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Free convection heat transfer from a horizontal fin attached cylinder between confined nearly adiabatic walls
Experimental Thermal and Fluid Science 34 (2010) 177–182
Contents lists available at ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Free convection heat transfer from a horizontal fin attached cylinder between confined nearly adiabatic walls Amir Abbas Rezaei a,*, Masoud Zia basharhagh a, Touraj Yousefi b a b
Khajeh Nasir Toosi University of Technology, Tehran, Iran Razi University, Kermanshah, Iran
a r t i c l e
i n f o
Article history: Received 13 December 2008 Received in revised form 12 October 2009 Accepted 12 October 2009
Keywords: Natural convection Fin attached cylinder Confining walls interferometry
a b s t r a c t Steady state two-dimensional free convection heat transfer from a horizontal, isothermal fin attached cylinder, located between nearly two adiabatic walls is studied experimentally using a Mach–Zehnder interferometer. Effects of the walls inclination angel (h) on heat transfer from the cylinder is investigated for Rayleigh number ranging from 1000 to 15,500. Two cylinders with different diameters of D = 10 and 20 mm are used to cover wide Rayleigh range. Results indicate that, heat transfer phenomena differ for different Rayleigh number. For Rayleigh numbers lower than 5500, heat transfer rate from cylinder surface is lower than the heat transfer from a single cylinder. In this range by the use of walls, heat transfer from the cylinder decreases slightly and walls’ inclination does not change heat transfer rate from the cylinder surface. For Rayleigh number ranging from 5500 to 15,500, amount of heat transfer from the cylinder surface is less than that of a single cylinder. However, by adding nearly adiabatic walls to experimental model heat transfer mechanism differs and chimney effect between fin and walls increases the heat transfer rate from the cylinder surface. By increasing the walls inclination angel from 0° to 20°, the chimney effect between walls and fin diminishes and heat transfer rate from the cylinder surface is approaching to the heat transfer rate of fin attached cylinder without adiabatic walls. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction Free convection heat transfer from a horizontal, isothermal fin attached cylinder placed between two nearly adiabatic walls has various applications in industry. In many applications, electronic components can be cooled using a conductive fin. Understanding of the influence of conductive fin and placing component between two adiabatic walls is important for electronic devices design application. All modes of free convention from a horizontal cylinder in a quiescent, infinite fluid have been studied extensively and well established correlations are available in the literature [1–5]. The effect of adiabatic confining walls on the heat transfer coefficient from a circular cylinder has been studied by some researchers [6–10]. But the available information on fluid flow and heat transfer from a heated fin attached cylinder between two adiabatic walls is very limited. The model geometry of the present investigation is shown in Fig. 1. One fin attached cylinder of diameter (D) and length (l) are located between two nearby adiabatic ceiling. One of the closely related studies for a fin attached horizontal cylinder has been done by Facas and Brown [11]. In this work they studied the effect of longitudinal fins on overall heat transfer from * Corresponding author. E-mail address: [email protected] (A.A. Rezaei). 0894-1777/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2009.10.007
the cylinder. They studied numerically effects of axisymmetric fins around the cylinder perimeter. It was found that the overall heat transfer from the cylinder increases and it relates to fins parameters. Abu-Hijleh [12], studied numerically forced convection heat transfer from an equally spaced fined cylinder for Reynolds number ranging from 1 to 200. They showed that there is an optimum configuration for fins and also optimum number of fins. Moreover, short fins decrease the amount of heat transfer from the cylinder surface. Conjugate numerical solution of laminar free convection about a horizontal cylinder with longitudinal fins has been carried out by Halder et al. [13]. Fins alone contributed extremely small to the overall heat transfer but they greatly influence the heat transfer from the cylinder. The rate of heat transfer was above that for the free cylinder just when the attached fins were very thin. For thin fins, there existed a fin length, which maximized the rate of heat transfer. The optimum number was obtained as 6 when fin thickness was the thinnest among those investigated in that study. Objective of the current study is to find local and average free convection heat transfer rate from a horizontal isothermal fin attached cylinder located between two nearly adiabatic walls. Experiments are performed for different walls inclination angel (h) and Rayleigh numbers. The walls height is (l W) which W is chosen to be three times the cylinders diameter. It is considered
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Nomenclature D g h h k l Nu Nu P r Ra
cylinder diameter (m) gravitational acceleration (m/s2) heat transfer coefficient (W/m2 k) average heat transfer coefficient (W/m2 k) thermal conductivity of air (W/m k) cylinder length (m) Nusselt number average Nusselt number pressure (Pa) radius (m) Rayleigh number based on cylinder diameter
to be very low conductive to act as an adiabatic boundary condition. The cylinder is heated to a temperature (Ts) and is located in air with ambient temperature (T1). A Mach–Zehnder interferometer is used to observe temperature field. Experiments are performed in air for cylinder diameter of 10 and 20 mm, and walls inclination angel (h) differs from 0° which is vertical condition to 20°. The horizontal space between cylinder and walls is about half of the cylinder diameter and the Rayleigh numbers range is 1000 < Ra < 15,500.
2. Experimental setup 2.1. Experimental apparatus To observe the temperature field around an electrically heated fin attached cylinder, which is located between two nearly adiabatic plates as walls, a Mach–Zehnder interferometer is used. In order to obtain the range of 1500 6 Ra 6 3000, hollow cylinder of 10 mm OD and 160 mm long and for Rayleigh number ranging from 5500 to 15,500, hollow cylinder of 20 mm OD and 340 mm long is used. A thin rod Ni–Cr spiral heater ðXtot ¼ 80 ohmsÞ was inserted at the core of the cylinder. To increase thermal conductivity between the tube and the heater, the hollow tube was filled with magnesium oxide powder. To eliminate 3D effects, length of the cylinders was chosen about seventeenth times the cylinder diameter to eliminate end flows. Cylinders structure was explained by Ashjaee et al. [14]. The walls are made by one layer insulation. The one layer was constructed from fiber bone sheet with dimensions 180 mm length along cylinders’ length and 35 mm width for slim cylinder and 380 mm length with 70 mm width for thick cylinder. Both sizes have 10 mm thickness. The corresponding overall thermal conductivity of walls was about 0.05 W/m K [20]. The walls width is about
Fig. 1. Model geometry of a fin attached cylinder confined by inclined walls.
T
temperature (K)
Greek symbols X heater electrical resistance (ohm) h walls inclination angel (°) U angle from stagnation point (°) Subscripts 1 ambient condition f film condition s at the cylinder surface
three times and half of the cylinders diameter to be the same size of the conductive fin and make a channel between fin and walls. Cylinders are heated by electrical power. Ambient temperature, reference and cylinders’ surface temperature are measured by Ktype thermocouples [14]. Two complicated positioning systems are used to align the walls and three linear positioners are used to align cylinders as shown in Fig. 2. 2.2. Interferometer A 10 cm diameter beam Mach–Zehnder interferometer (MZI) was used to measure the temperature field in the air surrounding the cylinder. [14]. All interferograms captured by ‘‘ARTCAM-320P”. Camera was connected to a PC, and by using video recorder software, interferograms captured online. In order to recognize the cylinder surface specific position, temperature differences between cylinder surface and ambient temperature are chosen to result in a constructive fringe which is attached to the cylinder surface. This temperature difference varied from 15 °C to 70 °C. Cylinder surface are smoothed with ±0.001 mm roughness and thermal emissivity of 0.05. More details of Mach–Zehnder interferometer, cylinder position and arrangement are described in [14]. The cylinders are supported by fine rods as illustrated in Fig. 2. 2.3. Data reduction To calculate local and average Nusselt numbers for the cylinder at a certain cylinder-to-ceiling spacing and Rayleigh number, data
Fig. 2. Experiment setup.
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179
processing are made by the method explained in literature [14] and explained in [14,18,19]. Equating the heat transferred by convection to the heat transferred by conduction in air at the cylinder surface, following expression for the local Nusselt number will result:
Nuh ¼
D ks dT dr r¼r s
ð1Þ
ðT s T 1 Þ kf
The average Nusselt number is calculated by integrating the local Nusselt numbers using Simpson’s rule.
h ¼ 1=p
Z p
hh dh;
Nu ¼ h D=kf
ð2Þ
0
In order to validate the experiments and data reduction method, an individual hot cylinder is tested in infinite medium for Ra = 1000 and results of heat transfer are compared with available relations [14]. Excellent agreement between results was observed as described in [14].
Fig. 3. Interferograms around an unconfined fin attached cylinder for (a) Ra = 3000, (b) Ra = 2000, (c) Ra = 1000.
2.4. Uncertainty analysis Analysis of uncertainty is required in order to evaluate the quality of experimental data [15]. For any measurement which results depend on uncorrelated input estimates, the standard uncertainty of the measurement can be obtained by appropriately combining the standard uncertainties of these input estimates [16–17]. Table 1 lists the experimental values of parameters in Eq. (1) and associated uncertainties for Ra = 3000, and when the cylinder is not confined by walls. Uncertainties of the parameters T1, Tw, P1, l, D can be estimated from the precision of measuring devices. Our measuring equipment is caliper, and it is able to read 0.05 mm and temperature is measured by K-type thermocouple with 0.2 K accuracy. The uncertainty of the parameter Dr, which is the difference in radial distance from the cylinder surface, is related to the precision of reading the digitized interferograms. From Table 1, it can be seen that the later is the dominant source of error. The uncertainties in the average Nusselt numbers for the mentioned Rayleigh number and test geometry is 3.42%. Using this analysis, uncertainties in the measured local Nusselt number has been estimated to be less than 5.87 ± 2.1%. 3. Results and discussion In many practical applications, horizontal fin attached cylinder can be seen in various electrical devices and different electrical components. In this simulation, cylinder is hanged parallel to large beam such as illustrated in Fig. 3. The cylinder length is equal to walls length. In this study effects of geometrical parameters and Rayleigh number on fluid flow and heat transfer from the fin attached cylinder have been investigated experimentally. The physical model of the present study is composed of one hollow, aluminum cylinder with a brass fin attached to it. For confined
Table 1 Deviation of each quantity for computing Nusselt number, Eq. (1).
a
Parameter
xi
dxi
@Nuh dxi @xi Nuh
Tw T1 P1 l D Dr
360.95 K 299.45 K 88,000 Pa 160 mm 10 mm 0.35–1.6 mma
0.1 K 0.1 K 100 Pa 0.025 mm 0.025 mm 0.027 mm
0.1–0.2 0.15–0.2 0.08–0.04 0.01–0.003 0.15–0.04 4.7–1.1
0.35 and 1.6 are radial distance differences for h ¼ 0 ; 180 .
(%)
configuration such as illustrated in Fig. 1, the walls inclination angel varied from 0° to 20° with respect to the vertical orientation, for Rayleigh numbers ranging from 1500 to 15,500. According to Sadeghipour and Razi [9], for a single cylinder between two confining walls, by increasing the distance between cylinder and neighboring wall, at first Nusselt number increased. By increasing the distance more than the optimum value, Nusselt number decreased again. This amount of optimum distance between walls is about two and half times of the cylinder diameter. To prevent the Nusselt number increase because of this optimum value, the distance between walls is less than two times of the cylinder diameter. The small distance between walls, entrap the rising plume between adiabatic walls and conductive fin; make a chimney effect on top of the cylinder especially for high Rayleigh number. Fig. 3 indicates infinite fringe interferograms for the Rayleigh numbers of 1000, 2000 and 3000 for unconfined cylinder. All the interferograms indicate that thermal plume resulted from the cylinder surface rises vertically close to the fin. Because of the fin existence right on top of the cylinder, cylinder raised plume faces a no slip boundary condition on top of the cylinder and this type of boundary condition is a great barrier for its velocity for such Rayleigh number. When there is not any fin on top of the cylinder, raised plume from right and left sides of the cylinder intricate on top of the cylinder. So, plume combination increases the plume velocity on top of the cylinder, and adding a fin on top of the cylinder eliminates this kind of enhancement. By adding nearly adiabatic walls to the fin attached cylinder configuration, a chimney type channel is created between walls and fin. So the chimney effect in the channel increase the velocity of raised plume from the cylinder and reduce the fringe distance on top of the cylinder, it also increases the heat transfer from the cylinder surface. By increasing the walls inclination angel from 0° to 20°, Nusselt number goes to the value of Nusselt number for an unconfined fin attached cylinder. Also, the surface temperature of the conductive fin is more than ambient. The temperature difference between fin surface and ambient air pull the ambient cold air and lower the boundary layer thickness on the cylinder surface. This phenomena increase the heat transfer and Nusselt number on the cylinder surface in comparison to the unconfined configuration. This effect is very obvious just for Rayleigh number more than 5500 because for this range of Rayleigh number the raised plume from the cylinder surface is strong enough to penetrate into the distance between fin and adiabatic walls. Figs. 4 and 5 show infinite fringe interferograms of confined cylinder between two walls, for the Rayleigh numbers of 1000, 2000 and 3000.
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Fig. 4. Interferograms around a confined fin attached cylinder between vertical walls for (a) Ra = 3000, (b) Ra = 2000, (c) Ra = 1000.
Fig. 6. Variation of local Nusselt number for various inclination angel (Ra = 7500).
Fig. 5. Interferograms around a confined fin attached cylinder between inclined walls for (a) Ra = 3000, (b) Ra = 2000, (c) Ra = 1000.
Raised plume of the cylinder surface enters the space between walls and fin, so a developing flow generates and velocity in this channel increases. This flow exits the hot plume of the cylinder easier and cooler air enters the channel inlet faster. In order to compute heat transfer rate from cylinder surface, heat flux is determined by the method discussed in Section 2.3, and Nusselt number is calculated from relation (1). To investigate the effects of velocity induction on heat transfer from the centered cylinder, the value of local Nusselt number has been plotted versus u on the half of the cylinder surface in Figs. 6 and 7. These graphs are plotted for confined and unconfined cylinder, Ra = 7500, 15,500 and h = 0°, 10°, 20°. It can be observed that for the unconfined cylinder the local Nusselt number trend by circumferential angel u is very similar to the local Nusselt number trend on an individual cylinder. However, the amount of local Nusselt number for the upper portion of the cylinder is lower than the value of local Nusselt number for the same location around an individual cylinder. For the value of the Rayleigh number less than 3000, the local Nusselt number trend is similar to the unconfined cylinder configuration. But, by increasing the Rayleigh number from 5500 to 15,500, local Nusselt number trend around the cylinder surface differs from the unconfined cylinder case. For this range of Rayleigh number, it is obvious that air velocity increases because of the developing flow between adiabatic walls and conductive fin. An increase in local Nusselt number value is shown in Figs. 6 and 7 for 40 < u < 110 and that is because of velocity raise at the channels inlet. By increasing the walls inclination angel from 0° to 20°, local Nusselt number graph around the cylinder become very similar to the local Nusselt number trend of an individual cylinder. Because by increasing the inclination angel, walls base distance from
Fig. 7. Variation of local Nusselt number for various inclination angel (Ra = 15,500).
the cylinder become larger. So, there is not any chimney flow between adiabatic walls and conductive fin, and flow field around the cylinder is very similar to the flow field of an unconfined cylinder. Thermal and velocity boundary layers are smaller than spacing between walls and cylinder. So, by increasing the walls inclination angel, walls distance from the cylinder become much more than the cylinder boundary layer thickness and do not affect the heat transfer rate from the cylinder surface. All the local Nusselt number graphs are from u = 0° to 170° and it is because of the fin orientation on u = 180°. Because the hot plume of the cylinder moves upward close to the fin surface, there is not a high Nusselt number region at the fin base. Fig. 8 represents the variation of average Nusselt number around the fin attached cylinder for confined and unconfined case and various Rayleigh numbers. As illustrated in this figure, average Nusselt number of the cylinder for confined and
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unconfined cases are very close to the average Nusselt number of the an individual cylinder for Rayleigh number ranging from 1000 to 3000. This amount of difference between fin attached cylinder Nusselt number value and individual cylinder Nusselt number is very little. However, by increasing the Rayleigh number, the average Nusselt number tendency with Rayleigh number changes. For Rayleigh number ranging from 5500 to 15,500, the difference between confined cylinder and unconfined cylinder become obvious. By increasing the Rayleigh number from 5500 to 15,500 it can be seen that average Nusselt number of the confined cylinder with vertical walls goes farther than an unconfined cylinder and an individual one. By increasing the walls inclination angel Fig. 8 shows that the average Nusselt number of the cylinder approaches to that of a single cylinder. It is rea-
181
son was explained before. This result is in agreement with the study of Sadeghipour and Razi [9] because the walls distant is in the region that the average Nusselt number of the cylinder is lower than that of an individual cylinder. Variation of average Nusselt number around the centered cylinder divided by Nusselt number for an individual cylinder (Nuave/ Nu1) for unconfined cylinder and confined cylinder between vertical walls for various Rayleigh numbers is determined and illustrated in Fig. 9. Average Nusselt number of an individual cylinder is calculated from the correlation presented by Morgan [3]. It can be indicated that for all configurations, the average Nusselt number of the centered cylinder is lower than that of an individual cylinder due to the no slip boundary condition of the conductive fin and distance between adiabatic walls. 4. Conclusion Laminar free convection from a horizontal fin attached cylinder which is confined between two nearly adiabatic walls is studied experimentally. Experiments are carried out using Mach–Zehnder interferometer for different walls orientation and Rayleigh numbers. 1. The experimental data showed that the average Nusselt number is lower than individual cylinder’s Nusselt number. 2. By putting the confining walls close to the cylinder the average Nusselt number of the cylinder increases.
Acknowledgement Special thanks to Mrs. Forough Nezam for editing this paper. References
Fig. 8. Variation of average Nusselt number versus Rayleigh number for different inclination angel.
Fig. 9. Variation of normalized average Nusselt number versus Rayleigh number for different inclination angel.
[1] T.H. Kuehn, R.J. Goldstein, Numerical solution to the Navier–Stokes equations for laminar natural convection about a horizontal isothermal circular cylinder, International Journal of Heat and Mass Transfer 23 (1980) 971–979. [2] T. Saitoh, T. Sajiki, K. Maruhara, Bench mark solution to natural convection heat transfer problem around the horizontal circular cylinder, International Journal of Heat and Mass Transfer 36 (1993) 1251–1259. [3] V.T. Morgan, The overall convective heat transfer from smooth circular cylinders, Advances in Heat Transfer 11 (1975) 199–264. [4] S.W. Churchill, H.H.S. Chu, Correlating equations for laminar and turbulent free convection from a horizontal cylinder, International Journal of Heat and Mass Transfer 18 (1975) 1049–1053. [5] J.V. Herraez, R. Belda, A study of free convection in air around horizontal cylinders of different diameters based on holographic interferometry. temperature field equations and heat transfer coefficients, International Journal of Thermal Science 41 (2002) 261–267. [6] G.F. Masters, Natural convection heat transfer from a horizontal cylinder in the presence of nearby walls, Canadian Journal of Chemical Engineering 53 (1975) 144–149. [7] S. Sparrow, D. Pfeil, Enhancement of natural convection heat transfer from a horizontal cylinder due to vertical shrouding surface, ASME Journal of Heat Transfer 106 (1984) 124–130. [8] F. Karim, B. Farouk, L. Nnmer, Natural convection heat transfer from a horizontal cylinder between vertical confining adiabatic walls, ASME Journal of Heat Transfer 108 (1986) 291–298. [9] M.S. Sadeghipour, Y.P. Razi, Natural convection from a horizontal cylinder: the optimum distance between the confining walls, International Journal of Heat and Mass Transfer 44 (2001) 367–374. [10] M.A. Atmane, V.S.S. Chan, D.B. Murray, Natural convection around a horizontal heated cylinder: the effects of vertical confinement, International Journal of Heat and Mass Transfer 46 (2003) 3661–3672. [11] G.N. Facas, H.L. Brown, Natural convection from a cylinder with multiple lowconductivity, longitudinal baffles, International Journal of Heat and Mass Transfer 39 (1996) 2077–2086. [12] B. Abu-Hijleh, Numerical simulation of forced convection heat transfer from a cylinder with high conductivity radial fins in cross-flow, International Journal of Thermal Sciences 42 (2003) 741–748. [13] S.C. Haldar, G.S. Kochhar, K. Manohar, R.K. Sahoo, Numerical study of laminar free convection about a horizontal cylinder with longitudinal fins of finite thickness, International Journal of Thermal Sciences 46 (2007) 692–698.
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[14] M. Ashjaee, A.H. Eshtiaghi, M. Yaghoubi, T. Yousefi, Experimental investigation on free convection from a horizontal cylinder beneath an adiabatic ceiling, Experimental Thermal and Fluid Science 32 (2007) 614–623. [15] P.L. Teoch, B. Shirinzadeh, C.W. Foong, G. Alici, The measurement uncertainties in the laser interferometry-based sensing and tracking technique, Measurement 32 (2002) 135–150. [16] S.J. Kline, F.A. McClintock, Describing experimental uncertainties in single sample experiments, Mechanical Engineering 75 (1953) 3–8.
[17] R.D. Flack, Mach–Zehnder interferometer errors resulting from test section misalignment, Applied Optics 17 (1978) 985–987. [18] W. Hauf, U. Grigull, Optical methods in heat transfer, advances in Heat Transfer, Academic Press, New York, 1970. [19] E.R.G. Eckert, R.J. Goldstein, Measurements in Heat Transfer, second ed., McGraw-Hill, New York, 1972. [20] B. Bever, Micheal, Encyclopedia of Materials Science and Engineering, vol.7, Pergamon press, Oxford, UK, 1986, pp. 4949.
Contents lists available at ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Free convection heat transfer from a horizontal fin attached cylinder between confined nearly adiabatic walls Amir Abbas Rezaei a,*, Masoud Zia basharhagh a, Touraj Yousefi b a b
Khajeh Nasir Toosi University of Technology, Tehran, Iran Razi University, Kermanshah, Iran
a r t i c l e
i n f o
Article history: Received 13 December 2008 Received in revised form 12 October 2009 Accepted 12 October 2009
Keywords: Natural convection Fin attached cylinder Confining walls interferometry
a b s t r a c t Steady state two-dimensional free convection heat transfer from a horizontal, isothermal fin attached cylinder, located between nearly two adiabatic walls is studied experimentally using a Mach–Zehnder interferometer. Effects of the walls inclination angel (h) on heat transfer from the cylinder is investigated for Rayleigh number ranging from 1000 to 15,500. Two cylinders with different diameters of D = 10 and 20 mm are used to cover wide Rayleigh range. Results indicate that, heat transfer phenomena differ for different Rayleigh number. For Rayleigh numbers lower than 5500, heat transfer rate from cylinder surface is lower than the heat transfer from a single cylinder. In this range by the use of walls, heat transfer from the cylinder decreases slightly and walls’ inclination does not change heat transfer rate from the cylinder surface. For Rayleigh number ranging from 5500 to 15,500, amount of heat transfer from the cylinder surface is less than that of a single cylinder. However, by adding nearly adiabatic walls to experimental model heat transfer mechanism differs and chimney effect between fin and walls increases the heat transfer rate from the cylinder surface. By increasing the walls inclination angel from 0° to 20°, the chimney effect between walls and fin diminishes and heat transfer rate from the cylinder surface is approaching to the heat transfer rate of fin attached cylinder without adiabatic walls. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction Free convection heat transfer from a horizontal, isothermal fin attached cylinder placed between two nearly adiabatic walls has various applications in industry. In many applications, electronic components can be cooled using a conductive fin. Understanding of the influence of conductive fin and placing component between two adiabatic walls is important for electronic devices design application. All modes of free convention from a horizontal cylinder in a quiescent, infinite fluid have been studied extensively and well established correlations are available in the literature [1–5]. The effect of adiabatic confining walls on the heat transfer coefficient from a circular cylinder has been studied by some researchers [6–10]. But the available information on fluid flow and heat transfer from a heated fin attached cylinder between two adiabatic walls is very limited. The model geometry of the present investigation is shown in Fig. 1. One fin attached cylinder of diameter (D) and length (l) are located between two nearby adiabatic ceiling. One of the closely related studies for a fin attached horizontal cylinder has been done by Facas and Brown [11]. In this work they studied the effect of longitudinal fins on overall heat transfer from * Corresponding author. E-mail address: [email protected] (A.A. Rezaei). 0894-1777/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2009.10.007
the cylinder. They studied numerically effects of axisymmetric fins around the cylinder perimeter. It was found that the overall heat transfer from the cylinder increases and it relates to fins parameters. Abu-Hijleh [12], studied numerically forced convection heat transfer from an equally spaced fined cylinder for Reynolds number ranging from 1 to 200. They showed that there is an optimum configuration for fins and also optimum number of fins. Moreover, short fins decrease the amount of heat transfer from the cylinder surface. Conjugate numerical solution of laminar free convection about a horizontal cylinder with longitudinal fins has been carried out by Halder et al. [13]. Fins alone contributed extremely small to the overall heat transfer but they greatly influence the heat transfer from the cylinder. The rate of heat transfer was above that for the free cylinder just when the attached fins were very thin. For thin fins, there existed a fin length, which maximized the rate of heat transfer. The optimum number was obtained as 6 when fin thickness was the thinnest among those investigated in that study. Objective of the current study is to find local and average free convection heat transfer rate from a horizontal isothermal fin attached cylinder located between two nearly adiabatic walls. Experiments are performed for different walls inclination angel (h) and Rayleigh numbers. The walls height is (l W) which W is chosen to be three times the cylinders diameter. It is considered
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Nomenclature D g h h k l Nu Nu P r Ra
cylinder diameter (m) gravitational acceleration (m/s2) heat transfer coefficient (W/m2 k) average heat transfer coefficient (W/m2 k) thermal conductivity of air (W/m k) cylinder length (m) Nusselt number average Nusselt number pressure (Pa) radius (m) Rayleigh number based on cylinder diameter
to be very low conductive to act as an adiabatic boundary condition. The cylinder is heated to a temperature (Ts) and is located in air with ambient temperature (T1). A Mach–Zehnder interferometer is used to observe temperature field. Experiments are performed in air for cylinder diameter of 10 and 20 mm, and walls inclination angel (h) differs from 0° which is vertical condition to 20°. The horizontal space between cylinder and walls is about half of the cylinder diameter and the Rayleigh numbers range is 1000 < Ra < 15,500.
2. Experimental setup 2.1. Experimental apparatus To observe the temperature field around an electrically heated fin attached cylinder, which is located between two nearly adiabatic plates as walls, a Mach–Zehnder interferometer is used. In order to obtain the range of 1500 6 Ra 6 3000, hollow cylinder of 10 mm OD and 160 mm long and for Rayleigh number ranging from 5500 to 15,500, hollow cylinder of 20 mm OD and 340 mm long is used. A thin rod Ni–Cr spiral heater ðXtot ¼ 80 ohmsÞ was inserted at the core of the cylinder. To increase thermal conductivity between the tube and the heater, the hollow tube was filled with magnesium oxide powder. To eliminate 3D effects, length of the cylinders was chosen about seventeenth times the cylinder diameter to eliminate end flows. Cylinders structure was explained by Ashjaee et al. [14]. The walls are made by one layer insulation. The one layer was constructed from fiber bone sheet with dimensions 180 mm length along cylinders’ length and 35 mm width for slim cylinder and 380 mm length with 70 mm width for thick cylinder. Both sizes have 10 mm thickness. The corresponding overall thermal conductivity of walls was about 0.05 W/m K [20]. The walls width is about
Fig. 1. Model geometry of a fin attached cylinder confined by inclined walls.
T
temperature (K)
Greek symbols X heater electrical resistance (ohm) h walls inclination angel (°) U angle from stagnation point (°) Subscripts 1 ambient condition f film condition s at the cylinder surface
three times and half of the cylinders diameter to be the same size of the conductive fin and make a channel between fin and walls. Cylinders are heated by electrical power. Ambient temperature, reference and cylinders’ surface temperature are measured by Ktype thermocouples [14]. Two complicated positioning systems are used to align the walls and three linear positioners are used to align cylinders as shown in Fig. 2. 2.2. Interferometer A 10 cm diameter beam Mach–Zehnder interferometer (MZI) was used to measure the temperature field in the air surrounding the cylinder. [14]. All interferograms captured by ‘‘ARTCAM-320P”. Camera was connected to a PC, and by using video recorder software, interferograms captured online. In order to recognize the cylinder surface specific position, temperature differences between cylinder surface and ambient temperature are chosen to result in a constructive fringe which is attached to the cylinder surface. This temperature difference varied from 15 °C to 70 °C. Cylinder surface are smoothed with ±0.001 mm roughness and thermal emissivity of 0.05. More details of Mach–Zehnder interferometer, cylinder position and arrangement are described in [14]. The cylinders are supported by fine rods as illustrated in Fig. 2. 2.3. Data reduction To calculate local and average Nusselt numbers for the cylinder at a certain cylinder-to-ceiling spacing and Rayleigh number, data
Fig. 2. Experiment setup.
A.A. Rezaei et al. / Experimental Thermal and Fluid Science 34 (2010) 177–182
179
processing are made by the method explained in literature [14] and explained in [14,18,19]. Equating the heat transferred by convection to the heat transferred by conduction in air at the cylinder surface, following expression for the local Nusselt number will result:
Nuh ¼
D ks dT dr r¼r s
ð1Þ
ðT s T 1 Þ kf
The average Nusselt number is calculated by integrating the local Nusselt numbers using Simpson’s rule.
h ¼ 1=p
Z p
hh dh;
Nu ¼ h D=kf
ð2Þ
0
In order to validate the experiments and data reduction method, an individual hot cylinder is tested in infinite medium for Ra = 1000 and results of heat transfer are compared with available relations [14]. Excellent agreement between results was observed as described in [14].
Fig. 3. Interferograms around an unconfined fin attached cylinder for (a) Ra = 3000, (b) Ra = 2000, (c) Ra = 1000.
2.4. Uncertainty analysis Analysis of uncertainty is required in order to evaluate the quality of experimental data [15]. For any measurement which results depend on uncorrelated input estimates, the standard uncertainty of the measurement can be obtained by appropriately combining the standard uncertainties of these input estimates [16–17]. Table 1 lists the experimental values of parameters in Eq. (1) and associated uncertainties for Ra = 3000, and when the cylinder is not confined by walls. Uncertainties of the parameters T1, Tw, P1, l, D can be estimated from the precision of measuring devices. Our measuring equipment is caliper, and it is able to read 0.05 mm and temperature is measured by K-type thermocouple with 0.2 K accuracy. The uncertainty of the parameter Dr, which is the difference in radial distance from the cylinder surface, is related to the precision of reading the digitized interferograms. From Table 1, it can be seen that the later is the dominant source of error. The uncertainties in the average Nusselt numbers for the mentioned Rayleigh number and test geometry is 3.42%. Using this analysis, uncertainties in the measured local Nusselt number has been estimated to be less than 5.87 ± 2.1%. 3. Results and discussion In many practical applications, horizontal fin attached cylinder can be seen in various electrical devices and different electrical components. In this simulation, cylinder is hanged parallel to large beam such as illustrated in Fig. 3. The cylinder length is equal to walls length. In this study effects of geometrical parameters and Rayleigh number on fluid flow and heat transfer from the fin attached cylinder have been investigated experimentally. The physical model of the present study is composed of one hollow, aluminum cylinder with a brass fin attached to it. For confined
Table 1 Deviation of each quantity for computing Nusselt number, Eq. (1).
a
Parameter
xi
dxi
@Nuh dxi @xi Nuh
Tw T1 P1 l D Dr
360.95 K 299.45 K 88,000 Pa 160 mm 10 mm 0.35–1.6 mma
0.1 K 0.1 K 100 Pa 0.025 mm 0.025 mm 0.027 mm
0.1–0.2 0.15–0.2 0.08–0.04 0.01–0.003 0.15–0.04 4.7–1.1
0.35 and 1.6 are radial distance differences for h ¼ 0 ; 180 .
(%)
configuration such as illustrated in Fig. 1, the walls inclination angel varied from 0° to 20° with respect to the vertical orientation, for Rayleigh numbers ranging from 1500 to 15,500. According to Sadeghipour and Razi [9], for a single cylinder between two confining walls, by increasing the distance between cylinder and neighboring wall, at first Nusselt number increased. By increasing the distance more than the optimum value, Nusselt number decreased again. This amount of optimum distance between walls is about two and half times of the cylinder diameter. To prevent the Nusselt number increase because of this optimum value, the distance between walls is less than two times of the cylinder diameter. The small distance between walls, entrap the rising plume between adiabatic walls and conductive fin; make a chimney effect on top of the cylinder especially for high Rayleigh number. Fig. 3 indicates infinite fringe interferograms for the Rayleigh numbers of 1000, 2000 and 3000 for unconfined cylinder. All the interferograms indicate that thermal plume resulted from the cylinder surface rises vertically close to the fin. Because of the fin existence right on top of the cylinder, cylinder raised plume faces a no slip boundary condition on top of the cylinder and this type of boundary condition is a great barrier for its velocity for such Rayleigh number. When there is not any fin on top of the cylinder, raised plume from right and left sides of the cylinder intricate on top of the cylinder. So, plume combination increases the plume velocity on top of the cylinder, and adding a fin on top of the cylinder eliminates this kind of enhancement. By adding nearly adiabatic walls to the fin attached cylinder configuration, a chimney type channel is created between walls and fin. So the chimney effect in the channel increase the velocity of raised plume from the cylinder and reduce the fringe distance on top of the cylinder, it also increases the heat transfer from the cylinder surface. By increasing the walls inclination angel from 0° to 20°, Nusselt number goes to the value of Nusselt number for an unconfined fin attached cylinder. Also, the surface temperature of the conductive fin is more than ambient. The temperature difference between fin surface and ambient air pull the ambient cold air and lower the boundary layer thickness on the cylinder surface. This phenomena increase the heat transfer and Nusselt number on the cylinder surface in comparison to the unconfined configuration. This effect is very obvious just for Rayleigh number more than 5500 because for this range of Rayleigh number the raised plume from the cylinder surface is strong enough to penetrate into the distance between fin and adiabatic walls. Figs. 4 and 5 show infinite fringe interferograms of confined cylinder between two walls, for the Rayleigh numbers of 1000, 2000 and 3000.
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Fig. 4. Interferograms around a confined fin attached cylinder between vertical walls for (a) Ra = 3000, (b) Ra = 2000, (c) Ra = 1000.
Fig. 6. Variation of local Nusselt number for various inclination angel (Ra = 7500).
Fig. 5. Interferograms around a confined fin attached cylinder between inclined walls for (a) Ra = 3000, (b) Ra = 2000, (c) Ra = 1000.
Raised plume of the cylinder surface enters the space between walls and fin, so a developing flow generates and velocity in this channel increases. This flow exits the hot plume of the cylinder easier and cooler air enters the channel inlet faster. In order to compute heat transfer rate from cylinder surface, heat flux is determined by the method discussed in Section 2.3, and Nusselt number is calculated from relation (1). To investigate the effects of velocity induction on heat transfer from the centered cylinder, the value of local Nusselt number has been plotted versus u on the half of the cylinder surface in Figs. 6 and 7. These graphs are plotted for confined and unconfined cylinder, Ra = 7500, 15,500 and h = 0°, 10°, 20°. It can be observed that for the unconfined cylinder the local Nusselt number trend by circumferential angel u is very similar to the local Nusselt number trend on an individual cylinder. However, the amount of local Nusselt number for the upper portion of the cylinder is lower than the value of local Nusselt number for the same location around an individual cylinder. For the value of the Rayleigh number less than 3000, the local Nusselt number trend is similar to the unconfined cylinder configuration. But, by increasing the Rayleigh number from 5500 to 15,500, local Nusselt number trend around the cylinder surface differs from the unconfined cylinder case. For this range of Rayleigh number, it is obvious that air velocity increases because of the developing flow between adiabatic walls and conductive fin. An increase in local Nusselt number value is shown in Figs. 6 and 7 for 40 < u < 110 and that is because of velocity raise at the channels inlet. By increasing the walls inclination angel from 0° to 20°, local Nusselt number graph around the cylinder become very similar to the local Nusselt number trend of an individual cylinder. Because by increasing the inclination angel, walls base distance from
Fig. 7. Variation of local Nusselt number for various inclination angel (Ra = 15,500).
the cylinder become larger. So, there is not any chimney flow between adiabatic walls and conductive fin, and flow field around the cylinder is very similar to the flow field of an unconfined cylinder. Thermal and velocity boundary layers are smaller than spacing between walls and cylinder. So, by increasing the walls inclination angel, walls distance from the cylinder become much more than the cylinder boundary layer thickness and do not affect the heat transfer rate from the cylinder surface. All the local Nusselt number graphs are from u = 0° to 170° and it is because of the fin orientation on u = 180°. Because the hot plume of the cylinder moves upward close to the fin surface, there is not a high Nusselt number region at the fin base. Fig. 8 represents the variation of average Nusselt number around the fin attached cylinder for confined and unconfined case and various Rayleigh numbers. As illustrated in this figure, average Nusselt number of the cylinder for confined and
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unconfined cases are very close to the average Nusselt number of the an individual cylinder for Rayleigh number ranging from 1000 to 3000. This amount of difference between fin attached cylinder Nusselt number value and individual cylinder Nusselt number is very little. However, by increasing the Rayleigh number, the average Nusselt number tendency with Rayleigh number changes. For Rayleigh number ranging from 5500 to 15,500, the difference between confined cylinder and unconfined cylinder become obvious. By increasing the Rayleigh number from 5500 to 15,500 it can be seen that average Nusselt number of the confined cylinder with vertical walls goes farther than an unconfined cylinder and an individual one. By increasing the walls inclination angel Fig. 8 shows that the average Nusselt number of the cylinder approaches to that of a single cylinder. It is rea-
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son was explained before. This result is in agreement with the study of Sadeghipour and Razi [9] because the walls distant is in the region that the average Nusselt number of the cylinder is lower than that of an individual cylinder. Variation of average Nusselt number around the centered cylinder divided by Nusselt number for an individual cylinder (Nuave/ Nu1) for unconfined cylinder and confined cylinder between vertical walls for various Rayleigh numbers is determined and illustrated in Fig. 9. Average Nusselt number of an individual cylinder is calculated from the correlation presented by Morgan [3]. It can be indicated that for all configurations, the average Nusselt number of the centered cylinder is lower than that of an individual cylinder due to the no slip boundary condition of the conductive fin and distance between adiabatic walls. 4. Conclusion Laminar free convection from a horizontal fin attached cylinder which is confined between two nearly adiabatic walls is studied experimentally. Experiments are carried out using Mach–Zehnder interferometer for different walls orientation and Rayleigh numbers. 1. The experimental data showed that the average Nusselt number is lower than individual cylinder’s Nusselt number. 2. By putting the confining walls close to the cylinder the average Nusselt number of the cylinder increases.
Acknowledgement Special thanks to Mrs. Forough Nezam for editing this paper. References
Fig. 8. Variation of average Nusselt number versus Rayleigh number for different inclination angel.
Fig. 9. Variation of normalized average Nusselt number versus Rayleigh number for different inclination angel.
[1] T.H. Kuehn, R.J. Goldstein, Numerical solution to the Navier–Stokes equations for laminar natural convection about a horizontal isothermal circular cylinder, International Journal of Heat and Mass Transfer 23 (1980) 971–979. [2] T. Saitoh, T. Sajiki, K. Maruhara, Bench mark solution to natural convection heat transfer problem around the horizontal circular cylinder, International Journal of Heat and Mass Transfer 36 (1993) 1251–1259. [3] V.T. Morgan, The overall convective heat transfer from smooth circular cylinders, Advances in Heat Transfer 11 (1975) 199–264. [4] S.W. Churchill, H.H.S. Chu, Correlating equations for laminar and turbulent free convection from a horizontal cylinder, International Journal of Heat and Mass Transfer 18 (1975) 1049–1053. [5] J.V. Herraez, R. Belda, A study of free convection in air around horizontal cylinders of different diameters based on holographic interferometry. temperature field equations and heat transfer coefficients, International Journal of Thermal Science 41 (2002) 261–267. [6] G.F. Masters, Natural convection heat transfer from a horizontal cylinder in the presence of nearby walls, Canadian Journal of Chemical Engineering 53 (1975) 144–149. [7] S. Sparrow, D. Pfeil, Enhancement of natural convection heat transfer from a horizontal cylinder due to vertical shrouding surface, ASME Journal of Heat Transfer 106 (1984) 124–130. [8] F. Karim, B. Farouk, L. Nnmer, Natural convection heat transfer from a horizontal cylinder between vertical confining adiabatic walls, ASME Journal of Heat Transfer 108 (1986) 291–298. [9] M.S. Sadeghipour, Y.P. Razi, Natural convection from a horizontal cylinder: the optimum distance between the confining walls, International Journal of Heat and Mass Transfer 44 (2001) 367–374. [10] M.A. Atmane, V.S.S. Chan, D.B. Murray, Natural convection around a horizontal heated cylinder: the effects of vertical confinement, International Journal of Heat and Mass Transfer 46 (2003) 3661–3672. [11] G.N. Facas, H.L. Brown, Natural convection from a cylinder with multiple lowconductivity, longitudinal baffles, International Journal of Heat and Mass Transfer 39 (1996) 2077–2086. [12] B. Abu-Hijleh, Numerical simulation of forced convection heat transfer from a cylinder with high conductivity radial fins in cross-flow, International Journal of Thermal Sciences 42 (2003) 741–748. [13] S.C. Haldar, G.S. Kochhar, K. Manohar, R.K. Sahoo, Numerical study of laminar free convection about a horizontal cylinder with longitudinal fins of finite thickness, International Journal of Thermal Sciences 46 (2007) 692–698.
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[14] M. Ashjaee, A.H. Eshtiaghi, M. Yaghoubi, T. Yousefi, Experimental investigation on free convection from a horizontal cylinder beneath an adiabatic ceiling, Experimental Thermal and Fluid Science 32 (2007) 614–623. [15] P.L. Teoch, B. Shirinzadeh, C.W. Foong, G. Alici, The measurement uncertainties in the laser interferometry-based sensing and tracking technique, Measurement 32 (2002) 135–150. [16] S.J. Kline, F.A. McClintock, Describing experimental uncertainties in single sample experiments, Mechanical Engineering 75 (1953) 3–8.
[17] R.D. Flack, Mach–Zehnder interferometer errors resulting from test section misalignment, Applied Optics 17 (1978) 985–987. [18] W. Hauf, U. Grigull, Optical methods in heat transfer, advances in Heat Transfer, Academic Press, New York, 1970. [19] E.R.G. Eckert, R.J. Goldstein, Measurements in Heat Transfer, second ed., McGraw-Hill, New York, 1972. [20] B. Bever, Micheal, Encyclopedia of Materials Science and Engineering, vol.7, Pergamon press, Oxford, UK, 1986, pp. 4949.