In this study, experimental investigation had been
conducted to examine the effects of mechanical vibrations and fin installation on the natural convection heat transfer in a cylindrical enclosure. Different configurations were
introduced in the investigation. They were: (1) absence and presence of fins, (2) with and without mechanical vibrations and (3) different enclosure height.
The comparison between theoretical and measured Nusselt number (Nu) of heated base plate without fins and mechanical vibrations is shown in Fig.7 for different enclosure height.
The empirical correlation is based on equation (3.6) for upper surface of heated plates and the deviation is within 10%-22%
from the experimental results.
Effect of fins
Fig. 8-10 depict the influence of fin on Nusselt number distribution. A dimensionless parameter 𝑝 for vibrational cases was adopted [27]. 𝑝 is defined as:
𝑝
=
𝜔2𝑎𝛽(𝑇𝜈𝑤2−𝑇𝑐)𝐻3 (4.1) where ω is angular velocity of rotating disc driven by stepper motor, a is vibrational amplitude. 𝑝 represents the ratio of buoyancy force induced by mechanical oscillation to viscous force.For any Ra and 𝑝, the Nu of finned plate is larger than smooth case. In stationary and vibrational cases without fins, the Nu increases with increasing Ra or 𝑝 continuously. In those cases with fins, however, the increase of Nu with Ra or 𝑝 is small compared to those of the cases without fins, and decreases with increasing Ra or 𝑝 occasionally. Therefore, the heat transfer rate enhancement due to fin attachment ( ( )) decreases with increasing Ra or 𝑝. In natural convection, the Ra is dominant because the flow circulation is
induced by spontaneous driven force (buoyancy force). When Ra is high enough, the other influential factors like heat transfer area become minor and relatively unimportant.
Therefore, the effectiveness of fin installation is smaller in higher Ra or 𝑝.
The fin insertion influences flow characteristics inside the enclosure. According to literature [17-19], the fin insertion enhances the probability of split of convection cells and increases the heat transfer area. The convection cells are almost square and the same size in bare base plate configuration.
The fin insertion increases the number of convection cells resulting in enhancement of heat transfer, and narrows down the convection cell development resulting in reduction of heat transfer due to decreasing of flow intensity. Moreover, increasing the heat transfer area induces further obstruction for flow circulation due to viscous effect along the fin wall.
The fin insertion increases the heat transfer generally due to increasing heat transfer area, however, the heat transfer may decrease under certain fin configurations like dense fin
spacing due to the results of [18].
In the present study, the fin configurations were:
𝑆 𝐻⁄ = 0.4, 0.8 and 𝐿 𝐻⁄ = 0.2, 0.4 where S is fin spacing, L is fin length, H is enclosure height. The fin spacing to enclosure height ratio is smaller or equal to the experimental
configurations of literature [18] which states that 𝑆 𝐻⁄ = 0.8 results in decreasing Nu compared to larger 𝑆 𝐻⁄ . For
𝑆 𝐻⁄ = 0.8 and 𝐿 𝐻⁄ = 0.4, the deviation of Nu of the base plate from the results of [18] at the same Ra is 8%-12%
approximately. For smaller 𝐿 𝐻⁄ , the reduced space between fin tip and top wall of enclosure results in increase of temperature gradient according to the results of [19]. More distinct convection cells appear in the space between fins at larger 𝐿 𝐻⁄ . Fig. 11 shows that the ( ) at smaller 𝐿 𝐻⁄ is always greater than the cases at larger 𝐿 𝐻⁄ in all stationary and vibrational cases. It is probably as a result of insufficient space where convection cells develop due to decreasing the enclosure height. The heat transfer enhancement due to more distinct convection cells cannot overcome the weakening of heat
transfer due to decreasing the space for convection cells development. The ( ) is listed in Table 2-4.
Effect of mechanical vibrations
Fig. 12-15 show the enhancement of heat transfer due to mechanical vibrations. In the cases without fins, the Nu of base plate increases at any 𝑝 compared to stationary cases.
These figures also show that the Nu increase tendency at lower H appears to be contrary to the case which is at larger H in all vibrational cases. It is probably due to the space for convection cells to develop. At smaller H, the space for convection cells development is insufficient for convection cells development due to superimposing mechanical vibrations.
Thus the increase of heat transfer due to mechanical vibrations is indistinct with increasing 𝑝 under the same vibrational conditions. Contrarily, at larger H, there is enough space to develop convection cells induced by mechanical vibrations.
is relatively significant at larger H. For finned base plate cases, the increase of heat transfer appears to be irregular.
To the author’s knowledge and the explanations of literature [5-6], the fluctuating velocity exists in the natural
convection flow due to mechanical vibrations and the rugged finned base plate surface also disturb the propagation of fluid momentum. Moreover, the velocity gradient is also induced because the base plate diameter was long compared to the vibration amplitude. The figure also shows that the heat transfer did not increase significantly in all vibrational cases. According to the results of [22], the Nusselt number did not change significantly upto a threshold value of vibrational intensity (af). The Nusselt number increases in large amplitude abruptly when the af is high enough to disturb the boundary layer and the fluid tends to be turbulent. According to the results of [8-9], the heat transfer rate increases
significantly and abruptly in a certain vibration frequency which is called the resonant frequency. At the resonant frequency, the intensity of the convection cell rotating can
be enhanced due to increasing the intensity of stream function.
In the present study, the af was probably not high enough to disturb the boundary layer and keep the fluid in laminar ,and the vibration frequency did not reach the resonant condition.
Fig. 16-17 shows the heat transfer rate enhancement tendency due to mechanical vibrations ( ( )). The ( ) was found to be not significant (maximum of 1.07) due to the reasons as mentioned above. To sum up, the crucial factor of increasing heat transfer for mechanical vibrations is the boundary layer transition for laminar to turbulent. The vibration amplitude to the characteristic length of object is also necessary to be considered in this sort of study. The ( ) is listed in Table 5-6.
Effect of enclosure height
The natural convection in an enclosure heated from below begins to form multiple convection cells which is known as
Bénard cells when the Ra exceeds a certain value. According to (3.1), the influence of characteristic length on Ra is greater than that of temperature difference. At the same temperature difference and vibrational conditions, the increase of Nu due to increasing enclosure height is about 79%-116% which is listed in Table 7-8. The higher enclosure height tends to not only induce higher buoyancy force due to enough space for convection cells to develop, but also enhance the probability of vortex forming, resulting in larger heat transfer rate. Also, the increase of Nusselt number at higher enclosure height with finned base plate is larger than those of smooth plate in most cases. The fin installation increases the heat transfer area.
Although increasing heat transfer area raises the viscous effect, the higher buoyancy effect due to increased enclosure height overcomes the viscous effect and the heat transfer is raised due to increasing heat transfer area.
Comparisons
In all cases, the heat transfer enhancement as a result of fin installation exceeds the one as a result of superimposing mechanical vibrations. This can be attributed to which the energy of vibrations can be consumed by viscous effect. The energy of vibrations must propagate through the interface between fluid layer and solid wall. The vibrational energy is transferred to the fluid medium incompletely. Thus the flow circulation is not intense as expected. According to the experimental results of this study, the change of heat transfer due to increasing heat transfer area is higher than the cases due to superimposing mechanical vibrations.
Chapter 5
Conclusion
Natural convection in a cylindrical horizontal narrow enclosure with finned heated base plate had been investigated experimentally. The influence of mechanical vibrations and enclosure height on natural convection heat transfer was studied for three cases of temperature difference (Tw − Tc).
For fin installation cases, the fin insertion increases the heat transfer area and the probability of convection cell splitting. Although increasing heat transfer area enhance viscous effect resulting in reducing flow intensity, the heat transfer rate was still improved under the conditions conducted in this study. Increasing Ra reduces ( ) due to the domination of Ra in natural convection. The ( ) also decreases with decreasing 𝐿 𝐻⁄ .
For mechanical vibrations effect, the heat transfer enhancement due to mechanical vibrations at any 𝑝 was not significant in the present study. Moreover, the increase of
Nusselt number due to mechanical vibrations increases with increasing 𝑝 at higher enclosure height and it is contrary to the cases at lower enclosure height.
For changing enclosure height, the higher enclosure height inducing larger buoyance effect due to increasing Ra was confirmed experimentally. The heat transfer enhancement at higher enclosure height with finned base plate was greater than those of bare base plate and the maximum heat transfer
enhancement due to increasing enclosure height (2.5cm → 5cm) was found to be about 79%-116%. Under any temperature and vibration conditions, the increase of Nusselt number due to increasing enclosure height was greater than the cases due to fin insertion and mechanical vibrations.
The ( ) was greater than ( ) in all temperature and vibration cases. With smooth base plate, the ( ) was always greater than one at any 𝑝, however, the ( ) development was found to become instable with finned base plate and is less than one at certain 𝑝.
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Figure 1. Experimental apparatus
Figure 2. Combination of test chamber and oscillation mechanism
Figure 3. NI-9213 device
Figure 4. Chiller
Figure 5. Test chamber cutaway view
Figure 6. Constants for equation (3.6) [24]
Figure 7. The comparison of Nu between theoretical and experimental results without fins and vibrations
Figure 8. Effect of fin installation on Nu without vibrations
Figure 9. Effect of fin installation on Nu with vibrations (f=1Hz)
Figure 10. Effect of fin installation on Nu with vibrations (f=2Hz)
Figure 11. The Ef(Nu) in different H for (a) f=0 (b) f=1Hz (c) f=2Hz
Figure 12. Effect of mechanical vibrations on Nu with smooth base plate (H=5cm)
Figure 13. Effect of mechanical vibrations on Nu with smooth base plate (H=2.5cm)
Figure 14. Effect of mechanical vibrations on Nu with finned base plate (H=5cm)
Figure 15. Effect of mechanical vibrations on Nu with finned base plate (H=2.5cm)
Figure 16. The Ev(Nu) in different G with smooth base plate
Figure 17. The ( ) in different 𝑝 with finned base plate