Thermal Convection in a Cylindrical Enclosure withWavy Sidewall - Selected Topics of Computational and Experimental Fluid Mechanics - page 392

Fig. 15 Average Nusselt
number for the enclosure
heated from the top and
different values of ʵ . For this

case ʛ = 1 / 5and ʓ = 0 . 1

5 Conclusions

An axisymmetric convection flow occurring within a vertical cylindrical enclosure
with adiabatic wavy sidewall was studied. Thermal convection of two important cases
were considered, heating from below and heating from the top, while the wavy side-
wall is adiabatic. Different convection patterns arise which modify the heat transfer
rate even for conditions where diffusion dominates. An analytical coordinate trans-
formation was used to solve the axisymmetric problem which allowed to obtain a
coordinate frame for computation in which the irregular domain fits into a square.
Thermally stratified flowwithmultiple convection cells near thewavywall arisewhen
the Rayleigh number is of order 10 3 . If the Rayleigh number increases the thermal
stratification remains while the fluid flow intensifies. When the Rayleigh number
increases even more, the flow presents two convection cells with notable tempera-
ture gradients near the upper and lower walls. For low values of the dimensionless
wavelength there exists an almost stagnant thermally stratified core with multiple
convection cells near the wavy wall. On the other hand, if the dimensionless wave-
length is large, there are two convection cells with no thermal stratification, which
resembles the well-known convection patterns corresponding to vertical cylindrical
enclosures (Martynenko and Khramtsov 2005 ). Foregoing results demonstrate that
the wave amplitude restricts the convection heat transfer. Tall cavities are related to
thermal stratification with low heat transfer and there exists a remarkable difference
between the heat transfer capabilities corresponding to short and tall cavities. The
remarkable finding is that the wavy wall promotes thermal stratification and multiple
cells patterns of low velocity, restricting the convection fluid flow which yields low
heat transfer through the cavity.

Acknowledgments Authors would like to thank financial support from PAICyT-UANL through
the Project IT 647-11.