**5. Conclusion**

*4.1.2.1 Isotherms*

**4.2 Overall results**

against the number of fins *H\**

its optimal value at the longest fin.

**Figure 5.** *(a)* H\*

**50**

lower near the inner wall of the outer pipe.

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gradients indicating the high rate of convection.

*H\** = 0.2 than the fin height *H\** = 0.4 and others.

*-Nu(Cu), for R*^ *= 0.5. (b) M-Nu(Cu), for R*^ *= 0.7.*

**Figure 4a** shows the isotherms for *M = 6, R*^ = 0.5, *H\** = 0.6, which shows that a region of higher temperature starts to develop in the middle of annulus and significant change occurs in temperature gradient. Whereas, **Figure 4b** shows the isotherms, when *M = 18*, the temperature gradient is higher in the entire cross section, and higher temperature region appears near the outer wall of the inner pipe, while

Apparently, in these isotherms conduction in wall and fin assembly is not being

The trend of isotherms is more understandable corresponding to the velocity contours. From these figures, it is observed that the region of high-velocity gradients near the heated surfaces of the inner pipe and fin also has high-temperature

There is an equivalent transfer of heat in fin and fluid on the interfaces; interfaces get smoother because of the continuity of fluxes. But in case of temperature

**Figure 5a** shows the plots of different values of Nusselt number of copper

radii *R*^ = 0.5. For fin height *M=6*, the value of Nusselt number decreases as we increase fin height. The plot of Nusselt number against these values shows monotonic decreasing behaviour. However, the value of Nu(Cu) remains higher for the

The plots of Nusselt numbers for *M=6* and *M = 18* clearly depict that the behaviour of Nusselt number significantly differs in these two graphs. An optimal value of Nusselt number is observed for some particular value of *H\** = 0.2 used.

While taking the higher number of fins into account, for *M = 18*, Nusselt number gradually decreases when fin height is increased from *H\** = 0.2 to *H\** = 0.4. Its shows a parabolic behaviour. After reaching its lowest value, it starts increasing and attains

It can be concluded that the value of Nusselt number for *R*^ = 0.5 at *H\** = 0.6 and

*H\** = 0.8 is the best choice when *M=9* and *M = 18* are taken, respectively.

Thus, for *M=6*, shorter fin gives better rate of heat conduction.

∈f0.2, 0.4, 0.6, 0.8} taking fixed value of ratio of

difference, it rises more rapidly in fluid than the solid (wall and fin).

shown, but if we increase the number of contours, the temperature gradient is shown in the solid part of the domain too. This is because of the very hightemperature gradient in fluid and because of convection and conduction.

The results presented in previous sections can be concluded as follows:


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