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Ind. Eng. Chem. Res. 1998, 37, 1560-1566
Convective Mass Transfer from Cylinders in a Jet Flow Turgay Pekdemir,*,† Thomas W. Davies,‡ and Osman N. Sara† Faculty of Engineering, University of Ataturk, 25240 Erzurum, Turkey, and School of Engineering, University of Exeter, Exeter EX4 4QF, U.K.
A photoevaporative mass-transfer measurement technique has been used to determine the convective mass-transfer behavior of stationary and rotating cylinders which were immersed in a two-dimensional jet of air. For a stationary cylinder, the circumferential distributions of the local mass-transfer rate were determined as a function of jet Reynolds number (45000-176000) and ranges of other parameters of practical importance (relative position of cylinder in jet (L/D) and relative size of cylinder and jet nozzle (d/D)). Circumferentially averaged values of the mass-transfer coefficient were estimated by integration and the results used to produce correlations for the mean Sherwood number. For a rotating cylinder immersed in the slot jet, circumferentially averaged values of Sherwood number were directly determined for a range of conditions similar to those used in the study of the stationary cylinder but with rotational speed as an additional variable. Predictions of the mean Sherwood number for cylinders drying in a slot jet have been made using a CFD package and are presented in the form of correlations. Introduction There are numerous examples of industrial processes in which convective heat/or mass transfer to or from cylinders and some convecting medium (usually air or water) plays an important part: drying of textiles, veneer, film materials and paper, cooling of glass, plastic, metal object of various sizes and shapes and parts of machinery, and maintenance of the temperatures of turbine blades below metallurgically allowed limits. The circumferential variation of heat/masstransfer coefficients as a function of flow Reynolds number for a cylinder in uniform cross-flow is striking and well-documented. Higher local convection rates are usually achieved when the fluid flow is in jet form, but the interaction of a cylinder with a jet flow is more complex and very dependent on the position of the cylinder within the jet, particularly in close proximity to the nozzle where the flow structure is changing rapidly. When designing such a system, it would clearly be of value to have available a correlation relating the surface Nusselt or Sherwood number to the principal independent variables of the configuration, namely the Reynolds number of the impinging jet flow, the wall Reynolds number of the cylinder (if the cylinder rotates), and its position relative to the origin of the jet. As far as the authors are aware, no such design data existed prior to the present study. There is much detailed information on the convective characteristics of jet flows impinging on flat stationary surfaces (Jambunathan et al., 1992) which may be adequate for the purposes of estimating the effect of similar jet flows impinging on stationary curved surface (Gau and Chung, 1991, (concave or convex)). An experimental study of a low-speed slot jet impinging on a slowly rotating cylinder showed little effect of surface rotation on the heat-transfer rate compared with a stationary system (Zhang and Wei, * To whom correspondence should be addressed. Fax and Telephone: +90 442 2331133. E-mail: tpekdemir@ rocketmail.com. † University of Ataturk. ‡ University of Exeter.
1986). Other experimental investigations of the stationary cylinders-in-slot jet system have reported the significant effects of parameters such as jet Reynolds number and relative nozzle/cylinder position and size (Schuh and Persson, 1964; Kumada et al., 1973). Theoretical studies of this system have been limited to laminar slot jet flow around a rotating cylinder (Chiou and Lee, 1993) and turbulent slot jet flow around a stationary cylinder (Kang and Grief, 1992) and are of no direct help in the design of systems which may span a wide range of geometries and jet/cylinder speeds. In many practical applications, other important design parameters exist, notably those due to the need to use multiple jets (which gives rise to jet interaction effects) and of course the need to use jet temperatures which are different from the surroundings and the impingement surface. Recently published work greatly assists the design engineer to predict the performance of multiple jet impingement systems (Journeaux, 1990, Polat, 1993; Goldstein and Seol, 1991; Huber and Viskanta, 1994; Seyedein et al., 1995). The experimental work reported in Journeaux (1990) and Polat (1993) clearly demonstrate that surface motion can begin to affect the impingement of a slot jet at surface velocities as low as 10% of the jet nozzle speed. The present work on a simple system was undertaken to acquire specific data on the convection rate from a cylinder rotating in a two-dimensional (or slot) jet. In this paper, we report only the results obtained for the cylinder when its axis and the longest axis of nozzle were parallel and in line (e.g., no offset [E/D ) 0] and normal impingement [φ ) 90°]). The data were to be used to validate CFD (computational fluid dynamics) predictions of the cooling rate of hot rotating cylinders subjected to impinging cold air jets at close range. The experimental mass-transfer system had a Schmidt number of 2 and a constant wall concentration boundary condition, so that a good analogue exists for gas-phase heat transfer at a constant wall temperature.
S0888-5885(97)00634-9 CCC: $15.00 © 1998 American Chemical Society Published on Web 03/03/1998
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Figure 1. Arrangement for measuring infrared reflectivity.
Figure 3. A schematic display of the experimental setup.
Figure 2. Comparison of the drying rate and the reflectivity change.
Experimental Details A photoevaporative mass-transfer measurement technique based on the infrared reflective properties of drying surfaces proposed by Utton and Sheppard (1985) has been established and validated by Pekdemir (1994). The essence of this technique is the direct relationship between the degree of wetness of certain absorbent surfaces and the reflectivity of visible or infrared light (IR). The convection surface of interest (the cylinder) is covered with chromatographic paper (surface roughness relative to cylinder diameter, ks/d ) 0.0014) and wetted with a volatile liquid (1-butanol). A small lowpower beam of IR is focused at a point on the surface (e.g., 1-mm diameter), and a detector monitors the decrease in reflected intensity as the paper is convectively dried (Figure 1). There is a simultaneous linear variation in both the reflected light intensity and moisture content with time in the constant drying rate period (Figure 2). Thus, it can be assumed that
dI/dt ) constant (dm/dt)
(1)
where dm/dt is the mass flux from the surface which can also be written as
dm/dt ) hm(Cs - C∞)
(2)
Assuming that C∞ ) 0 and with Cs ) PvM/RTs, then
hm ) (1/constant) (dI/dt)(RTs/PvM)
(3)
Thus, a measurement of the intensity change, dI/dt, can be used to determine the local mass-transfer coefficient, once the paper has been calibrated and the value of the calibration constant (1/constant) determined. The surface vapor pressure (Pv) of the evaporating liquid can be estimated from the Antoine equation if the wet bulb temperature of the paper (Ts) is measured at or near the point where the reflection is measured. In the present experiments, an array of nine miniature IR emitter/detectors alternating with nine thermocouples were positioned in a row inside a hollow cylinder (50cm long, 10-cm outer diameter, and 0.45-cm wall thick-
ness) and immediately underneath the paper coating which was glued to the surface of the cylinder (Figures 1 and 3). A detailed description and validation of the technique are given by Pekdemir (1994). A conventional open-circuit wind tunnel designed according to the recommendations in Pankhurst and Holder (1952) was used to generate the jet flow. Air was drawn into a contraction via a dust filter by two contra-rotating axial flow fans and then passed to a settling chamber via wire mesh screens from where the flow entered a contraction with an adjustable slot nozzle exit which produced the slot jet. The slot nozzle constructed from two sharp-edged blades had a fixed width (30.5 cm) parallel to the cylinder axis and variable height (maximum opening D ) 4.5 cm). The contraction ratio of the nozzle (inlet area/outlet area) was 6.8 with the nozzle fully open. The jet exit velocity (uj) could be varied in the range 4.5-27.5 ms-1. Velocity and the turbulence intensity distributions in the jet (with and without cylinder) were determined by hot wire anemometry. For the free slot jet, the distributions were similar to those reported by Corrsin (1969) and Gardon and Akfirat (1965) and the full results are given by Pekdemir (1994). The air temperature was measured using a thermocouple flush-mounted on the inner surface of the nozzle exit. The test cylinder was mounted on a traversing system, enabling the position and orientation of the cylinder relative to the jet exit to be determined accurately. The test cylinder was rotated by a direct current motor which was connected directly to the cylinder axle. The maximum rotational speed of the cylinder was 1000 rpm (surface speed ) 5.24 ms-1). The data from the IR sensors and thermocouples were collected using a data acquisition system consisting of an inner electronic board fixed on a shaft on the axis of the cylinder, an outer electronic board, an interface, and a personal computer (Figure 3). Having selected an experimental configuration (jet/cylinder geometry and rotational and jet speed) the paper was saturated with 1-butanol and readings were taken of the local light intensity and temperature at fixed time intervals (lowest 2 s) as the paper was convectively dried by the impinging air jet. Prior to each single mass-transfer measurement, the paper was freshly saturated. The time taken during the constant drying period varied from 50-1500 s, depending on the jet velocity. The sensitivity of the technique is not high enough to allow detection of the very rapid changes in the local mass-transfer rate as the sensor passes through the impingement zone. To simplify the experimental work, the system was isothermal (i.e., the nozzle air, the surrounding air, and the cylinder were all at the same (room) temperature).
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Simulation Procedure Convective heat-transfer behavior of a turbulent twodimensional jet flow impinging on a circular cylinder with a certain rotational speed uw were simulated by using a CFD computer package known as EasyFlow, which is based on a computer code, PHOENICS (Easy Flow User Manual, 1991), using a K- turbulence model. The cylinder wall was hot and the air jet was at ambient conditions to avoid complications in the calculations. The boundary condition chosen at the cylinder wall was at constant surface temperature so that a good analogy existed for a constant wall concentration boundary condition. The Chilton-Colburn analogy was assumed to apply. For the other details of the simulation procedure, please see Pekdemir (1994). Results
Figure 4. A comparison between the present circumferential mass-transfer measurement around a circular cylinder in a uniform cross-flow and those from the literature. Present: Re ) 2.39 × 104, Tu ) 0.6%, d/H ) 0.3, L/d ) 3.3, ks/d ) 1.40 × 10-3. Zukauskas (1972): Re ) 2.5 × 104, smooth. Goldstein and Karni (1984): Re ) 1.9 × 104, Tu ) 0.43%, d/H ) 0.0417, L/d ) 12, smooth.
The flow and mass-transfer characteristics of the rotating cylinder in the jet flow are represented by the rotational Reynolds number (Rew), the jet exit Reynolds number, (Rej), and the mean Sherwood number (Sh) which are defined as follows:
Rew )
uwdF , µ
Rej )
ujdF , µ
Sh )
and
( )
N hd dI/dt d )c (4) FsDAB I0 FsDAB
where uw is the cylinder surface velocity, uj the jet exit velocity, d the diameter of the cylinder, F the density of the free stream fluid, µ the dynamic viscosity of the free stream fluid, N h mean mass flux, Fs the density (concentration) of the vapor of the volatile liquid at the surface conditions, DAB the diffusion coefficient of the volatile liquid in air, c the paper calibration constant, dI/dt the slope of the constant drying section of the drying curve, and I0 the overall light intensity change. An error analysis was carried out for estimating the accuracy of the mass-transfer measurements. The result showed that the mass-transfer data could be in error up to 12%. The repeatability of the results was also investigated and it was shown that mass-transfer coefficient values could be repeatedly determined within 11% of the mean value. The results indicated that the flow was acceptably two-dimensional in the central part of the measurement region. The results reported below are those obtained with an axially central sensor and thus exemplify the behavior in the central two-dimensional region of the flow. The full results obtained from all the sensors evenly spaced along the length of the cylinder are given in Pekdemir (1994). Stationary Cylinders. To validate the experimental technique and to create a reference point, the masstransfer behavior of stationary cylinders in a uniform cross-flow of air and also in a slot air jet was studied by measuring the local evaporation of 1-butanol at the cylinder surface. The initial validation tests using a cylinder in a uniform cross-flow produced results which established confidence in the photoevaporative technique. Figure 4 shows a comparison of the circumferential variation of local Sherwood number for a cylinder in uniform cross-flow, determined by the authors, with other published data. The difference in the magnitude of the minima around 90° is attributable to the differences in the experimental conditions (e.g., free stream
Figure 5. The effect of the ratio of L/D on the circumferential Sherwood number distribution for a cylinder in jet flow, Rej ) 1.77 × 105, d/D ) 2.222.
turbulence (Tu), surface roughens (ks/d), wind tunnel blockage (d/H)) between these studies. Given the inevitable differences under which the measurements were made, the agreement was considered good enough to justify extension of the technique to the measurement of mass transfer from cylinders in jet flows of similar flow velocity but much higher turbulence levels. The mass-transfer characteristics of a stationary cylinder in a cross jet depend on system features such as the aerodynamics of jet flow (Rej), the position of the cylinder in the flow relative to the nozzle (L/D), and the size of the cylinder relative to the nozzle (d/D). To maximize heat or mass transfer, in the impinging jet system, it is well-known that the target surface must be within 6-8 nozzle diameters of the (round) nozzle exit (Martin, 1977). In this region of flow development, there exists an optimum combination of high turbulence level and high mean velocity (Pekdemir, 1994). The optimum position depends on the design of the nozzle, the shape of the nozzle exit, and the flow rate. The results obtained during the present study show considerable changes in circumferential distribution of local Sherwood number as the cylinder was moved along the streamwise axis of the jet (Figure 5). Close to the jet nozzle (i.e., in the potential core region), there is evidence of the Coanda effect (Pekdemir, 1994), creating a wall jet which diminishes or removes the recirculation zone. Further downstream the circumferential masstransfer rate resembles the classical pattern associated with the cylinder immersed in a uniform cross-flow, which is as one would expect. This positional effect was
Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998 1563 Table 1. Summary of the Convective Mass-Transfer Correlations Obtained in the Present Study for Different Flow Systems (The Relative Surface Roughness (ks/d) for All Cases Is Equal to 1.4 × 10-3) geometry
correlation equation
Correlations Obtained from the Experimental Data stationary cylinders in a uniform cross-flow Sh ) 0.0539Re0.771Sc1/3 stationary cylinders in a two-dimensional slot jet flow
Sh ) 0.1148Rej0.7081 Sh0 ) 0.7088Rej0.536(L/D)0.118(d/D)0.1443
rotating cylinders in still air
Sh ) 0.169Rew2/3
rotating cylinders in a two-dimensional slot jet flow
Sh ) 0.357Rej0.598
Sh ) 0.323Rej0.617 Sh ) 156.22(Rew/Rej)-0.6666(L/D)-0.1948 Sh ) 104.79(Rew/Rej)-0.6493(L/D)0.0015 Correlations Obtained from the Predicted Data stationary cylinders in a two-dimensional Sh ) 0.293Rej0.6374 slot jet flow Sh ) 0.033Rej0.8242
Figure 6. A comparison of the circumferential distribution of local Sherwood number around a cylinder between slot jet flows and a uniform cross-flow. Experimental details: present jet flow. Rej ) 1.75 × 105, L/D ) 6, d/D ) 3.75. Present cross-flow: Re ) 2.13 × 105, d/H ) 0.3, W/d ) 3.3 (here H is height and W width of the wind tunnel test section). Kumada et al. (1973): Re ) 1.99 × 105, L/D ) 4, d/D ) 3.75.
repeated at the different jet Reynolds numbers studied (45000-170000) and for different values of d/D (2.27.1). The optimum standoff distance between the slot nozzle and a stationary or rotating cylinder was found to be in the range 6 < L/D < 10. In contrast to some previous work (Schuh and Persson, 1964; Kumada and Mabuchi, 1986), no optimum value of d/D was observed. These two observations are probably linked to the range of d/D used in the present study. Examples of some of the data correlations arising from the present work are given Table 1. An example of the circumferential variation of the local Sherwood number is shown Figure 6, from which it will be noticed that the jet flow produces a less dramatic change in Shθ than that which occurs in uniform cross-flow. For any particular values of L/D and d/D, one can integrate the circumferential distribution data to obtain average Sherwood numbers which
restrictions 2.0 × 104 e Re e 2.5 × 105 d/H ) 0.3, Tu ) 0.6% 7.77 × 104 e Rej e 1.78 × 105 Sc = 2.0, L/D ) 6, d/D ) 2.222 7.77 × 104 e Rej e 1.78 × 105 Sc = 2.0, 2 e L/D e 10 2.222 e d/D e 10 1.0 × 104 e Rew e 1.0 × 105 Sc = 2.0, Gr = 2.0 × 106 5.0 × 104 e Rej e 1.7 × 105 3.3 × 103 e Rew e 2.29 × 104 Sc = 2.0, L/D ) 6 d/D ) 3.333, Gr = 2.0 × 106 1.7 × 105 e Rej e 2.7 × 105 others as above 0.057 e Rew/Rej e 0.333 8 e L/D e 16, d/D ) 3.333 Sc = 2.0, Gr = 2.0 × 106 1 e L/D < 8 others as above 2.0 × 102 e Rej e 1.7 × 104 L/D ) 6, d/D ) 2.222 1.7 × 104 e Rej e 4.0 × 105 others as above
Figure 7. A comparison of measured mean Sherwood number with correlations produced by using the measured data.
can than be correlated with the jet Reynolds number. This produces a series of correlation of the form Sh ) a(Re)n an example of which is given in Table 1. For similar cross-flow Reynolds number, the average Sherwood number for the jet flow system in the present experiments is lower than that for uniform cross-flow. Rotating Cylinders. The rotational speed expressed as a rotational Reynolds number (Rew) based on peripheral velocity was varied in the range 2200-80000. Various correlations for the mean Sherwood number (Sh) are given in Table 1 and in Figure 7 together with the experimental data. The results indicated that the effect of rotational speed on Sh was complex and varied with jet velocity. In the absence of the jet flow, Sh increased slightly with increasing Rew for smaller rotational speeds. The effect of rotation was negligible at higher jet Reynolds number (Rej) for Rew e 2.5 × 104 (200 rpm), indicating that the rotational speed was still below the critical velocity (Pekdemir, 1994) for this Rew range. A typical result is shown in Figure 8a. This
1564 Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998
Figure 8. (a) A comparison of the variation of Sh from a rotating cylinder with Rew in a two-dimensional slot jet flow of air with that in stagnant air. (b) Variation of Sh from a rotating cylinder in a two-dimensional jet flow with Rew for various Rej, L/D ) 6, and d/D ) 3.333.
figure indicates that the mass-transfer variation with Rew for a sufficiently small Rej (4.6 × 104) exhibits three different regimes: at very low Rew, up to (Rew/Rej) ) 0.15, Sh decreases with increasing Rew, indicating that the negative effect of rotation is more dominant than that of the positive effect. Beyond this region, up to (Rew/Rej) ) 0.55, Sh is independent of Rew as the positive and the negative effect of the rotation cancels each other out. For (Rew/Rej) g 0.55, Sh increases with increasing Rew because the positive effect of the rotation becomes more and more dominant. Figure 8b shows the variation of Sh with Rew for various Rej. It is seen from the figure that for Rej > 6.2 × 104 the three regimes identified above can no longer be observed. This is because at higher Rej the effect of the rotation on the mass transfer is negligible in comparison with that of the jet flow. Figure 9a shows a comparison of the variation of the mean mass-transfer with the free stream Reynolds number (Re∞) for a stationary cylinder in a cross-flow, a stationary cylinder in a jet flow, and a rotating cylinder in a jet flow. It is seen from the figure that for Re∞ < 6.0 × 104 a rotating cylinder with a higher rotational speed (1000 rpm) exposed to a jet flow system gives higher mass transfer than other flow systems. As the free stream Reynolds number increases, this behavior is reversed and for Re∞ g 1.3 × 105, it gives the smallest mass-transfer. In general, for Re∞ g 6.0 × 104, the mean mass-transfer performance decreases in the
Figure 9. (a) A comparison of Sh for a stationary cylinder in a cross-flow, a stationary cylinder in a jet flow, and a rotating cylinder of various rotational speeds in a jet flow. (b) The effect of the rotational speed on Sh for a rotating cylinder in a jet flow for L/D ) 6 and d/D ) 3.333.
order of a stationary cylinder in a cross-flow, a stationary cylinder in a jet flow, and a rotating cylinder in a jet flow. This means that although the jet flow systems give higher local transport coefficients in the impingement region, their overall mass-transfer performance is lower than that of a uniform cross-flow. The rotation of the cylinder causes a further decrease in the masstransfer performance of a jet flow system beyond a critical jet exit Reynolds number. This phenomena can be seen more clearly in Figure 9b where Sh from a rotating cylinder at various rotational speeds is plotted against the jet exit Reynolds number. It is seen from this figure that at smaller jet exit Reynolds numbers the smaller rotational speeds give lower Sh while at higher jet exit Reynolds numbers this behavior is reversed. This suggests that for a higher Sh from a rotating cylinder the rotational speed should be adjusted according to the range of the jet exit Reynolds number. The effect of rotation on impingement mass-transfer caused by a slot jet may be the result of large-scale interference by the rotating boundary layer with the impinging flow, such that the cylinder surface is shielded from the full effect of impingement by a blanket of recirculating fluid. It has been shown by Polat (1993) that with round impinging jets the circulating boundary layer flow is swept aside by a sufficiently strong impingement flow with the consequence of high convection rates. Validation of CFD Predictions. Figure 10a shows the variation of the predicted mean Sherwood number
Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998 1565
(2) The mean and stagnation point Sherwood numbers have been correlated as the function of flow and geometrical parameters, of which examples are given in Table 1. (3) The variation of the mass-transfer with Rew for a sufficiently small Rej undergoes three different stages: (i) for (Rew/Rej) e 0.15, Sh decreases with increasing Rew, (ii) for 0.15 < (Rew/Rej) e 0.55, Sh is independent of Rew, and (iii) for (Rew/Rej) > 0.55, Sh increases with increasing Rew. (4) In general, for Re∞ g 6.0 × 104, the mean masstransfer performance decreases in the order of a stationary cylinder in a uniform cross-flow, a stationary cylinder in a jet flow, and a rotating cylinder in a jet flow. (5) At smaller jet exit Reynolds numbers the smaller rotational speeds provide a lower mass-transfer rate, while at higher jet exit Reynolds numbers this behavior is reversed. This suggests that the rotational speed should be adjusted according to the range of the jet exit velocities. (6) CFD simulations of the effect of impingement flow and rotational speed showed a similar influence on average mass-transfer rates to those determined experimentally. Notation Figure 10. Comparison between predicted and measured data (a) for a stationary cylinder and (b) for a rotating cylinder.
with the jet exit Reynolds number in comparison with that of the experimentally obtained mean Sherwood number for a stationary cylinder. The small step displayed by the predicted data at about Rej ) 1.0 × 104 may be an indication of a change in the flow regime around the cylinder. Thus, the predicted Sherwood number curve may be divided into two sections (curve 1 and curve 2). The agreement between the predicted and the experimental mass-transfer results is very good. In case of the rotating cylinder a comparison of the predicted results with the experimental data is given in Figure 10b for various jet exit Reynolds numbers. The agreement between the experimental and predicted mass transfer seems to be reasonably good, but is better at the slower rotations in the case of lower jet exit Reynolds number and at higher rotational speeds in the case of higher jet exit Reynolds number. But in both stationary and rotating cylinder cases the differences between the experimental and the predicted data are within the experimental error range. Conclusions Convective mass-transfer characteristics of cylinders in a two-dimensional slot jet of air have been investigated by experimental measurements as well as by CFD simulations. The major conclusions derived are summarized below. (1) The mass-transfer characteristics of cylinders in jet flow are complex and significantly dependent on the geometrical (L/D, d/D) and flow (Rew, Rej) parameters. The optimum standoff distance was found to be in the range of 6 < L/D < 10, while no optimum value of d/D was observed.
C ) concentration of the volatile liquid (kg m-3) c ) calibration constant (kg m-2) D ) jet nozzle height (m) d ) diameter of the cylinder (m) DAB ) mass-diffusion coefficient of the solvent in air (m2 s-1) E ) offset between the cylinder axis and the jet symmetry plane (m) Gr ) Grashof number H ) wind tunnel test section height (m) hm ) local convective mass-transfer coefficient (ms-1) I ) intensity of reflected infrared light (V) I0 ) overall intensity change between completely wet and dry paper (V) ks ) averaged height of the surface roughness elements L ) the distance between the jet exit and the cylinder surface (m) M ) molar mass of the volatile liquid (kg mol-1) m ) volatile liquid mass content per unit area (kg m-2) N ) mass flux (kg m-2 s-1) Pv ) vapor pressure of the volatile liquid (kg m-1 s-2) R ) universal gas constant (8.314) (J mol-1 K-1) Re ) Reynolds number Sc ) Schmidt number Sh ) Sherwood number T ) temperature (°C) t ) time (s) Tu ) turbulence level (%) u ) velocity (ms-1) W ) wind tunnel test section width (m) Greek Symbols θ ) circumferential angle φ ) jet impact angle (deg) µ ) viscosity (kg m1 s-1) F ) density (kg m-3) Subscripts j ) jet nozzle exit conditions s ) surface conditions
1566 Ind. Eng. Chem. Res., Vol. 37, No. 4, 1998 w ) cylinder wall conditions ∞ ) free stream conditions 0 ) stagnation point conditions
Literature Cited Chiou, C. C.; Lee, S. L. Forced convection on a rotating cylinder with an incident air jet. Int. J. Heat Mass Transfer 1993, 36 (15), 3841. Corrsin, S. Investigation of flow in an axially symmetrical heated jet of air. NACA Wartime Reports, Series WR-94, 1969. Gardon, R.; Akfirat, J. C. The role of turbulence in determining the heat transfer characteristics of impinging jets. Int. J. Heat Mass Transfer 1965, 8, 1261. Gau, A. C.; Chung, C. M. Surface curvature effect on slot air jet impingement cooling flow heat transfer processes. J. Heat Transfer 1991, 113, 858. Goldstein, R. J.; Seol, W. S. Heat transfer to a row of impinging circular air jets including the effect of entrainment. Int. J. Heat Mass Transfer 1991, 34 (8), 2133. Huber, A. M.; Viskanta, R. Effect of jet-jet spacing on convective heat transfer to confined, impinging arrays of axisymmetric air jets. Int. J. Heat Mass Transfer 1994, 37 (18), 2859. Jambunathan, K.; Lai, E.; Moss, M. A.; Button, L. A review of heat transfer data for single circular jet impingement. Int. J. Heat Fluid Flow 1992, 13, 106. Journeaux, I. A. Impinging jet heat transfer and thermal deformation for calendar rolls. Ph.D. Thesis, McGill University, 1990. Kang, S. H.; Grief, R. Flow and heat transfer to a circular cylinder with a hot impinging air jet, Int. J. Heat Mass Transfer 1992, 35 (9), 2173.
Kumada, M.; Mabuchi, I.; Kawashima, Y. Mass transfer on a cylinder in the potential core region of two dimensional jet. Heat Transfer-Jpn. Res. 1973, 2 (3), 53. Martin, H. Heat and mass-transfer between impinging gas jets and solid surfaces. In Advances in Heat Transfer; Hartnett, J. P., Irvine, T. F., Eds.; Academic Press: New York , 1977; Vol. 13. Pankhurst, R. C.; Holder, D. W. Wind Tunnel Techniques; Pitman and Sons Ltd.: London, 1952. Pekdemir, T. Convective mass transfer from stationary and rotating cylinders in a jet flow. Ph.D. Thesis, University of Exeter, U.K., 1994. Polat, S. Heat and mass-transfer in impingement drying. Drying Technol. 1993, 11(6), 1147. Schuh, H.; Persson, B. Heat transfer on circular cylinders exposed to free jet flow. Int. J. Heat Mass Transfer 1964, 7, 1257. Seyedein, S. H.; Hasan, M.; Mujumdar, A. S. Turbulent flow and heat transfer from confined multiple impinging slot jets. Numer. Heat Transfer 1995, A27, 35. Utton, D. B.; Sheppard, M. A. The determination convective heat transfer using a new optical technique. Proc. Int. Centre Heat Mass Transfer 1985, 155. Zhang, X. L. W.; Wei, L. A study of heat transfer associated with the cooling of a horizontal rotating cylinder using air jet flow. 8th Int. Heat Transfer Conf. 1986, 3, 1265.
Received for review September 10, 1997 Revised manuscript received January 6, 1998 Accepted January 14, 1998 IE970634N
