term satisfied the criteria of accounting for variation of transport properties from the average free stream to the wall temperature. c2
YIJ = C, Pe
J
-
c3
-
The first objective was to determine a single value of Cr which best represented the data correlation for each gas. Secondly, evaluation of Ci required a trial and error method such that the correlation was representative of both gases. And finally, C, was determined from the slope of the resulting curve fit. Equations. Average Nusselt numbers were determined from the fin heat transfer coefficients, hi,in the calorimeter
N u = h,&/K (2) where 1( is the gas thermal conductivity and h is the hydraulic diameter (0.0366 foot) weighted over the finned
(3)
E A = A , + A2
(4)
where A i is the unfinned entrance surface area (7.06 x lo-' ft'), and Al is the finned surface area
A?=@Aj+Ab
(5)
where Ai is the fin base surface area (8.16 X 10 ' ft') and Ab is the clear base area-z.e., remaining surface area not covered by fin attachment, 2.39 x ft2. The fin root effectiveness, a, is given by @ =
( N K , / & ) tanh (N1)
(6)
with
N
= (2
h,/K,6)'
(7)
where K , is the brass fin thermal conductivity (65 Btu/ hr f t OF),6 is the fin thickness (0.021 in.), and 1 is the fin length (0.394 in.). The logarithmic mean temperature difference, e,, was evaluated from 8, =
AT^ - AT2)/ln ( A T , / A T ? )
(8)
where A T 1 and A T 2 are the respective heat exchanger inlet and exit gas to coolant temperature differences; thus
AT, = Tg - T,, ATP = Tg - T ,
(9) (10)
where T , is the inlet gas temperature, T , is the exit gas temperature, T , is inlet water temperature, and T , is the exit water temperature. Gas properties in the Nusselt, Peclet, and viscosity ratios were evaluated using an average reference temperature based on an assumed exponential gas temperature decay from the inlet to the exit. This reference temperature was determined from
T = ( T g -, T,)/ln
(T,/T,)
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 1, 1971
(11) 123
Gas properties tabulated by Svehla (1962) as functions of temperature were used for argon and nitrogen. The Peclet number resulted from the Reynolds and Prandtl number product. Reynolds numbers were evaluated using the expression -
__
Re = mdh,lp A,,
l5
I
10 -
(12)
8 -
where m is the gas mass flow, p is the average gas viscosity and K,, is the cross-sectional area t o gas flow (weighted over the finned and unfinned surfaces, 3.4 x ft'). The Prandtl number values were determined from
6 -
-
4 -
where ZP is the average gas specific heat. The viscosity was determined using the gas viscoscorrection term, pL/pLiu, ity, p k , based on the average water coolant temperature.
3 -
Results
The effect of the particular plasma gas on the Nusselt number is shown in Figure 2. A least squares data fit for each gas yielded exponents whose best fit was C? = 0.93. Numerous viscosity correction exponent values were tried to achieve a common correlation for both gases. Best results were obtained when a value of C3 = 0.50 was used. The final correlation is shown in Figure 3. The leading coefficient (C, = 1.61) resulted from the best line fit of the total argon and nitrogen data. Final correlation results for argon and nitrogen plasma gases flowing in an internally-finned tube are I
2 -
Figure 3. Heat transfer correlation with internal fins for argon and nitrogen plasmas
0 0.93
V
- 0.50
where L is the calorimeter length (1.5 feet). Use of the common C2 = 0.93 exponent resulted in a reasonable data spread for both gases as is shown in Figure 2. However, when the viscosity correction was applied, this subsequently caused more argon data scatter
10
Argon Nitrogen
as shown by the 5 points clustered below the line fit in Figure 3. This resulted from an over-shift of these data caused by the extremely large, heat rejection rate which characterized the 5 points. Thus, higher inlet gas temperatures were evaluated resulting in larger (than normal) viscosity corrections. The range of variables measured for the two-gas correlation is summarized in Table I. All data were recorded for a 1.0 atmosphere pressure system. Discussion
The final correlation (Equation 14) was compared with the commonly quoted, unfinned Sieder and Tate equation,
8
0 14
6 where the subscript B represents a bulk reference temperature for evaluation of properties. Three differences were apparent: the leading coefficient and the exponents on both the Peclet and viscosity correction terms. Two
4
3
Table 1. Range of Measured and Calculated Results
2
Variable
1.5
2
1
3
4
6
8
ped, / L Figure 2. Effect of plasma gas on heat transfer correlation 0 Argon
V 124
Nitrogen
Ind. Eng. Chem. Process Des. Develop., Vol.
10, No. 1, 1971
Argon
Gas m a s flow Inlet gas temp. Fin coefficient
rk (1bJhr) 3, (" R)
Nusselt number Reynolds number Peclet number Heat transfer
Nu
hi (Btuihr ft2 F)
Re
Pe Q(Btu/hr)
Nitrogen
1.22-2.61 1770-10.600
1.46-1.87 1060-8460
1.35-3.21 1.92-6.17 86-277 57-189 225-2680
4.52-5.90 3.42-10.10 121-372 69-256 382-3900
of these differences can be accounted for; that is, use of the respectively defined reference temperature balances the effects associated with the leading coefficient and viscosity correction exponent. The remaining difference stems from the exponents on the Peclet term. One possible solution for this difference is given in an article by Incropera and Kingsbury (1969). There was doubt expressed as to the feasibility of achieving a general heat transfer correlation because of the strong effects caused by varying entrance velocity and temperature profiles. Because of the presence of the internal fins in this work, there may have resulted differing entrance conditions which probably caused higher turbulence level in the tube. Hence, greater heat transfer would result in a larger exponent on the Peclet term. One final feature of this finned, heat transfer correlation was that by using both the same plasma source and downstream heat exchanger during all runs, it was possible to obtain a single correlation for two different molecularbased plasma gases.
this study. Computations related to data reduction were performed at the DFVLR facilities, Stuttgart, Germany. literature Cited Barzelay, M. E., Amer. Inst. Aeron. Astronaut. J . 4, 815 (1966). Bird, R . B., Steward, W. E., and Lightfoot, E. N., “Transport Phenomena,” p 399, Wiley, New York, 1960. Emmons, H. W., “Modern Developments in Heat Transfer,” W. E. Ibele, Ed., pp 401-78, Academic Press, New York, 1963. Henry, R. J., Ph.D. thesis, University of Connecticut, Storrs, Conn., 1970. Incropera, F. P., Kingsbury, R . L., Int. J . Heat Mass Transfer 12, 1641-59 (1969). Johnson, J. R., Choksi, N. M., Eubank, P. T., IND.ENG. DES. DEVELOP.7, 34-41 (1968). CHEM.PROCESS Skrivan, J. F., von Jaskowsky, W., IND. ENG. CHEM. PROCESS DES. DEVELOP.4, 371-9 (1965). Svehla, R. A., N A S A T R . 132, 1962.
Acknowledgment The author wishes to thank Robert Lester, who constructed the calorimeter and aided in recording data for
RECEIVED for review April 24, 1970 ACCEPTED August 4, 1970
Kinetics of the Hydrodenitrification of Pyridine Howard G. Mcllvried Gulf Research & Development Co., P . 0. Drauer 2038, Pittsburgh, Pa. 15230 The hydrodenitrification of pyridine involves successive conversion to piperidine, to n-pentylamine, and finally to ammonia. To elucidate the kinetics of this reaction, three sets of runs were made in a bench scale, fixed-bed, flow reactor feeding, respectively, solutions of n-hexylamine, piperidine, and pyridine in mixed xylenes. Nitrogen concentration in the feed ranged from 100 to 51 15 ppm. The catalyst was 2.25% nickel, 1.25% cobalt, a n d 1 1 % molybdenum supported on alumina and was presulfided before use. All runs were made at 600°F; pressure was varied from 750 to 1500 psig. Denitrification of n-hexylamine was so rapid that at all times the concentration of amine in the system would be too low to affect the overall kinetics of pyridine denitrification. Denitrification data obtained with piperidine fit a Langmuir-Hinshelwoodtype kinetic model. This rate expression was then used to develop an equation which fit the data for pyridine denitrification. With pyridine, the rate of hydrogenation to piperidine was very fast compared to the rate of piperidine denitrification.
N
itrogen compounds are almost universally present in naturally occurring hydrocarbons and must, therefore, be reckoned with in the refining of these materials. Not only does their presence impart undesirable characteristics to many finished products, but their basic nature makes them effective poisons for the acidic catalysts used in such processes as catalytic reforming and hydrocracking. I t is. therefore. frequently necessary to remove nitrogen from refinery streams. This is most often accomplished through hydrodenitrification in which the nitrogen in the oil is converted t o ammonia which is easily separated from the product.
I n spite of the importance of this process. few comprehensive investigations of hydrodenitrification kinetics have appeared in the literature. Rosenheimer and Kiovsky (1967) found the denitrification of diesel fuel t o be first order in nitrogen content and second order in hydrogen partial pressure. Cox (1961) studied the denitrification of pyridine and a number of pyridine derivatives. In general, he found first-order kinetics to hold. but the apparent first-order rate constant decreased in magnitude as the nitrogen content of the feed increased. In a study of furnace oil denitrification. Somers (1965) found the rate to be first order in nitrogen content and first order Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 1, 1971
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